adding & subtracting with fluency, flexibility & number … · adding & subtracting...

© Valerie Henry, August 2013 … www.ellipsismath.com i

FactsWise +-

Adding & Subtracting with Fluency, Flexibility & Number Sense

By Valerie Henry, NBCT, Ed.D.

Ellipsis Math

http://www.ellipsismath.com/�

© Valerie Henry, August 2013 … www.ellipsismath.com i

NINE GOALS FOR BASIC FACTS SUCCESS Once a child is fluent with the addition facts in each goal, begin work on the related subtraction facts.

Goal 1 – Within 4s & 5s

Add: 1+3, 2+2, 3+1, 1+4, 2+3, 3+2, 4+1 Sub: 4-1, 4-2, 4-3, 5-1, 5-2, 5-3, 5-4 Goal 2 – With 5s (part 1)

Add: 1+5, 2+5, 3+5, 4+5, 5+5 Sub: 6-1, 6-5, 7-2, 7-5, 8-3, 8-5, 9-4, 9-5, 10-5 Goal 3 – Within 10s

Add: 0+10, 1+9, 2+8, 3+7, 4+6 Sub: 10-0, 10-10, 10-1, 10-9, 10-2, 10-8, 10-3, 10-7, 10-4, 10-6 Goal 4 – With 10s

Add: 10+1, 10+2, 10+3, 10+4, 10+5, 10+6, 10+7, 10+8, 10+9, 10+10 Sub: 11-1, 11-10, 12-2, 12-10, 13-3, 13-10, 14-4, 14-10, 15-5, 15-10,

16-6, 16-10, 17-7, 17-10, 18-8, 18-10, 19-9, 19-10, 20-10 Goal 5 – With 5s (part 2)

Add: 5+6, 5+7, 5+8, 5+9 Sub: 11-5, 11-6, 12-5, 12-7, 13-5, 13-8, 14-5, 14-9 Goal 6 – Doubles

Add: 3+3, 4+4, 6+6, 7+7, 8+8, 9+9 Sub: 6-3, 8-4, 12-6, 14-7, 16-8, 18-9 Goal 7 – Under Tens

Add: 2+4, 2+6, 2+7, 3+4, 3+6 Sub: 6-2, 6-4, 8-2, 8-6, 9-2, 9-7, 7-3, 7-4, 9-3, 9-6 Goal 8 – With 9s

Add: 2+9, 3+9, 4+9, 6+9, 7+9, 8+9 Sub: 11-2, 11-9, 12-3, 12-9, 13-4, 13-9, 15-6, 15-9, 16-7, 16-9, 17-8, 17-9 Goal 9 – With 7s & 8s

Add: 4+7, 6+7, 3+8, 4+8, 6+8, 7+8 Sub: 11-4, 11-7, 13-6, 13-7, 11-3, 11-8, 12-4, 12-8, 14-6, 14-8, 15-7, 15-8


© Valerie Henry, August 2013 … www.ellipsismath.com - 1 -

TABLE OF CONTENTS

Page Section 1: Introduction ………………………………………………………………………………………………….. 2 1.1 Correlating Common Core Standards and FactsWise Goals ……………………………. 3 1.2 Research Findings ………………………………………………………………………………………………….. 4 Section 2: Key Principles and Strategies …………………………………………………………………… 6 2.1. Basic Facts for Number Sense + Number Sense Strate Stages Chart…….. 6 2.2. Part-Whole Thinking and the Power of Tens ………….………………………………………. 8 2.3. Subtraction …………………………………………………………………………………………………………… 9 2.4. A Special Note about Doubles ………………………………………………………………………….. 9 Section 3: Getting Started ……………………………………………………………………………………………. 10 3.1. FactsWise Overview …………………………………………………………………………………………. 10 3.2. Pre-Assessing Your Students …………………………………………………………………………….. 11 3.3. Pre-Assessment and Ongoing Assessment Techniques ………………………………… 11 3.4. Pre-Assessment and Ongoing Assessment Record-Keeping ………………………… 12 Section 4: Whole Class Routines and Mini-Lessons ………………………………………………….. 13 4.1. Allocating Time on a Daily Basis for FactsWise …………………………………………….. 13 4.2. Incorporating FactsWise into Your Existing Routines ……………….………………… 13 4.3. Whole-Class Powerpoint “Commercials” ….……………………………………………………….. 13 4.4. Mini-Lessons and Routines: Goals 1 through 4 ……………………………………………………….. 14 4.5. Concrete/Representational/Abstract Whole-Class Routines Goals 1 through 4 ... 18 4.6. After Goal 4: Building Fluency and Part-Whole Thinking through Number Talks .. 23 4.7. Goals 5 through 7 ………………………………………………………………………………………………….. 25 4.8. Goals 8 and 9 ………………………………………………………………………………………………………….. 26 Section 5: Individual and Small-Group Practice ……………………………………………………….. 27 Section 6: Moving Basic Facts into Permanent Memory ………………………………………… 29 Section 7: Goal-by-Goal Assessments ………………………………………………………………………… 31

• Assessment Mats and Cards ……………………………. 80 Section 8: Record-Keeping Resources …………………………………………………………………………. 89

• FactsWise Pre-Assessment (for individual students) ……………………………. 90 • FactsWise Pre-Assessment Chart (for detailed whole-class data) …….. 93 • Basic Fact Progress Chart (running record for individual students) ….. 94 • Whole-Class Progress Chart …………………………………………………………………………. 96 • Basic Fact Goals Progress Reports (to send home to parents) …………….. 97 • Basic Facts Weekly Planner …………………………………………………………………………… 98 • Basic Math Facts Running Record Form ………………………………………………………… 100

Section 9: Pairs Practice Fold-Overs …………………………………………………………………………… 101 Section 10: Sample Calendars …………………………………………………………………………………………………… 111 Section 11: Common Core Standards related to Addition & Subtraction Facts Fluency 127


© Valerie Henry, August 2013 … www.ellipsismath.com 2

SECTION ONE: INTRODUCTION

We know from research that the vast majority of first-grade students from some countries (e.g., Japan, China, Korea) are able to develop a fluency with their basic facts that many U.S. students never acquire. Their fluency is built on more than simply memorization. These students seem to progress from counting to part-whole thinking while simultaneously working on memorization. Their sense of numbers develops as they take numbers apart and put them back together again.

Some U.S. students develop this same fluency with numbers – but many don’t. FactsWise provides a systematic approach to basic facts fluency for all our students. It builds on the research from many countries, including China, Japan, Korea, Singapore, Australia, and New Zealand. In addition, it incorporates cognitive research on ways to move facts into long-term memory, and then to help build strong retrieval mechanisms.

As we all know, memorizing a large set of facts works best when we break it up into smaller chunks. FactsWise breaks the job of memorizing the addition and subtraction facts up into nine goals. These goals are strategic – they work on fives and tens early in the program, so they can be used as tools with the remaining facts. We also know that students find subtraction much more cognitively challenging than addition, particularly when they don’t see the connections between them. So FactsWise incorporates the related subtraction facts right after each addition goal.

This program is different in one other important aspect – no timed tests! We all know how much anxiety timed tests can create in our classrooms. But equally troublesome, timed tests don’t really tell us much about how students are solving their facts problems. If we want to help students move beyond counting, we need a different assessment tool. FactsWise provides an easy one-on-one assessment system that can be implemented by the classroom teacher, classroom aids, or parent volunteers. Teachers who have used this program are sold on what they can learn about a student’s math thinking in just a minute or two of one-on-one assessment.



1.1 Correlating Common Core State Standards and FactsWise Goals

Even though FactsWise was developed several years before the Common Core State Standards, it closely mirrors the basic facts standards:

FactsWise Goals Common Core State Standards Expectations

Kindergarten 1st Grade 2nd Grade By end of 2nd Grade

1: Within 4s & 5s (1+3, 2+2, ...) F + - F + - F + - M + - 2: With 5s (5+1 to 5+5) D + - F + - F + - M + - 3: Within 10s (1+9, 2+8, ...) D + - F + - F + - M + - 4: With 10s (10+1 to 10+10) D + F + - F + - M + - 5: With 5s (5+6 to 5+9) S + - F + - M + - 6: Doubles S + - F + - M + - 7: Misc. Under 10s (2+6, 3+7, ...) D + - F + - F + - M + - 8: With 9s (2+9 to 8+9) S + - F + - M + - 9: With 7s & 8s (4+7, 6+7, ...) S + - F + - M + - D - Developing: Solve by using objects or drawings to represent the problem F - Fluently add and subtract using mental strategies M - Know from memory S - Use strategies such as decomposing, making ten, creating equivalent but easier or known sums, ... Kindergarten: 2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. 3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). 4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. 5. Fluently add and subtract within 5. 1 (BT). Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. 1st Grade Common Core Standard: Add and subtract within 20 5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 2nd Grade Common Core Standard: Add and subtract within 20 2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.



1.2: Research Findings The results of this program are remarkable! The average basic facts fluency

(memorized or part-whole strategy in 3 seconds or less) was significantly higher for FactsWise first-graders compared to “control” students who experienced other basic facts approaches.1

Average Basic Facts Fluency

58%

41%

81%

70%

Addition Subtraction

ControlTreatment

Girls in the control classrooms were significantly less fluent in both addition and subtraction. This disparity was virtually eliminated in FactsWise classrooms.

Average Addition Basic Facts Fluency

52%

65%

80% 81%

Girls Boys

ControlTreatment

Average Subtraction Basic Facts Fluency

31%

51%

69%72%

Girls Boys

ControlTreatment

1 One-on-one basic fact assessments were conducted in June, 2007 with 141 students from 14 FactsWise first-grade classrooms and 98 students from 10 “control” classrooms in a high-performing California school district. Assessed students were randomly selected from each classroom.



Results were even more pronounced in classrooms with teachers who were implementing FactsWise for the second year. As the yellow portions of the circle graphs below show, only 16% of the girls and 29% of the boys in the control classrooms demonstrated mastery of basic facts (80% or more memorized or correctly solved using part-whole thinking in 3 seconds or less). In classrooms with teachers implementing FactsWise for the second year, 78% of the girls and 70% of the boys demonstrated mastery.

Total Fluency - Girls - Control

66%

18%

16%

<5050-7980-100

Total Fluency - Boys - Control

36%

35%

29%

<5050-7980-100

Total Fluency - Girls - ENuF 2ndYr

8%

14%

78%

<5050-7980-100

Total Fluency - Boys - ENuF 2ndYr

8%

22%

70%

<5050-7980-100

Yellow – 80-100% fluent; Red – 50-79% fluent; Blue – less than 50% fluent

Percent Basic Facts Fluency

No. of Student

s

1st Quartil

e

Median 3rd Quartil

e 2nd-Yr FactsWise Girls (blue)

37 81.8 86.4 95.5

2nd-Yr FactsWise Boys (red)

36 65.9 90.9 95.5

Control Girls (green)

50 18.2 36.4 59.1

Control Boys (black)

48 31.8 59.1 81.8



SECTION TWO: KEY PRINCIPLES AND STRATEGIES

2.1 Basic Facts for Number Sense

It turns out that the way a child learns to add and subtract small numbers up to 9+9 and 18-9 is likely to set the stage for how that child makes sense of mathematics for years to come.

All children begin to make sense of addition and subtraction by counting with objects and their fingers. This is an important first step towards making sense of numbers. In fact, counting seems to be to mathematics what phonemic awareness is to reading.

At some point, though, some children begin to take numbers apart and put them back together in ways that allow them to add and subtract without counting. For example, 9 + 7 can be thought of as 9 + (1 + 6) which allows the child to make a ten with six more: (9 + 1) + 6 = 10 + 6 = 16. This type of part-whole thinking is an exceptionally important step forward in a child’s mathematical career! Research has found a strong link between part-whole thinking and number sense in general. Children who use part-whole thinking to solve addition and subtraction problems have a big advantage over children who continue to rely solely on counting.

In the past, we have thought of speed and accuracy as the twin goals of basic facts instruction. If a student could answer basic fact problems correctly and quickly, we have often overlooked the way in which the problems were solved – particularly if fingers were out of sight! In fact, students are often very proud when they can count mentally, and don’t need their fingers at all. Yet they are still counting. When students continually use counting as their primary method for solving problems, they generally aren’t looking at the relationships between numbers. Even when they are as quick (or even quicker) at solving a problem than part-whole thinkers, they are missing opportunities to develop an important key to mathematical power – number sense.

Eventually, of course, we hope that students will memorize their facts. The ability to retrieve basic facts from long-term memory without needing to count or use part-whole strategies frees up working memory. This becomes very important in later years when multi-step mathematical problems tax working memory limits. What is becoming increasingly clear, though, is the long-term difference between students who practice their way to memorization through rote counting versus students who gain part-whole strategies and number sense relationships on their road to memorization. Based on new research, we now know just how important an impact primary teachers can have on their students’ long-term mathematical power. In reading, primary teachers have learned to simultaneously teach for accuracy, fluency, and comprehension. Now, in basic facts development, primary teachers have a similar challenge – to teach simultaneously for accuracy, fluency, and part-whole thinking.



Number Sense Strategy Stages

Stage & Behavioral Indicator

Grade

0 E Emergent The student has no reliable strategy to count an unstructured collection of items.

K

1 CA1 Counting All 1 (One-to-One Counting) The student has a reliable strategy to count an unstructured collection of items.

K

2 CA2 Counting All 2 (Counting from One with Materials) The student’s most advanced strategy is counting from one with materials to solve addition problems.

1

3 AC1 Advanced Counting 1 (Counting On with Materials) The student’s the most advanced strategy is counting-on, or counting-back, with materials to solve addition or subtraction tasks.

1

4 AC2 Advanced Counting 2 (Counting On by Imaging) The student’s most advanced strategy is counting on without the use of materials to solve addition problems.

1

5 PWEA

Part-Whole Thinking -- Early Additive The student shows any Part-Whole strategy to solve addition or subtraction problems mentally by reasoning the answer from basic facts and/or place value knowledge.

2

6 PWAA Part-Whole Thinking -- Advanced Additive The student is able to use at least two different mental strategies to solve addition or subtraction problems with multi-digit numbers.

3

7 PWAM Part-Whole Thinking - Advanced Multiplicative The student is able to use at least two different mental strategies to solve multiplication and division problems with whole numbers.

4

8 PWPro1 Part-Whole Thinking -- Proportional Reasoning 1 The student uses at least two different strategies to solve problems that involve equivalence with and between fractions, ratios and proportions.

5

9 PWPro2 Part-Whole Thinking -- Proportional Reasoning 2 The student uses mental math to solve ratio, rate & proportion problems.

6

Adapted from New Zealand Maths Numeracy Project (http://www.nzmaths.co.nz/numeracy/)



2.2 Part-Whole Thinking and the Power of Tens

There are three main kinds of part-whole strategies for addition: making tens, working with fives, and relating to known facts.

Many U.S. teachers have focused their part-whole instruction on known-fact strategies such as doubles plus and minus one. Doubles part-whole thinking has short-term value in that it helps students solve some of the more challenging basic facts, including 5+6, 6+7, 7+8, and 8+9. It has two limitations, though. First, this strategy does not easily translate to other basic fact problems such as 6 + 9 and 5 + 8. Thus, teachers often attempt to teach their students several strategies to solve the complete range of over-ten basic fact problems, including doubles strategies, the nines rule, two-aparts, the eights rule, … With so many strategies and “tricks” to remember, many students just seem overwhelmed and continue to rely on counting to solve their facts.

A second limitation to focusing on known-fact strategies is that they have limited long-term value in solving multi-digit problems mentally (e.g., 27+9 or 35+18). Very few multi-digit problems will fall into the doubles-plus-one or two-aparts categories.

A more powerful part-whole strategy for addition is making tens. This is the strategy many Asian students learn for over-ten facts. Once students have memorized their combinations of 10 (1+9, 2+8, 3+7, 4+6, 5+5), they are ready to make tens. For example:

9 + 6 8 + 5 9 + 1 + 5 and 8 + 2 + 3 10 + 5 = 15 10 + 3 = 13 The ability to make tens is a powerful mental math strategy that is extremely useful

as students move into higher levels of mathematics. When students are done with the nine goals of this program, they will be ready to learn more advanced part-whole thinking to solve problems such as:

29 + 16 38 + 45 29 + 1 + 15 and 38 + 2 + 43 30 + 15 = 45 40 + 43 = 83



2.3 Subtraction

Most students find subtraction even more challenging than addition. Perhaps because of this, many instructional programs wait until students have achieved success with all of the addition facts before tackling the subtraction facts. For many students, this means they actually have less time during the school year to learn about the facts that are more difficult for them.

This program takes a different approach. Students start with a small chunk of addition facts (1+3, 2+2, 1+4, 2+3). Once they have memorized these facts, they are immediately asked to begin memorizing the related subtraction facts. For each new goal, this same approach provides students with a stable addition foundation on which to develop subtraction confidence.

Once students have completed memorizing the facts through Goal 4, they have the tools to use a part-whole subtraction strategy to solve larger subtraction fact problems. By subtracting from 10 first, students can advance beyond the cognitively demanding method of counting back to solve larger subtraction facts.

Subtracting from 10 First

15 - 8 or 15 10 + 5 - 8 - 8 5 + 10 - 8 2 + 5 = 7 5 + 2 = 7

Try some for yourself, using both of the recording methods above: 1) 12 – 9 2) 13 – 4 3) 11 – 7 4) 15 – 6

2.4 A Special Note about Doubles

Because doubles seem to be more easily memorized than other facts, many teachers have placed an early emphasis on doubles and doubles plus/minus one and two strategies in their classrooms. You may have noticed that doubles are not addressed until Goal 6 in this program. This is primarily because we want to provide students with the tens tools early on, to maximize the extremely powerful tens strategies for both addition and subtraction. When students get to the doubles in Goal 6, they are often pleased to notice how quickly they progress through this goal – at least for addition. It is quite striking how many students who find the addition doubles facts relatively easy need time to make the connections to the doubles subtraction facts.



SECTION THREE: GETTING STARTED

3.1: Early Number Fluency Overview

FactsWise is a very flexible program. You can start off very simply, and add instructional strategies, materials, and technology as you choose. The core of the program revolves around: 1) quick one-on-one assessments, 2) whole-class routines and mini-lessons, and 3) goal-specific practice and games.

FactsWise has three distinct stages: • Goals 1-4 – continue developing conceptual understanding, particularly making

connections between addition and subtraction. As you work with patterns and ten-based visual relationships, you will focus on memorization of these key facts.

• Goals 5-7 – focus on developing ten-based part-whole strategies. This part-whole thinking has long-term value for multi-digit mental math. Ultimately, students will benefit from having these facts memorized.

• Goals 8-9 – focus on part-whole thinking with these facts. As long as students have efficient part-whole strategies for these facts, it does not seem critical that they memorize all of these, although memorization is definitely optimal.

Ongoing assessment

Pre-assessment

Whole-class routines & mini-lessons

Individual/small group practice & games

Communicating with Parents

Before you begin this program, be sure that your students have developed a good conceptual understanding of both addition and subtraction. It is very important that students not work on memorizing math facts before they understand what the operations mean.

Be sure to have students do cumulative reviews after Goals 3, 6, and 9. Teachers have reported that when these are skipped, students tend to forget earlier goals.



3.2 Pre-Assessing Your Students

To get started, you have two good options:

1) Start everyone at Goal 1 addition and be ready for some students to move quickly through one or more goals.

2) Do a quick-start FactsWise Pre-Assessment (Section 8) with each student to gain a good sense of which goal each student is ready to work on. This generally takes 3 to 5 minutes per student.

3.3 Pre-Assessment and Ongoing Assessment Techniques

When you do one-on-one assessments with your students, you will want to have made some decisions ahead of time:

1) Will you be asking the students the questions verbally? Will you also be showing the students the problems in writing (see FactsWise Pre-Assessment Visuals)? Or will you simply be asking your students to look at the problems in writing? We have found a great deal of success using verbal prompts while also showing the students the problems in writing, If, however, you have second-language students who have learned their numbers and at least some of their facts in their first language, you may want to avoid saying the problems aloud in English. For these students, this necessitates that they then translate them into their first language, and then back again when they state the answers. You may get a truer sense of their fluency if they don’t have to make that first translation. Be aware that the need to translate their answers into English may still cause these students to have a certain time lag.

2) What are your criteria for passing students on a goal? a. If a student is counting on one or more problems, then he or she is not ready to

move on yet. Sometimes you’ll be able to see the student using fingers or sub-vocalizing the counting.

b. In all cases where you’re not sure what a student is doing, ask “How did you get that?” Most students will be able and willing to tell you. If they say “I just knew it”, it’s most likely that they are retrieving from long term memory. If they say they were counting in their heads, they’re still not ready to move on. Remember, our goal is to help students develop part-whole strategies and ultimately memorization!

c. If a student is retrieving from long-term memory, or using a part-whole strategy, you have one last decision to make – was it fluent enough? Your criteria for fluency (speed of response) may differ depending on the grade you’re working with.

i. For second grade and above, we recommend setting a standard of two seconds or less for response time (just mentally count “one thousand one,



one thousand two” while you’re waiting for the response). If the student is taking longer than this, then their retrieval or part-whole strategy is still cognitively demanding.

ii. For first grade and kindergarten, you may want to set a more forgiving fluency expectation – perhaps three seconds. One thing we definitely want to encourage at this age is part-whole thinking. If we demand that they answer too quickly during this developmental phase, we may simply encourage guessing.

3.4 Pre-Assessment and Ongoing Assessment Record Keeping

You’ll find a couple of different recording options in the Record-Keeping Resources (Section 8). 1) If you do the quick-start pre-assessment, you’ll want copies of the FactsWise Pre-

Assessment form for all of your students. 2) Once you have started the program, and are conducting weekly or bi-weekly ongoing

assessments, we recommend that you use individual student records (FactsWise Progress Chart). These allow you to notice students who are not making steady progress, and also provide good information for parent conferences.

3) In addition, we have provided a FactsWise Class Progress Chart that can provide you with flexible grouping options for small-group instruction and for FactsWise stations. You can write students’ initials or class numbers on small dots with removable adhesive (available at most office supply stores). These dots are able to move from goal to goal as students progress. We generally recommend that this chart be reserved for the teacher’s eyes only.



SECTION FOUR: WHOLE-CLASS ROUTINES AND MINI-LESSONS

4.1 Teaching Basic Facts Every Day

As you prepare to implement FactsWise, it is important to develop a plan for incorporating basic facts teaching into your daily routines. To maximize results, it is also important to understand the keys to helping learners move information into long-term memory. All too often, we see students practice their facts with worksheets, flashcards, or timed tests over and over, with seemingly no improvement in retention.

Research has identified four keys for effective processing of information in working memory that increase the probability that basic facts will move into long-term memory: 1) the information is processed multiple times with 1- or 2-day intervals in between, 2) detail is added, 3) associations are made with other information, and 4) students receive immediate feedback on the accuracy of their practice attempts. With these four keys in mind, we recommend that you allocate fifteen to twenty minutes every day to basic facts mini-lessons, routines, and individual/small group practice sessions. Work on the same goal for several days/weeks in a row, providing new detail and associations with each new mini-lesson. Don’t move too quickly to a new goal – overlearning leads to accuracy and fluency!

4.2 Incorporating FactsWise into Your Existing Routines

Many primary teachers have a daily routine that often involves the calendar, weather, place value, and other math-related activities. If you already use such a system, consider incorporating at least some of your FactsWise time here. However, you will probably need to make some hard decisions about what parts of your current routine you will decrease or eliminate in order to make room for basic facts. It may help to review your state’s math standards to get a sense of the relative importance of various concepts and skills.

4.3 Whole-Class Powerpoint “Commercials”

Advertisers know that after watching a commercial 7 times, viewers are likely to remember large chunks of the message. We’ve developed several basic fact “commercials” for FactsWise goals --- students seem to enjoy watching and interacting with them. Feel free to download them from the Free Resources section at www.ellipsismath.com. Once you coach your students on the way you would like them to interact with the presentations (e.g., choral response, silently, …), these “commercials” can give you a few minutes to take attendance or set up for your math lesson!




4.4 Mini-Lessons and Routines: Goals 1 through 4

Goal 1 – Within 4s & 5s

Add: 1+3, 2+2, 3+1, 1+4, 2+3, 3+2, 4+1 Sub: 4-1, 4-2, 4-3, 5-1, 5-2, 5-3, 5-4

Goal 2 – With 5s (part 1)

Add: 1+5, 2+5, 3+5, 4+5, 5+5 Sub: 6-1, 6-5, 7-2, 7-5, 8-3, 8-5, 9-4, 9-5, 10-5

Goal 3 – Within 10s

Add: 0+10, 1+9, 2+8, 3+7, 4+6 Sub: 10-0, 10-10, 10-1, 10-9, 10-2, 10-8, 10-3, 10-7, 10-4, 10-6

Goal 4 – With 10s

Add: 10+1, 10+2, 10+3, 10+4, 10+5, 10+6, 10+7, 10+8, 10+9, 10+10 Sub: 11-1, 11-10, 12-2, 12-10, 13-3, 13-10, 14-4, 14-10, 15-5, 15-10,

16-6, 16-10, 17-7, 17-10, 18-8, 18-10, 19-9, 19-10, 20-10

During the first four goals of FactsWise, you are working primarily on conceptual understanding, patterns, visualization, and memorization. We share below a starter set of routines and mini-lessons you may want to consider for Goal 1. Notice that a mini-lesson introduces a new visual representation or concept the day before it is used during your routine time. You’ll also notice that some of the routines and mini-lessons we share incorporate the Slavonic abacus. This is an excellent way to help students visualize numbers and number relationships, as well as to model part-whole thinking. If you do not yet have Slavonic abacuses, you may want to use ten-frames as an alternative representation.2

Sample Routines and Mini-Lessons for Goal 1 Addition

(a possible progression that provides students with immediate feedback, and adds details and associations each day)

Day Routine Mini-Lesson 1 What are all the ways to make 5? Students use

two colors of Unifix cubes and record their results. Students share patterns.

2 • What are all the ways to make 5? (Students use two colors of Unifix cubes)

• What patterns can we find?

What are all the ways to make 5? Students spill 5 two-colored counters, arrange the various ways on 10-frames, and record their results. Students share patterns.

3 • What are all the ways to make 5? (Students use two-colored counters on 10-frames)

• What patterns can we find? • What is 1+4? 1+3? 2+3? 0 + 4? 3+2? …

Students color all of the combinations of 5 on pre-cut ten-frames. When they are done, they arrange them following patterns they notice. Have students share patterns. Ask how many different ways to make 5.

2 You can learn more about Slavonic abacuses and ten-frames at www.ellipsismath.com.




Goal 1 Addition (continued) (a possible progression that provides students with immediate feedback, and adds details and associations each day)

Day Routine Mini-Lesson 4 • What are all the ways to make 5?

(Students use two-colored counters on 10-frames)

• How can we list the combinations efficiently, using patterns to help us?

• What is 1+4? 1+3? 2+3? 0 + 4? 3+2? …

Have students work on rapid identification of the fingers on one hand. Give them sets of cards showing the finger patterns, the numerals, tally marks, and dot patterns for numbers from zero to five (see p. ___). Teach them how to play a matching game with these cards.

5 • What are all the ways to make 5? (Students show with their fingers)

• How can we list the combinations efficiently?

• What is 1+4? 1+3? 2+3? 0 + 4? 3+2? …

Introduce students to part-part-whole grids using a word problem such as: Zack has 3 books and Leah has 2 books. How many do they have altogether? Show students how the two side-by-side parts are the same length and area as the total. Ask students to fill in their own part-part-whole grids with addition story problems to 4 and 5.

6 • What are all the ways to make 5, efficiently? (Students show with their fingers)

• Let’s record the facts on part-part-whole grids.

• What is 1+4? 1+3? 2+3? 0 + 4? 3+2? … • What is the turn-around for 2+3? … 1+4?

Introduce students to the Goal 1 addition flashcards. Point out the part-part-whole grids on the front and back, and how they can use these to practice their facts. Be sure to model the metacognitive process of deciding when a card can be removed from the deck – when you are sure you know it without even pausing.

7 • What are all the ways to make 5, efficiently? (Students say as student volunteer shows on large Slavonic abacus)

• Let’s put the part-part-whole grids in order to see the patterns.

• What is 1+4? 1+3? 2+3? 0 + 4? 3+2? … • What is the turn-around for 2+3? … 1+4?

If students have not used individual Slavonic abacuses before, this is a good time to introduce them to your classroom expectations and the zero set-up. Encourage students to show the patterns with ways to make 5.

Sample Routines and Mini-Lessons for Goal 1 Subtraction

(a possible progression that provides students with immediate feedback, and adds details and associations each day)

Day Routine Mini-Lesson 1 • “I’m holding 5 balls. Oops – I dropped

one. Now how many am I holding?” Record 5 – 1 = 4. Have students volunteer to create other subtraction dropping ball problems with 5s. Record each one. (Note: This is the “separate” meaning for subtraction.)

• What is 5-1? 5-3? 5-0? …

“I’m holding 3 balls and Jessie gives me 2 more. Now how many do I have?” Record the problem in a part-part-whole grid. “Oops, I dropped 2 of the 5 balls. How many do I have now?” Help students make connections between the same part-part-whole grid and this subtraction problem. Then consider 5 balls dropping 3 with the same grid. Continue with other problems and part-part-whole grids.


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Goal 1 Subtraction (continued) (a possible progression that provides students with immediate feedback, and adds details and associations each day)

Day Routine Mini-Lesson 2 • “I have 5 pencils and I give 2 of them to

Max. Now how many do I have?” Record the problem in a part-part-whole grid. Write the grid for 5-1 and ask students to tell the associated pencil story and the answer to the problem. Continue with other pencil sharing stories with 5s.

• What is 5-1? 5-3? 5-0? …

Write the 4,1,5 part-part-whole grid on the board. Ask students to tell their partners a pencil story for this problem. Record the various stories – some will be addition, some will be subtraction. Ask students to write equations for all the equations that relate to this part-part-whole grid (4+1=5, 1+4=5, 5-4=1, 5-1=4). Repeat with other part-part-whole grids totaling 5.

3 • I had $5 last night, and then I spent $3. How much did I have then? Have students model this problem using ten-frames or Slavonic abacuses. Record in part-part-whole grid and in equation. Continue with additional money stories.

• What is 5-1? 5-3? 5-0? …

Write the 2,3,5 part-part-whole grid on the board. Ask students to write all possible equations, and to write/tell money stories for each equation. Repeat with other combinations to 5.

4 • Have student volunteers select pre-made part-part-whole grids for ways to make 5 and have them tell the related addition and subtraction equations, with other students recording on the board.

• What is 5-1? 5-3? 5-0? …

“Cal has 5 books and Joanne has 1 book. How many more books does Cal have?” (Note: This is the comparison meaning of subtraction.) Have two student volunteers match up their books, which will show the 4 extra Cal has. Also show how this problem can be modeled with the part-part-whole grid. Ask students what equations they would use for this problem (some will think 1+?=5 and some will think 5-1=?). Repeat with 5-4, and other 5s problems.

5 • Show students two Unifix rods with 5 blue cubes in one and 3 red cubes in the other. Ask students how many more blue cubes there are than red cubes. Have student volunteers record the part-part-whole grid and the related addition and subtraction equations (i.e., 3+?=5 and 5-3=?). Repeat with other 5s combinations.

• What is 5-1? 5-3? 5-0? …

Teach students the Fives Comparison Game – Players can use tally cards from 0 to 5, dot pattern cards from 0 to 5, or finger pattern cards from 0 to 5. Place one of the “5” cards face up between the players, and deal the rest of the cards to the players. On her turn, each player draws one card from her pack of cards. After determining how many more the face-up card is than the card she has drawn, she will move her marker on a generic gameboard (p. ___) that many spaces.



Goal 1 Subtraction (continued) (a possible progression that provides students with immediate feedback, and adds details and associations each day)

Day Routine Mini-Lesson 6 • Show students two Unifix rods with 5

blue cubes in one and 3 red cubes in the other. Ask students how many more blue cubes there are than red cubes. Have student volunteers record the part-part-whole grid and the related addition and subtraction equations (i.e., 3+?=5 and 5-3=?). Repeat with other 5s combinations.

• What is 5-1? 5-3? 5-0? …

Show students 5s part-part-whole grids and ask them to create Unifix rod comparisons to match the grids. Record their equations.

7 • Have student volunteers select pre-made part-part-whole grids for ways to make 5 and have them tell the related addition and subtraction equations, with other students recording on the board.

• What is 5-1? 5-3? 5-0? …

Show students 5s part-part-whole grids and ask them to create two subtraction word problems for each: a separate problem and a comparison word problem. Encourage students to share, and then record their equations.



4.5 Concrete/Representational/Abstract Whole-Class Routines Goals 1 through 4

Goal 1 – Ways to make 4 and 5

Concrete Routines 1) Show Me – have students, on one hand, show 1, 2, 3, 4, 5. Do this routine for 1 or 2

minutes per day until they are able to do this automatically. 2) Abacus Show Me – have some students show 1, 2, 3, 4, 5 on the abacus while other

students show on one hand. 3) All the Ways – have 4 or 5 students stand in front of the class on the right side of

the room – this represents 4=0+4. Have one student at a time walk to a designated area on the left side of the room. Have the students in the class choral chant 4=1+3, 4=2+2, 4=3+1, 4=4+0. Use this same procedure for ways to make 5. (Note: in order to help students understand the that = means the same value on both sides, it’s important to expose students to the operations on the right as well as the left, and also to equations such as 4=4.)

4) One Hand Choral – have students use one hand to model addition problems first (1+3 makes, 2+3 makes, …). As students become fluent with the addition facts, have students use one hand to model subtraction problems (4-1 makes, 4-3 makes, 5-2 makes, …).

5) Abacus Choral – have student(s) model addition problems first, and then addition and subtraction problems interchangeably.

6) Snap Cube Student Leaders – have one or more students use snap cubes (unifix, multilink, …) to model ways to make 4 and 5 and lead students in choral responses such as “4+1 makes” and “5-4 makes”.

Representational Routines 7) Ten Frame Choral – show students ways to make 4 and 5 on ten-frame cards and

use choral response – “1+3 makes”. You can find ten-frame cards at http://www.wsd1.org/pc_math/Dot%20Card%20and%20Ten%20Frame%20Package2005.pdf.

8) Part-Whole Grid Choral – show students a part-whole grid (see FactsWise Part-Whole Resources) for a way to make 4 or 5 and have students state both the addition and subtraction relationships while you write them on the board.

Abstract Routines 9) Snap Facts – Say a fact such as “2+3 makes” and then use a hand signal for wait.

Give students 2 or 3 seconds to process, and then snap your fingers, at which time students will choral respond with the answer. Watch carefully for facts where some students are delaying their answers, and repeat those several times before you end the activity. Remember to spend more time on subtraction facts than you do on addition facts!


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Goal 2 – With 5s (5+1, 5+2, 5+3, 5+4, 5+5, and related subtractions)

Concrete Routines 1) Show Me – have students, on two hands, show 6, 7, 8, 9, 10 (be sure students show

6 as 5 and 1, 7 as 5 and 2, 8 as 5 and 3, 9 as 5 and 4). Do this routine for 1 or 2 minutes per day until they are able to do this automatically.

2) Abacus Show Me – have some students show 6, 7, 8, 9, 10 on the abacus while others show on two hands.

3) Two Hand Choral – have students use two hands to model addition problems first (5+1 makes, 5+2 makes, …). As students become fluent with the addition facts, have students use two hands to model subtraction problems (6-1 makes, 7-5 makes, …).

4) Abacus Choral – have student(s) model addition problems first, and then addition and subtraction problems interchangeably.

5) Human Ten Frames – Use chalk, tape, or paint to create a large ten frame in your room or outside. Ask students to model “with 5s” problems, both addition and subtraction, by standing in the squares of the ten frame.

6) Snap Cube Student Leaders – have one or more students use snap cubes (unifix, multilink, …) to model “with 5s” addition and subtraction problems and lead students in choral responses such as “5+3 makes” and “8-5 makes”.

Representational Routines 7) Two Hands Cards Choral – show students the “With 5s” two-hand cards and use

choral response, such as “5+3 makes” and “8-5 makes”. (see FactsWise Part-Whole Resources)

8) Ten Frame Choral – show students With 5s ten-frame cards and use choral response, such as “4+5 makes” and “9-4 makes”. You can find ten-frame cards at http://www.wsd1.org/pc_math/Dot%20Card%20and%20Ten%20Frame%20Package2005.pdf.

9) Ten Frame Powerpoint – work with students to develop a choral response routine for the “With 5s” powerpoints for addition and subtraction.

10) Part-Whole Grid Choral – show students a part-whole grid (see FactsWise Part-Whole Resources) for “With 5s” and have students state both the addition and subtraction relationships while you write them on the board.






Goal 3 – Within 10

Concrete Routines 1) All the Ways – have students show all the ways to make 10 on their abacuses or on

the large class abacus. At first they may do this without an organized system, but provide assistance in noticing patterns and encourage students to develop a systematic approach (e.g., 0+10, 1+9, 2+8, 3+7, …). Have students write and/or say all the ways to make 10 in the following ways:

a) Using equations such as 10=0+10, 10=1+9, … b) In part-whole grids etc. c) In a table (horizontal and/or vertical)

0 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 0

2) Abacus Choral – have student(s) model “Within 10” addition problems first, and then addition and subtraction problems interchangeably. When working on Goal 3 addition, you’ll need to include problems from Goals 1 and 2, since all of the Goal 3 addition problems make 10. For subtraction, at least at first, you’ll probably want to focus in on the Goal 3 facts. When students are relatively fluent with Goal 3 subtraction, be sure to incorporate Goal 1 and Goal 2 subtraction.

3) Ten Frame Choral – have students model “Within 10” problems using individual ten frames (see FactsWise Part-Whole Resources) and two colored counters.

4) Snap Cube Student Leaders – have one or more students use snap cubes (unifix, multilink, …) to model “within 10” addition and subtraction problems and lead students in choral responses such as “10=6 + what?” and “10-6 makes”.

Representational Routines 5) Two Hands Cards Choral – show students the “Within 10” two-hand cards (see

FactsWise Part-Whole Resources) and use choral response, such as “10=7 + what?” and “10-7 makes”.

6) Ten Frame Choral – show students “Within 10” ten-frame cards and use choral response, such as “10=7 + what?” and “10-7 makes”. Ten-frame cards - http://www.wsd1.org/pc_math/Dot%20Card%20and%20Ten%20Frame%20Package2005.pdf.

7) Ten Frame Powerpoint – work with students to develop a choral response routine for the “Within 10” powerpoints for addition and subtraction.

8) Part-Whole Grid Choral – show students part-whole grids for “Within 10” (see FactsWise Part-Whole Resources) and have students state both the addition and subtraction relationships while you write them on the board.

10

0 10

10

1 9

10

2 8




Goal 4 – With 10s

Concrete Routines

1) Abacus Choral – have student(s) model “With 10s” addition problems first, and then addition and subtraction problems interchangeably.

2) Snap Cube Student Leaders – have one or more students use snap cubes (unifix, multilink, …) to model “with 10s” addition and subtraction problems and lead students in choral responses such as “10+8 makes?” and “18-8 makes”.

Representational Routines 3) Ten Frame Choral – show students “With 10s” ten-frame cards and use choral

response, such as “10+7 makes” and “17-10 makes”. Ten-frame cards - http://www.wsd1.org/pc_math/Dot%20Card%20and%20Ten%20Frame%20Package2005.pdf.

4) Ten Frame Powerpoint – work with students to develop a choral response routine for the “Within 10” powerpoints for addition and subtraction.

5) Arrow Cards – show students a 10 arrow card and any 1-digit arrow card (see FactsWise Part-Whole Resources). Have students respond chorally as you slide the two arrow cards together. Consider having the students respond in two different ways: 1) in “place value order” (e.g., 10+8 makes “ten eight”) and 2) in standard number language (e.g., 10+8 makes eighteen).

6) Part-Whole Grid Choral – show students part-whole grids for “With 10s” (see FactsWise Part-Whole Resources) and have students state both the addition and subtraction relationships while you write them on the board.

7) Hundred Chart Choral – use the first two rows of a hundreds chart (see FactsWise Part-Whole Resources):

a. Point to a single-digit number such as 8 and ask students to add 10. Move your finger down to 18.

b. Point to a double-digit number such as 15 and ask students to subtract 10. Move your finger up to 5.

c. Point to a double-digit number such as 15 and ask students to subtract 5. Slide you finger to 10.






4.6 After Goal 4: Building Fluency and Part-Whole Thinking through Number Talks

Now that your students are fluent with their 5s and 10s, the next phase of FactsWise is to focus on developing part-whole strategies that use 5s and 10s. A way to engage all of your students in this process is to use number talks. If you're a second or third grade teacher, you can start using number talks focused on part-whole thinking as you start Goal 5. For instance, on day 1 of Goal 5 you could use the following progression (string) of problems: 1) 5 + 5 2) 5 + 6 3) 5 + 8 1) When you pose 5 + 5, it's likely that most of your students will simply tell you that they "know" it. By now, this fact is most likely a strongly memorized fact -- so you won't need to spend much time discussing it. 2) When you pose 5 + 6, it's likely that you'll get at least two or three different approaches, including: a) counting on from 6 or 5; b) 5 + 5 = 10, so 5 + 6 is one more than that; c) 6 + 6 = 12, so 5 + 6 is one less than that. Since this is the beginning of Goal 5, you'll want to have a visual for at least part of the discussion. You could use ten-frames, or a Slavonic Abacus.

3) When you pose 5 + 8, you'll want to encourage students to see how 8 can be decomposed into 5+3, and that the two 5s make 10, and then 10+3=13. Over the next several days, your number strings will seem very repetitive -- since there are only four new facts in Goal 5+. When most of your students are telling you that they now "know" the facts, and are also able to explain how to decompose and make 10s to explain their results, then you will be ready to move on to Goal 5 subtraction. Note: When you include 5 + 9 in a number talk string, you will hopefully see students using a subtraction strategy as well as additive strategies. This is particularly useful when adding 9s. For instance, a student might say, "I know that 5 + 10 is 15, so 5 + 9 is one less than that." When your students are fluent with Goal 5+, then you will be able to use number talks to work on Goal 5-. A string you might want to start with is: 1) 10 - 5 2) 11 - 5 3) 11 - 6 4) 12 - 5



Since you're starting a new set of facts, you'll want to start Goal 5- with a concrete model such as ten-frames or the Slavonic Abacus. For example, with 11-5 a student might look at the ten-frames and say: "10 take away 5 is 5, and 1 more makes 6." Another student might say: "I know that 5 + 6 = 11, so 11 minus 5 is 6." This would be a good time to make a connection to the part-part-whole grid.

Once your students are fluent with Goal 5-, you'll be able to use number talks as a primary activity for the rest of the FactsWise goals. The reason for concentrating on this approach is to encourage students to verbalize different part-whole strategies, and to give all students multiple opportunities to build confidence with the three 10s strategies (Addition Make-a-Ten, Subtraction Take-from-Ten and Down-over-Ten).

(images excerpted from a Korean 1st grade textbook)



If you're a first grade teacher, you may decide that you want to solidify Goals 1 through 4 and possibly Goal 7 in first grade, and leave Goals 5 through 9 fluency for second grade. Even if you decide to take this approach, it will still be extremely important to include number talks with various "over-ten" facts during the last several months of first grade. If your students leave first grade with a solid ability to engage in part-whole thinking, they will already be thinking as they enter second grade that this is an important part of mathematics. So many students get trapped in a mathematical dead-end when they think that getting the answer right is the major point of mathematics. But if they have already learned in first grade that a key to becoming mathematically powerful is to develop efficient and varied strategies, you will have given them an amazing start on their mathematical futures! 4.7 Goals 5 through 7

Goal 5 – With 5s (part 2)

Add: 5+6, 5+7, 5+8, 5+9 Sub: 11-5, 11-6, 12-5, 12-7, 13-5, 13-8, 14-5, 14-9

Goal 6 – Doubles

Add: 3+3, 4+4, 6+6, 7+7, 8+8, 9+9 Sub: 6-3, 8-4, 12-6, 14-7, 16-8, 18-9

Goal 7 – Under Tens

Add: 2+4, 2+6, 2+7, 3+4, 3+6 Sub: 6-2, 6-4, 8-2, 8-6, 9-2, 9-7, 7-3, 7-4, 9-3, 9-6

Even though we eventually hope that students will memorize these facts, the goal

here is to help students become confident using ten-based part-whole strategies to solve these problems first. For example, 8+5 can be visualized as (3+5)+5 or 8+(2+3).

In the first case -- 8+5 = (3+5)+5 = 3+(5+5) = 3+10 -- a student would be paying attention to the fact that 5+5=10 and that 3+10 is easy to find.

Students who see 8+5 = 8+(2+3) = (8+2)+3 = 10+3 are breaking the smaller number into two parts in order to turn the 8 into a 10, and then 10+3 is easy.

The power of part-whole thinking cannot be overstated. Researchers have found that students who use part-whole thinking have a significant advantage in developing a strong number sense. In addition, they have a way of thinking about numbers that can help them develop many mental math strategies for larger numbers as well as the part-whole techniques needed in algebra.

Ten frames and the Slavonic abacus are two powerful tools for helping students visualize and demonstrate part-whole strategies. They are very simple to use, because they provide a visual way of building tens. After one student has explained and demonstrated her/his thinking, ask your class to share other ways of thinking about the



problem. Encouraging students to verbalize, and providing students with models of various part-whole strategies, is at the core of this program. Beyond encouraging students to model their thinking, there is very little the teacher needs to do. If you’d like to know more about these tools, you can download information and links from www.ellipsismath.com.

Goal 5 tends to be a challenge for most students. This is a goal where you’ll want to provide lots of encouragement and many whole-class and small-group lessons, games, and immediate-feedback practice opportunities.

Goal 6 addition may go quickly for many of your students, although the larger doubles may take a bit of work. It will be important for you to help students see the connection between doubles addition and subtraction facts, since this is not automatically understood by many students.

Goal 7 problems are all under-ten facts. Part-whole strategies can build up from 5, down from 10, or build off of other known facts. For example, a student thinking about 8-6 might remember that 8-7 is 1, and then build off of that to 8-6=2.

4.8 Goals 8 and 9

Goal 8 – With 9s

Add: 2+9, 3+9, 4+9, 6+9, 7+9, 8+9 Sub: 11-2, 11-9, 12-3, 12-9, 13-4, 13-9, 15-6, 15-9, 16-7, 16-9, 17-8, 17-9

Goal 9 – With 7s & 8s

Add: 4+7, 6+7, 3+8, 4+8, 6+8, 7+8 Sub: 11-4, 11-7, 13-6, 13-7, 11-3, 11-8, 12-4, 12-8, 14-6, 14-8, 15-7, 15-8

Students seem to embrace making tens more easily with the +9 facts than with the +8 and +7 facts. Even though it is relatively easy for students, I encourage you not to simply teach them the “9s trick”3

Building 10s with +7s and +8s is more challenging for students. Be sure to give them many opportunities to visualize this with ten frames, the Slavonic abacus, or another ten-based model you have found helpful.

. It is much more powerful for students to build tens, and this strategy generalizes to multi-digit situations. For example, 24+9 can be quickly simplified by giving one from the 24 to the 9, and then adding 23+10.

3 When students are taught to add 9 by reducing the addend by 1, and then putting a 1 in front of it, they’re being taught a trick they generally don’t understand.




SECTION FIVE: INDIVIDUAL AND SMALL-GROUP PRACTICE

5.1 Coordinating Goal-Alike Practice

One of the key principles of FactsWise is that students work with small chunks of facts to facilitate their memorization. For this reason, we have put together a range of resources that provide students with multiple opportunities to interact with each goal. Our objective is to engage students in elaborative rehearsal, where they look at the facts from many different perspectives. This approach to memorization has been found to more effective than simple repetition. For this reason, it will be important for you to know which students are working on the same goal. You can use the Whole-Class Progress Chart and reusable dots (similar to Post-Its) to keep track of your students’ progress. Then, when you want students to work together, it will be easy to get goal-alike groups together.

5.2 Flashcards and Pairs Practice

Many teachers grew up using flashcards to practice their basic facts, and we often assume that this is an essential tool in this enterprise. Goal-specific flashcards are available for this program, in both cardstock and online formats, and they are certainly one of the many ways students can practice their facts. Cognitive research provides evidence, however, that elaborative rehearsal is a more powerful method of building long-term memories than repetitive practice. So while some students may thrive using flashcards, many others will find other forms of practice more valuable. Included in this resource are Pairs Practice pages for each of the goals. These pages are designed to be folded in half, and then held between two students. While one student is reading and answering the problems, the other student is able to check the answers by looking at the other side of the folded page. This way, students can get immediate feedback, even when their partners are not yet experts themselves. These Pairs Practice pages can be reused many times because no writing is required. Just be sure to help the students learn to give positive feedback and assistance when using these pages. Jeff Simpson (http://masterylearningsystems.com), who created this practice method, encourages students to respond to an error with the phrase “try again”. It can be particularly helpful to have a Slavonic abacus or ten frames ready for students to use if they are still in the early learning phases of a goal. Not only can Pairs Practice pages be used at school, they are also a good option for at-home practice. Rather than asking parents to cut out and manage flashcards, you may want to send home Pairs Practice pages – they don’t require any cutting, they’re easy to store, and just as reusable as flashcards.


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5.3 Online Flashcards, Games and Quizzes

Online flashcards, games, and quizzes are available for each of the FactsWise goals. These can be used both at school and at home, and provide an easy way to have students working on their appropriate goals.

5.4 In-Class and At-Home Games

We have also found and developed quick goal-specific games that allow students to practice their facts. While a few of the games can be played in solitaire fashion, many of them are perfect for two or more players. Some teachers find it helpful to teach a new game to a small group of students, and then let them act as instructors when other students are ready to learn the game. In addition, we have designed a parent letter with several pages of goal-specific games that parents can play with their children. We encourage teachers to set up a 4-night-a-week homework expectation where parents spend 5 to 10 minutes doing flashcards, playing the games, or supervising their children with the online resources.



SECTION 6: MOVING BASIC FACTS INTO PERMANENT MEMORY (excerpts from Building Background Knowledge for

Academic Achievement by Robert J. Marzano, 2004) Sensory memory is a (very) temporary repository for information from our senses. However, we cannot process all of the information from the senses. Rather, we pick and choose. Permanent memory contains information that has been stored in such a way that it is available to us. Working memory is the third type of memory. Working memory can receive data from sensory memory (where it is held only briefly), from permanent memory (where it resides permanently), or from both. The amount of time data can reside in working memory has no theoretical limit. As long as we focus conscious attention on the data in working memory, it stays active. … All things being equal, it is the quality and type of processing that occurs in working memory that dictates whether that information makes it to permanent memory. If processing does not go well, information does not make it to permanent memory. At least three interacting dynamics of working-memory processing dictate whether information makes it into permanent memory. One is strength of the “memory trace,” or the pathway to the information. As Anderson (1995) explains: “Memory records are assumed to have a property called strength, which increases with repeated practice” (p. 193). In simple terms, the more times we engage information in working memory, the higher the probability that it will be embedded in permanent memory. In educational terms, the more times a student processes information, the more likely the student will remember it. … Nuthall found that students require about four exposures to information to adequately integrate it into their background knowledge. Nuthall also notes that these exposures should be no more than about two days apart. … However, sheer repetition of information in working memory is not enough to ensure that it will be stored in permanent memory. Depth of processing is the second aspect of effective processing in working memory. … Deep processing of information adds detail to our understanding of information. Elaboration is the third aspect of effective processing of information in working memory. Elaboration deals with the variety of associations we make with information. Although



depth of processing and elaboration are related, depth of processing refers to going into more detail; elaboration, on the other hand, refers to making new or varied connections. Effective processing of information in working memory depends on certain critical activities: 1) the information is processed multiple times with 1- or 2-day intervals in between, 2) detail is added, and 3) associations are made with other information. Based on the above research, you may want to try the following during class:

Work on a small number of facts several days in a row (perhaps target each goal for one entire week)

Help students identify the connections between the facts in each goal Help students make connections between the addition and subtraction facts

(try using the part-whole grids) Have students solve basic fact problems from classroom-based stories as well

as in “naked number” format Have students look for patterns within goals and between goals Have students learn to look for clues as to whether a sum or difference will

be odd or even Once students have become fluent with the first five goals, begin building

part-whole strategies for the remaining facts Focus in particular on part-whole strategies involving tens Help students learn names for the types of facts in some goals



SECTION 7: GOAL-BY-GOAL ASSESSMENTS



GOAL 1A - Memorize Within 5s (Version A)

4 + 1

1 + 3

2 + 2

3 + 2

3 + 1

2 + 3

1 + 4



GOAL 1A - Memorize Within 5s (Version B)

1 + 3

3 + 2

4 + 1

2 + 2

1 + 4

2 + 3

3 + 1



GOAL 1S - Memorize Within 5s (Version A)

4 - 2

5 - 1

4 - 3

5 - 2

5 - 4

4 - 1

5 - 3



GOAL 1S - Memorize Within 5s (Version B)

4 - 1

5 - 4

4 - 2

5 - 1

5 - 3

5 - 2

4 - 3



GOAL 2+ - Memorize With 5s (Version A)

2 + 5

5 + 4

1 + 5

5 + 3

5 + 5



GOAL 2+ - Memorize With 5s (Version B)

5 + 4

2 + 5

5 + 5

3 + 5

5 + 1



GOAL 2- - Memorize With 5s (Version A)

8 - 5

9 - 4

6 - 5

10 - 5

7 - 2



GOAL 2- - Memorize With 5s (Version B)

7 - 5

6 - 1

8 - 3

9 - 5

10 - 5



GOAL 3+ Memorize Within 10s (Version A)

10 = 3 + ?

10 = 10 + ?

10 = 1 + ?

10 = 6 + ?

10 = 2 + ?



GOAL 3+ Memorize Within 10s (Version B)

10 = 6 + ?

10 = 1 + ?

10 = 3 + ?

10 = 10 + ?

10 = 2 + ?



GOAL 3- Memorize Within 10s (Version A)

10 - 3

10 - 9

10 - 6

10 - 2

10 - 10



GOAL 3- Memorize Within 10s (Version B)

10 - 4

10 - 8

10 - 10

10 - 1

10 - 7



GOALS 1,2 & 3 + (Version A)

5 + 4

3 + 2

1 + 9

2 + 5

3 + 7

1 + 4

4 + 6

5 + 3

2 + 8

2 + 3

5 + 5

2 + 2

5 + 1

0 + 10



GOALS 1,2 & 3 + (Version B)

5 + 3

8 + 2

1 + 4

4 + 5

3 + 5

9 + 1

2 + 2

5 + 5

10 + 0

7 + 3

5 + 1

2 + 3

5 + 2

6 + 4



GOALS 1,2 & 3 - (Version A)

9 - 4

5 - 2

10 - 9

7 - 5

10 - 7

5 - 4

10 - 6

8 - 3

10 - 8

5 - 3

10 - 5

4 - 2

6 - 1

10 - 10



GOALS 1,2 & 3 - (Version B)

8 - 5

10 - 2

5 - 1

9 - 5

4 - 2

10 - 9

8 - 5

10 - 5

10 - 0

6 - 5

10 - 3

5 - 2

7 - 5

10 - 4



GOAL 4+ (Version A)

10 + 5

3 + 10

10 + 1

7 + 10

10 + 2

6 + 10

10 + 8

9 + 10

4 + 10

10 + 10



GOAL 4+ (Version B)

10 + 2

7 + 10

10 + 10

10 + 3

5 + 10

10 + 9

10 + 4

6 + 10

8 + 10

1 + 10



GOAL 4- (Version A)

15 - 5

13 - 10

11 - 10

17 - 7

12 - 10

16 - 6

18 - 10

19 - 9

14 - 10

20 - 10



GOAL 4- (Version B)

12 - 2

17 - 10

20 - 10

13 - 3

15 - 10

19 - 10

14 - 4

16 - 10

18 - 8

11 - 1



GOAL 5+ (Version A)

8 + 5

5 + 6

5 + 9

7 + 5



GOAL 5+ (Version B)

5 + 9

5 + 6

8 + 5

5 + 7



GOAL 5- (Version A)

13 - 8

11 - 6

14 - 5

12 - 7



GOAL 5- (Version B)

12 - 7

11 - 6

13 - 5

14 - 9



GOAL 6+ (Version A)

3 + 3

7 + 7

9 + 9

6 + 6

8 + 8

4 + 4



GOAL 6+ (Version B)

8 + 8

3 + 3

9 + 9

7 + 7

4 + 4

6 + 6



GOAL 6- (Version A)

6 - 3

14 - 7

18 - 9

12 - 6

16 - 8

8 - 4



GOAL 6- (Version B)

16 - 8

6 - 3

18 - 9

14 - 7

8 - 4

12 - 6



GOALS 1-6 + (Version A)

2 + 3

4 + 5

3 + 7

10 + 3

5 + 6

9 + 9

1 + 4

5 + 3

6 + 4

8 + 10

9 + 5

7 + 7



GOALS 1-6 + (Version B)

4 + 1

2 + 5

4 + 6

2 + 10

5 + 9

6 + 6

2 + 3

5 + 4

2 + 8

10 + 9

7 + 5

8 + 8



GOALS 1-6 - (Version A)

5 - 3

9 - 4

10 - 7

13 - 3

11 – 5

18 - 9

5 - 1

8 - 3

10 - 4

18 - 10

14 - 9

14 - 7



GOALS 1-6 - (Version B)

5 - 4

7 - 5

10 - 6

12 – 10

14 - 5

16 - 8

5 - 2

9 - 4

10 - 8

19 – 9

12 - 7

12 - 6



GOAL 7+ Memorize Under 10s (Version A)

3 + 6

4 + 2

2 + 7

3 + 4

6 + 2



GOAL 7+ Memorize Under 10s (Version B)

2 + 6

3 + 4

7 + 2

2 + 4

6 + 3



GOAL 7- Memorize Under 10s (Version A)

9 - 3

6 - 4

9 - 7

7 - 3

8 - 6



GOAL 7- Memorize Under 10s (Version B)

8 - 2

7 - 4

9 - 2

6 - 4

9 - 6



GOAL 8+ Develop Fluency with 9s (Version A)

9 + 4

7 + 9

9 + 2

8 + 9

3 + 9

9 + 6



GOAL 8+ Develop Fluency with 9s (Version B)

6 + 9

3 + 9

9 + 8

2 + 9

4 + 9

9 + 7



GOAL 8- Develop Fluency with 9s (Version A)

13 - 4

16 - 9

11 - 2

17 - 9

12 - 9

15 - 6



GOAL 8- Develop Fluency with 9s (Version B)

15 - 9

12 - 9

17 - 8

11 - 9

13 - 9

16 - 7



GOAL 9+ Develop Fluency with 7s & 8s (Version A)

7 + 4

6 + 8

8 + 3

7 + 6

4 + 8

8 + 7



GOAL 9+ Develop Fluency with 7s & 8s (Version B)

7 + 8

4 + 8

6 + 7

3 + 8

8 + 6

4 + 7



GOAL 9- Develop Fluency with 7s & 8s (Version A)

11 - 4

14 - 8

11 - 3

13 - 6

12 - 8

15 - 7



GOAL 9- Develop Fluency with 7s & 8s (Version B)

15 - 8

12 - 4

13 - 7

11 - 8

14 - 6

11 - 7



GOALS 1-9 + (Version A)

1 + 4

2 + 5

8 + 2

10 + 7

6 + 5

8 + 8

3 + 6

4 + 9

8 + 7

2 + 2

5 + 4

3 + 7

1 + 10

5 + 8

6 + 6

4 + 2

9 + 8

7 + 4



GOALS 1-9 + (Version B)

2 + 3

4 + 5

3 + 7

10 + 3

5 + 6

9 + 9

2 + 7

6 + 9

8 + 4

1 + 4

5 + 3

6 + 4

8 + 10

9 + 5

7 + 7

3 + 4

9 + 3

6 + 7



GOALS 1-9 - (Version A)

5 - 4

7 - 5

10 - 2

17 – 7

11 - 5

16 - 8

9 - 6

13 – 9

15 - 7

4 - 2

9 - 4

10 - 7

11 – 10

13 - 8

12 - 6

6 - 2

17 – 8

11 - 4



GOALS 1-9 - (Version B)

5 - 3

9 - 5

10 - 7

13 - 3

11 - 6

18 - 9

9 - 7

15 – 9

12 - 4

5 - 4

8 - 3

10 - 4

18 – 10

14 - 5

14 - 7

7 - 4

12 – 3

13 - 7



FactsWise +-

Assessment Mats and Cards

Ellipsis Math



1 + 3

G1

2 + 2

G1

3 + 1

G1

1 + 4

G1

2 + 3

G1

3 + 2

G1

4 + 1

G1

4 - 1

G1

4 - 2

G1

4 - 3

G1

5 - 1

G1

5 - 2

G1

5 - 3

G1

5 - 4

G1

1 + 5

G2

2 + 5

G2

3 + 5

G2

4 + 5

G2

5 + 5

G2

6 - 1

G2

6 - 5

G2

7 - 2

G2

7 - 5

G2

8 - 3

G2



8 - 5

G2

9 - 4

G2

9 - 5

G2

10 - 5

G2

1 + ? = 10

G3

2 + ? = 10

G3

3 + ? = 10

G3

4 + ? = 10

G3

6 + ? = 10

G3

7 + ? = 10

G3

8 + ? = 10

G3

9 + ? = 10

G3

10 - 0

G3

10 - 10

G3

10 - 1

G3

10 - 9

G3

10 - 2

G3

10 - 8

G3

10 - 3

G3

10 - 7

G3

10 - 4

G3

10 - 6

G3

10 + 1

G4

10 + 2

G4



10 + 3

G4

10 + 4

G4

10 + 5

G4

10 + 6

G4

10 + 7

G4

10 + 8

G4

10 + 9

G4

10 + 10

G4

11 - 1

G4

11 - 10

G4

12 - 2

G4

12 - 10

G4

13 - 3

G4

13 - 10

G4

14 - 4

G4

15 - 10

G4

16 - 6

G4

17 - 10

G4

18 - 8

G4

19 - 9

G4

20 - 10

G4

5 + 6

G5

5 + 7

G5

5 + 8

G5



11 - 6

G5

12 - 5

G5

5 + 9

G5

11 - 5

G5

13 - 8

G5

14 - 5

G5

12 - 7

G5

13 - 5

G5

14 - 9

G5

3 + 3

G6

4 + 4

G6

6 + 6

G6

7 + 7

G6

8 + 8

G6

9 + 9

G6

6 - 3

G6

14 - 7

G6

16 - 8

G6

8 - 4

G6

12 – 6

G6

18 - 9

G6

3 + 6

G7

2 + 7

G7

3 + 4

G7



2 + 4

G7

2 + 6

G7

8 - 2

G7

8 - 6

G7

6 - 2

G7

6 - 4

G7

7 - 3

G7

7 – 4

G7

9 - 2

G7

9 - 7

G7

9 - 3

G7

9 - 6

G7

4 + 9

G8

6 + 9

G8

2 + 9

G8

3 + 9

G8

7 + 9

G8

8 + 9

G8

12 - 3

G8

12 – 9

G8

11 - 2

G8

11 - 9

G8

15 - 6

G8

15 - 9

G8



13 - 4

G8

13 - 9

G8

17 - 8

G8

17 – 9

G8

16 - 7

G8

16 - 9

G8

3 + 8

G9

4 + 8

G9

4 + 7

G9

6 + 7

G9

6 + 8

G9

7 + 8

G9

13 - 6

G9

13 - 7

G9

11 - 4

G9

11 - 7

G9

12 - 4

G9

12 - 8

G9

11 - 3

G9

11 – 8

G9

15 - 7

G9

15 - 8

G9

14 - 6

G9

14 – 8

G9



FluentMemorized (<3 seconds)

FluentStrategy (<3 seconds)

SlowMemorized

SlowStrategy

Counting

Incorrect/Don't Know



FM

FS

SM

SS

C

I/DK



SECTION 8: RECORD-KEEPING RESOURCES



Name _____________________________ Grade _________ Teacher ______________ School __________

FactsWise Pre-Assessment (Revised 8/8/2011)

Begin assessment by asking the G1–G3 Addition questions in random order. If student is fluent with these, ask the G1-G3 Subtraction questions in random order. If student is fluent with those, continue process with G4-6, and finally with G7-9. You should stop the assessment when you have found the point at which the student should begin working.

When not apparent, ask student “How did you get that?” (C=counted, FM=fluent memorized, SM=slow memorized, FS=fluent strategy, SS=slow strategy):

G1 G2 G3 G4 G5 G6 G7 G8 G9 1+4 3+5 4+6 10+4 5+7 7+7 2+6 6+9 3+8

2+3 4+5 3+7 8+10 5+9 6+6 3+4 8+9 7+8

5-3 9-5 10-2 16-6 11-6 18-9 9-7 13-4 12-8

5-4 8-3 10-9 19-10 13-5 14-7 9-3 15-9 14-6

Strategy Development

Counting All

Counting On

Early Additive

Adv. Additive

+ = Frequently used - = Seldom used 0 = Never used

Recommended Starting Point for Basic Facts: Recommended for further screening?



FactsWise Pre-Assessment Visuals

Goals 1-4

1 + 4

3 + 5

4 + 6

10+4

2 + 3

4 + 5

3 + 7

8 + 10

5 – 3

9 – 5

10 – 2

16 - 6

5 – 4

8 – 3

10 - 9

19-10

Goals 5 – 9 Part 1

5 + 7

7 + 7

2 + 6

6 + 9

3 + 8

11 - 6

18 - 9

9 - 7

13 - 4

12 - 8



Goals 5 - 9 Part 2

5 + 9

6 + 6

3 + 4

8 + 9

7 + 8

13 - 5

14 - 7

9 - 3

15 - 9

14 - 6



FACTSWISE PRE-ASSESSMENT CLASS CHART

TEACHER: ___________________________________ SCHOOL: ___________________ DATE: ________________

Name Age Lang 1+ 1- 2+ 2- 3+ 3- 4+ 4- 5+ 5- 6+ 6- 7+ 7- 8+ 8- 9+ 9- Rec

I: Inaccurate on 1 or more problems C: Counting on 1 or more problems S: Strategies + memory M: Memorized



Name:____________________________

FactsWise Progress Chart

Goal 1+

Goal 1-

Goal 2+

Goal 2-

Goal 3+

Goal 3-

Goal 1-3 +

Goal 1-3 -

Goal 4+

Goal 4-

Goal 5+

Goal 5-

W – working to learn the facts; inaccurate on one or more problems C – counts to solve one or more problems A – accurately solves all problems using strategies & memorization M – accurately solves all problems from memory



Goal 6+

Goal 6-

Goal 1-6 +

Goal 1-6 -

Goal 7+

Goal 7-

Goal 8+

Goal 8-

Goal 9+

Goal 9-

Goal 1-9 +

Goal 1-9 -

W – working to learn the facts; inaccurate on one or more problems C – counts to solve one or more problems A – accurately solves all problems using strategies & memorization M – accurately solves all problems from memory



WHOLE-CLASS PROGRESS CHART Goal Addition Subtraction

1

2

3

4

5

6

7

8

9



BASIC FACT GOALS Progress Report

____________________/_________

Name Date

Keep working on Goal _____ And/or start on Goal ______


____________________/_________

Name Date


BASIC FACT GOALS

Progress Report

____________________/_________ Name Date



____________________/_________

Name Date


BASIC FACT GOALS

Progress Report

____________________/_________ Name Date



____________________/_________

Name Date




BASIC FACTS WEEKLY PLANNER Week of _________________

Concrete Representational Abstract Monday

Tuesday

Wednesday

Thursday

Friday



BASIC MATH FACTS RUNNING RECORD Student __________________________ ID ____________________ Birthdate _____________ Other __________________________ Grade Addition Subtraction Multiplication Division

K

1

2

3

4

5

6



SECTION 9: PAIRS PRACTICE FOLD-OVERS



SECTION 10: SAMPLE CALENDARS



Goal 1 Pre-Addition -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample) Monday Tuesday Wednesday Thursday Friday Routine (C): How Many in All? 1, 2, 3, 4, 5

Routine (C): How Many in All? 1, 2, 3, 4, 5

Routine (C-C): How Many in All? + Show Me 1, 2, 3, 4, 5 Pairs Practice (C-C): How Many in All? + Show Me

Routine (C-C): How Many in All? + Show Me 1, 2, 3, 4, 5

Pairs Practice (C-C): How Many in All? + Show Me

Routine (C-C): How Many in All? + Show Me 1, 2, 3, 4, 5 Pairs Practice (C-C): How Many in All? + Show Me

How Many in All? Materials: 5 objects that are large enough for the group you are working with (e.g., teddy bears, blocks, shoes, ...) Activity: 1) Scatter some of the objects (varying from 1 of them, 2 of them, ..., up to all 5 of them). 2) Ask the students to help you count them as you move them into an organized row or column. 3) After they have all been counted, ask: "How many are there in all?" (Note - this is important for students who are still developing cardinality.) 4) Repeat with a different number of objects.

How Many in All? + Show Me Materials: 5 objects Activity: 1) Follow the same routine as in the How Many in All? activity. 2) Ask students to show you on their fingers the number they have said there are "in all". (Note - you may need to help students learn how to maneuver their fingers for some of the quantities.) Pairs Practice: How Many in All? + Show Me Materials: 5 objects for each pair of students (e.g., blocks, small plastic teddy bears or dinosaurs, ...) Activity: Have students take turns being Partner A and Partner B. 1) Partner A: Selects some or all of the objects and scatters them on the floor or desk. 2) Partner B: Moves and counts the objects. 3) Partner A asks: "Show me how many in all." 4) Partner B shows the number of blocks using fingers and Partner A confirms by showing fingers as well.

Routine with Pairs Participation (C-C): Get This Many, Please! 0, 1, 2, 3, 4, 5

Routine with Pairs Participation (C-C): Get This Many, Please! 0, 1, 2, 3, 4, 5

Routine (C-R): Five Little Monkeys Ten-Frame (PPT) -- 1, 2, 3, 4, 5 Pairs Practice (C-R): Show Me w/10 Frames 0, 1, 2, 3, 4, 5



Get This Many, Please! Materials: 7 or more objects for each pair of students Activity: 1) Have each pair of students scatter their objects on the floor or desk in front of them. 2) Show a number of fingers from 0 to 5 and say "Get this many, please!" 3) Have students work (silently?) to move the correct number of objects into a row or column. 4) If students are having difficulty, you may need to model with large objects and have them make a 2nd attempt before moving on to the next quantity.

Five Little Monkeys Ten-Frame Materials: A large ten-frame (can be drawn on the board) and 5 monkey images (can be copied -- see below) Activity: 1) Place some monkeys in the ten-frame (be sure to keep all of the monkeys in one column of 5). 2) Ask students to show "How many monkeys in all?" with the fingers on one hand, and then ask them to say the number in chorus. 3) Before you move on to the next quantity, ask one or two students to share how they knew "how many". Pairs Practice: Show Me w/10 Frames Materials: Ten-frame cards placed face down (can be copied from the page later in this document) Activity: 1) Student A: Turns over a 10-frame card and shows it to Student B 2) Student B: Shows the number using fingers 3) Student A: Says the number and confirms Student B is correct. If Student B is correct, he/she gets the card. If not, it goes to the bottom of the deck.



Goal 1 Addition -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample) Monday Tuesday Wednesday Thursday Friday Routine (C-R): Teddy Bear +1 Stories 1+1, 2+1, 3+1, 4+1 Pairs Practice (C-R): Shake It Up +1 Activity

Routine (C-R): Teddy Bear +1 Stories 1+1, 2+1, 3+1, 4+1 Pairs Practice (C-R): Shake It Up +1 Activity

Routine (C): Teddy Bear +2 Stories 1+2, 2+2, 3+2 Pairs Practice (C-R): Shake It Up +2 Activity



Teddy Bear +1 Stories Materials: 5 large objects such as stuffed teddy bears; 100 chart Activity: 1) Tell a short story such as "Two teddy bears were playing outside, and one more bear joined in the fun. Now how many teddy bears are playing?" 2) Ask students to show the story with their fingers while you or student helpers enact it with the teddy bears. 3) Ask students to chorally say the answer, and then write an equation for the story on the board. Help students make connections between the story, the symbols in the equation, their fingers, and also how the story can be shown on a 100 chart. 4) Continue telling +1 stories in the 0+1 to 4+1 range. 5) Ask students to explain their strategies for answering any +1 story.

Teddy Bear +2 Stories - follow same routine as Teddy Bear +1 Stories, now telling +2 stories in the 0+2 to 3+2 range. (Note: If class is very comfortable with these small problems, may want to move to larger quantities, such as 5+2, 6+2, ... Shake It Up +1 Activity (follow same directions for Shake It Up +2 Activity) Materials: one die for every pair of students Activity: 1) Student A: Rolls the die and says the number shown 2) Student B: Says the number shown "plus one makes ____" 3) Student A: Points to the original number on the 100 chart, and then moves to the next larger number to verify Student B's response

Routine (C): All the Ways to Make 4 0+4, 1+3, 2+2, 3+1, 4+0 Pairs Practice (C): All the Ways with Two-Sided Counters

Routine (C-A): All the Ways to Make 4 Patterns 0+4, 1+3, 2+2, 3+1, 4+0 Pairs Practice (C-A): All the Ways Tally Game

Routine (C-A): All the Ways to Make 4 Patterns 0+4, 1+3, 2+2, 3+1, 4+0 Pairs Practice (C-A): All the Ways Tally Game

Routine (C-R): Ten-Frame + One Hand Small sums to 4 Pairs Practice (C-A): All the Ways Tally Game


All the Ways Activity: Have 4 students stand in front of the class on the right side of the room – this represents 4=0+4. Have one student at a time walk to a designated area on the left side of the room. Have the students in the class choral chant 4=1+3, 4=2+2, 4=3+1, 4=4+0. (Note: in order to help students understand the that = means the same value on both sides, it’s important to expose students to the operations on the right as well as the left, and also to equations such as 4=4.) Extension: All the Ways ... Patterns -- As students move in the All the Ways activity, record the equations on the board. Ask students to find and share patterns. Have students copy the equations in the recorded order. If appropriate, see if students can write all of the equations without looking at the board. All the Ways with Two-Sided Counters (need 4 two-sided counters for each pair of students) Student A: Shakes and scatters 4 counters Student B: States the mathematical equation (i.e., "4 equals 1 plus 3") Extension: All the Ways Tally Game -- have students record each equation the first time they roll it, and then have them use tally marks to keep track of how many times each equation is rolled. Have students count up how many times it takes for them to roll all of the possible equations.

Ten-Frame + One Hand Materials: A large ten-frame (can be drawn on the board) and 4 monkey images (can be copied from a page later in this document) Activity: 1) Place some monkeys in the ten-frame (be sure to keep all of the monkeys in one column of 5). 2) Place additional monkeys underneath the ten-frame 3) Ask a student to tell the story (e.g., "Two monkeys were jumping on the bed and one more wants to join in. Now how many will be jumping on the bed?" 4) Ask students to show the story with fingers on one hand and then say the sum chorally.



Monday Tuesday Wednesday Thursday Friday Routine (R-A): Part-Whole Grids Ways to Make 4 Pairs Practice (R-A): Writing equations from part-whole grids

Routine (R-A): Part-Whole Grids Ways to Make 4 Pairs Practice (R-A): Writing equations from part-whole grids

Routine (A): Snap Facts Small Sums to 4 Individual Practice (A): Accordion Practice Small Sums to 4



Part-Whole Grids Activity: 1) Ask students to recall all of the ways to make 4. Then draw part-whole grids for 0/4/4, 1/3/4, and 2/2/4. Have students discuss how these three part-part-whole grids can tell the stories of all of the equations they have recalled. Tell teddy bear stories and emphasize that each grid shows two parts and a whole. 2) Have students chorally recite all of the ways to make 4 while you point out the connections to the part-whole grids. Writing Equations from Part-Whole Grids Materials: One copy of the Ways to Make Four worksheet for each pair Activity: Have students take turns dictating and recording for each of the part-part-whole grids and the related equations.

Snap Facts Say a fact such as “1+3 makes” and then use a hand signal for wait. Give students 2 or 3 seconds to process, and then snap your fingers (or clap your hands), at which time students will choral respond with the answer. Watch carefully for facts where some students are delaying their answers, and repeat those several times before you end the activity. Accordion Practice Have each student fold a paper into half and half again, "hot dog style". Write several Small Sums to 4 problems on the board in vertical format. Be sure to randomize the problems. Have the students copy these on the first row of their paper. They can then work individually as follows: 1) Write the sum for each problem in the second row. When all students are finished, record the answers on the board and have them check and correct their answers on their papers. 2) Now have the students make an accordion fold so the answers in the second row are covered up. Now have the students write their answers again. Have each student check this set of answers with the answers that should be correct from the second row. 3) Repeat. (Note: This type of practice can be extended by having the students fold more rows.)

Routine (C): All the Ways to Make 5 0+5, 1+4, 2+3, 3+2, 4+1, 5+0 Pairs Practice (C): All the Ways with Two-Sided Counters

Routine (C-A): All the Ways to Make 5 Patterns 0+5, 1+4, 2+3, 3+2, 4+1, 5+0 Pairs Practice (C-A): All the Ways Tally Game

Routine (C-A): All the Ways to Make 5 Patterns 0+5, 1+4, 2+3, 3+2, 4+1, 5+0 Pairs Practice (C-A): All the Ways Tally Game



See directions for these routines and activities above See directions for these routines and activities above Routine (R-A): Part-Whole Grids Ways to Make 5 Pairs Practice (R-A): Writing equations from part-whole grids

Routine (R-A): Part-Whole Grids Ways to Make 5 Pairs Practice (R-A): Writing equations from part-whole grids

Routine (A): Snap Facts Small Sums to 5 Individual Practice (A): Accordion Practice Small Sums to 4 Begin Goal 1 assessments

Routine (A): Snap Facts Small Sums to 5 Pairs Practice (A): Pairs Practice Tents: Goal 1 First 2 rows only

Routine (A): Snap Facts Small Sums to 5 Pairs Practice (A): Pairs Practice Tents: Goal 1 First 2 rows only

See directions for these routines and activities above See directions for these routines and activities above

... Continue to work on Goal 1 addition as needed, using these or other routines and practice activities ...



Goal 1 Subtraction -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample) Monday Tuesday Wednesday Thursday Friday Routine (C-R): Teddy Bear -1 Stories 5-1, 4-1, 3-1, 2-1, 1-1 Pairs Practice (C-R): Shake It Up -1 Activity

Routine (C-R): Teddy Bear -1 Stories 5-1, 4-1, 3-1, 2-1, 1-1 Pairs Practice (C-R): Shake It Up -1 Activity

Routine (C): Teddy Bear -2 Stories 5-2, 4-2, 3-2, 2-2 Pairs Practice (C-R): Shake It Up -2 Activity



Teddy Bear -1 Stories Materials: 5 large objects such as stuffed teddy bears; 100 chart Activity: 1) Tell a short story such as "Three teddy bears were playing outside, and one bear had to go home. Now how many teddy bears are playing?" 2) Ask students to show the story with their fingers while you or student helpers enact it with the teddy bears. 3) Ask students to chorally say the answer, and then write an equation for the story on the board. Help students make connections between the story, the symbols in the equation, their fingers, and also how the story can be shown on a 100 chart. 4) Continue telling -1 stories in the 5-1 to 1-1 range. 5) Ask students to explain their strategies for answering any -1 story.

Teddy Bear -2 Stories - follow same routine as Teddy Bear -1 Stories, now telling -2 stories in the 5-2 to 2-2 range. Shake It Up -1 Activity (follow same directions for Shake It Up -2 Activity) Materials: one die for every pair of students Activity: 1) Student A: Rolls the die and says the number shown 2) Student B: Says the number shown "minus one makes ____" 3) Student A: Points to the original number on the 100 chart, and then moves to the previous number to verify Student B's response

Routine (C-R): Ten-Frame + One Hand 3-0, 3-1, 3-2, 3-3 Pairs Practice (C-A): Accordion Practice 3-0, 3-1, 3-2, 3-3



Routine (C-R): Part-Whole Grids 3-0, 3-1, 3-2, 3-3 Pairs Practice (C-A): Accordion Practice 3-0, 3-1, 3-2, 3-3

Routine (C-R): Part-Whole Grids 3-0, 3-1, 3-2, 3-3 Pairs Practice (C-A): Accordion Practice 3-0, 3-1, 3-2, 3-3

Ten-Frame + One Hand Materials: A large ten-frame (can be drawn on the board) and 5 monkey images (can be copied from a page later in this document) Activity: 1) Place some monkeys in the ten-frame (be sure to keep all of the monkeys in one column of 5). 2) Tell a story (e.g., "Three monkeys were jumping on the bed and two fell off the bed. Now how many were jumping on the bed?" 4) Ask students to show the story with fingers on one hand and then say the difference chorally.

Part-Whole Grids Activity: 1) Show students a part-whole grid for 1/2/3 and tell a story such as "One monkey was jumping on the bed and two more joined in. How many were jumping then?" Write the equation 1+2=3. 2) Now tell the reverse story, such as "Three monkeys were jumping on the bed and two had to leave. How many were jumping then?" Write the equation 3-2=1. Make connections between the two equations and the part-whole grid. 3) Ask students to make up other stories that relate to the part-whole grid, both for addition and the related subtraction. 4) Have students recite all of the equations that can be created with the part-whole grid.



Monday Tuesday Wednesday Thursday Friday Routine (C-R): Ten-Frame + One Hand 4-0, 4-1, 4-2, 4-3, 4-4 Pairs Practice (C-A): Accordion Practice 4-0, 4-1, 4-2, 4-3, 4-4

Routine (C-R): Ten-Frame + One Hand 4-0, 4-1, 4-2, 4-3, 4-4 Pairs Practice (C-A): Accordion Practice 4-0, 4-1, 4-2, 4-3, 4-4

Routine (C-R): Ten-Frame + One Hand 4-0, 4-1, 4-2, 4-3, 4-4 Pairs Practice (C-A): Accordion Practice 4-0, 4-1, 4-2, 4-3, 4-4

Routine (C-R): Part-Whole Grids 4-0, 4-1, 4-2, 4-3, 4-4 Pairs Practice (C-A): Accordion Practice 4-0, 4-1, 4-2, 4-3, 4-4

Routine (C-R): Part-Whole Grids 4-0, 4-1, 4-2, 4-3, 4-4 Pairs Practice (C-A): Accordion Practice 4-0, 4-1, 4-2, 4-3, 4-4

See directions for these routines and activities above See directions for these routines and activities above Routine (C-R): Ten-Frame (or 5 Little Monkeys PPT) + One Hand 5-0, 5-1, 5-2, 5-3, 5-4, 5-5

Pairs Practice (C-A): Accordion Practice 5-0, 5-1, 5-2, 5-3, 5-4, 5-5

Routine (C-R): Ten-Frame (or 5 Little Monkeys PPT) + One Hand 5-0, 5-1, 5-2, 5-3, 5-4, 5-5 Pairs Practice (C-A): Accordion Practice 5-0, 5-1, 5-2, 5-3, 5-4, 5-5

Routine (C-R): Ten-Frame (or 5 Little Monkeys PPT) + One Hand 5-0, 5-1, 5-2, 5-3, 5-4, 5-5 Pairs Practice (C-A): Accordion Practice 5-0, 5-1, 5-2, 5-3, 5-4, 5-5

Routine (C-R): Part-Whole Grids 5-0, 5-1, 5-2, 5-3, 5-4, 5-5 Pairs Practice (C-A): Accordion Practice 5-0, 5-1, 5-2, 5-3, 5-4, 5-5

Routine (C-R): Part-Whole Grids 5-0, 5-1, 5-2, 5-3, 5-4, 5-5 Pairs Practice (C-A): Accordion Practice 5-0, 5-1, 5-2, 5-3, 5-4, 5-5

See directions for these routines and activities above See directions for these routines and activities above Routine (A): Snap Facts - Goal 1 + and - Pairs Practice (A): Pairs Practice Tents: Goal 1 Begin Goal 1 assessments

Routine (A): Snap Facts - Goal 1 + and - Pairs Practice (A): Pairs Practice Tents: Goal 1




See directions for these routines and activities above See directions for these routines and activities above

... Continue to work on Goal 1 addition and subtraction as needed, using these or other routines and practice activities ...



Goal 2 Addition -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample)

Monday Tuesday Wednesday Thursday Friday Routine (C): Show Me 6, 7, 8, 9, 10

Routine (C): Show Me 6, 7, 8, 9, 10

Routine (C): Show Me 6, 7, 8, 9, 10 Pairs Practice (C): Show Me 6, 7, 8, 9, 10

Routine (C-C): Abacus/Ten Frame Show Me 6, 7, 8, 9, 10 Pairs Practice (C): Show Me 6, 7, 8, 9, 10

Routine (C-C): Abacus/Ten Frame Show Me 6, 7, 8, 9, 10 Pairs Practice (C): Show Me 6, 7, 8, 9, 10

Show Me Activity: Have students, on two hands, show 6, 7, 8, 9, 10 (be sure students show 6 as 5 and 1, 7 as 5 and 2, 8 as 5 and 3, 9 as 5 and 4). Do this routine for 1 or 2 minutes per day until they are able to do this automatically.

Abacus/Ten Frame Show Me Activity: Have some students show 6, 7, 8, 9, 10 on the abacus or ten-frame drawn on the board while others show on two hands.

Routine (C-C): Abacus Show Me 6, 7, 8, 9, 10 Pairs Practice (C): Show Me 6, 7, 8, 9, 10

Routine (C-C): Snap Cubes + Two-Hands 5+1, 5+2, 5+3, 5+4, 5+5 Pairs Practice (C): Show Me 6, 7, 8, 9, 10

Routine (C-C): Snap Cubes + Two-Hands 5+1, 5+2, 5+3, 5+4, 5+5 Practice (C-C): Snap Cubes (partner 1) and Two-Hands (partner 2) using facts written on poster

Routine (C-C): Snap Cubes + Two-Hands 5+1, 5+2, 5+3, 5+4, 5+5 Practice (C-C): Snap Cubes (partner 1) and Two-Hands (partner 2) using facts written on poster

Routine (C-R): Two-Hands + Ten Frame 5+1, 5+2, 5+3, 5+4, 5+5 Practice (C-R): Ten Frame (partner 1) + Two-Hands (partner 2)

See directions above Snap Cube + Two Hands Materials: Ten snap cubes (5 of one color and 5 of a second color) Activity: Show students the stack of cubes that represents 5+1, 5+2, etc. and have students show the same problem on their hands. Have the students choral chant the sum.

See directions below

Routine (C-R): Two-Hands + Ten Frame 5+1, 5+2, 5+3, 5+4, 5+5 Practice (C-R): Ten Frame (partner 1) + Two-Hands (partner 2) Begin Goal 2 Assessments

Routine (C-R): Two-Hands + Ten Frame 5+1, 5+2, 5+3, 5+4, 5+5 Practice (C-R): Ten Frame (partner 1) + Two-Hands (partner 2)

Routine (C-R): Two-Hands + Part-Whole Grids 5+1, 5+2, 5+3, 5+4, 5+5 Practice (C-C-R): Snap Cubes (partner 1) and Two-Hands (partner 2) using part-whole grids

Routine (C-R): Two-Hands + Part-Whole Grids 5+1, 5+2, 5+3, 5+4, 5+5 Practice (C-C-R): Snap Cubes (partner 1) and Two-Hands (partner 2) using part-whole grids

Routine (C-R): Two-Hands + Part-Whole Grids 5+1, 5+2, 5+3, 5+4, 5+5 Practice (R-A): Pairs Practice Tents -- First 2 Rows Only using part-whole grids for support

Two Hands + Ten Frame Activity: Draw a ten frame on the board and use magnets or draw circles to represent 5+1, 5+2, etc. Have students show the problem on their hands and choral chant the sum.

Two Hands + Part-Whole Grids Activity: Work with students to create the part-whole grids for 5+1 to 5+5. Once made, you can cover the top box and ask students to choral chant the sums.



Monday Tuesday Wednesday Thursday Friday Routine (R-A): Part-Whole Grids + Snap Facts 5+1, 5+2, 5+3, 5+4, 5+5 Practice (R-A): Pairs Practice Tents -- First 2 Rows Only using part-whole grids Goal 2 Assessments cont.

Routine (R-A): Part-Whole Grids + Snap Facts 5+1, 5+2, 5+3, 5+4, 5+5 Practice (A): Pairs Practice Tents -- First 2 Rows Only

Routine (A): Snap Facts 5+1, 5+2, 5+3, 5+4, 5+5 Practice (A): Pairs Practice Tents -- First 2 Rows Only






Goal 2 Subtraction -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample) Monday Tuesday Wednesday Thursday Friday Routine (C-C): Snap Cubes + Two-Hands 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1

Routine (C-C): Snap Cubes + Two-Hands 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1

Routine (C-C): Snap Cubes + Two-Hands 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (C-C): Snap Cubes (partner 1) + Two-Hands (partner 2)

Routine (C-C): Snap Cubes + Two-Hands 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (C-C): Snap Cubes (partner 1) + Two-Hands (partner 2)

Routine (C-R): Ten-Frame + Two-Hands 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (C-R): Ten-Frame (partner 1) + Two-Hands (partner 2)



Routine (C-R-R): Ten-Frame + Two-Hands + Part-Whole Grid 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (C-R): Part-Whole Grid (partner 1) + Two-Hands (partner 2)

Routine (C-R-R): Ten-Frame + Two-Hands + Part-Whole Grid 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (C-R): Part-Whole Grid (partner 1) + Two-Hands (partner 2)

Routine (C-R): Two-Hands + Part-Whole Grid 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (C-R): Part-Whole Grid (partner 1) + Two-Hands (partner 2)

Routine (R): Part-Whole Grid 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (C-R): Part-Whole Grid (partner 1) + Two-Hands (partner 2) Begin Goal 2S Assessments

Routine (R): Part-Whole Grid 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (C-R): Part-Whole Grid (partner 1) + Two-Hands (partner 2)

Routine (R-A): Snap Facts with Part-Whole Grid 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (A): Pairs Practice Tents - All Rows



Routine (R-A): Snap Facts with Part-Whole Grid 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (A): Pairs Practice Tents - All Rows Cont. Goal 2S Assessments

Routine (A): Snap Facts 10-5, 9-5, 9-4, 8-5, 8-3, 7-5, 7-2, 6-5, 6-1 Practice (A): Pairs Practice Tents - All Rows






Goal 3 Addition -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample) Monday Tuesday Wednesday Thursday Friday Routine (C): All the Ways to Make 10 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C): All the Ways with Two-Sided Counters

Routine (C-A): All the Ways to Make 10 Patterns 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C-A): All the Ways Tally Game

Routine (C-A): All the Ways to Make 10 Patterns 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C-A): All the Ways Tally Game

Routine (C): Two Hands Choral 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C-A): All the Ways Tally Game

Routine (C-R): Two Hands Choral 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C-A): All the Ways Tally Game

All the Ways Activity: Have 10 students stand in front of the class on the right side of the room – this represents 10=0+10. Have one student at a time walk to a designated area on the left side of the room. Have the students in the class choral chant 10=1+9, 10=2+8, ..., 10=10+0. (Note: in order to help students understand the that = means the same value on both sides, it’s important to expose students to the operations on the right as well as the left, and also to equations such as 10=10.) Extension: All the Ways ... Patterns -- As students move in the All the Ways activity, record the equations on the board. Ask students to find and share patterns. Have students copy the equations in the recorded order. If appropriate, see if students can write all of the equations without looking at the board.

All the Ways with Two-Sided Counters (need 10 two-sided counters for each pair of students) Student A: Shakes and scatters 10 counters Student B: States the mathematical equation (i.e., "10 equals 1 plus 9") Extension: All the Ways Tally Game -- have students record each equation the first time they roll it, and then have them use tally marks to keep track of how many times each equation is rolled. Have students count up how many times it takes for them to roll all of the possible equations. Two Hands Choral - Activity: Have students use the fingers on their hands to model as they recite all of the ways to make 10 (e.g., 1+9, 2+8, ...)

Routine (C): Snap Cube Student Leaders 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C): Tens Hand Chant

Routine (C): Snap Cube Student Leaders 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C): Tens Hand Chant

Routine (C): Ten Frame Choral 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C): Tens Hand Chant

Routine (C-R): Ten Frame Choral 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C): Tens Hand Chant

Routine (C-R): Ten Frame Choral 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C): Tens Hand Chant

Snap Cube Student Leaderss (need 10 cubes that snap together -- 5 of one color and 5 of a second color) Activity: Have one or more students use snap cubes to model “within 10” addition and subtraction problems and lead students in choral responses such as “10=6 + what?” Tens Hand Chant Activity: Student A shows 1 finger and says "one plus" and then Student B shows 9 fingers and says "nine makes ten". Then Student B shows 2 fingers and says "two plus" and Student A follows by showing 8 fingers and says "eight makes ten." The it's Student B's turn to start the next round, continuing this way until they have gone through all the ways to make 10. (NOTE: The goal here is for students to become very smooth and fluent with these facts.) Ten Frame Choral -- Activity: Show students "within 10" ten-frame cards (with blue and red dots) and have students respond chorally. (NOTE: Ask individual students to share how they are seeing the quantities on the cards.)



Monday Tuesday Wednesday Thursday Friday Small Group Practice (A): Go to the Dump Card Game Begin Assessing Goal 3 +

Routine (A): Snap Facts 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C): Goal 3 + Pairs Practice Tents

Small Group Practice (A): Go to the Dump Card Game

Routine (A): Snap Facts 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1, 10+0 Pairs Practice (C): Goal 3 + Pairs Practice Tents


Go to the Dump Card Game (need a deck of cards for each 4 to 5 students; be sure to take out all of the 10s and face cards; adapted from Math Card Games at www.alabacus.com)

1. This activity is based on the card game Go Fish and is played in groups of 2 to 4. 2. Shuffle and then deal out all the cards to the players. 3. The children look through their cards and make pairs of cards that sum to 10. These pairs are placed front up in front of each child. 4. The children take turns asking one another for a card that they can use to make 10 with a card in their hand. 5. If the child asked has the card they must give it up. If not, the child says “Go to the Dump.” 6. If the turn-taking child makes a pair, he/she places it on the table. His/her turn is over whether or not a pair is made. 7. The aim of the activity is to get the most pairs that sum to 10.


8 2 4 6


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Goal 3 Subtraction -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample) Monday Tuesday Wednesday Thursday Friday Routine (C-C): Snap Cube Subtraction (10-0, 10-1, 10-2, 10-3, ..., 10-10) Pairs Practice (C): Tens Hand Chant Subt.

Routine (C-C): Snap Cube Subtraction (10-0, 10-1, 10-2, 10-3, ..., 10-10) Pairs Practice (C): Tens Hand Chant Subt.


Routine (C-R): Ten-Frame Choral (10-0, 10-1, 10-2, 10-3, 10-4, ..., 10-10) Pairs Practice (C-A): Tens Hand Chant Subt.

Routine (C-R): Ten-Frame Choral (10-0, 10-1, 10-2, 10-3, 10-4, ..., 10-10) Pairs Practice (C-A): Tens Hand Chant Subt.

Snap Cube Student Leaders - Subtraction (need 10 cubes that snap together -- 5 of one color and 5 of a second color) Activity: Have one or more students use snap cubes to model Goal 3 subtraction problems and lead students in choral responses such as “10-6 makes ?” Have the rest of the students model the problems with their hands. Tens Hand Chant - Subtraction -- Activity: Student A shows 1 finger and says "one plus" and then Student B shows 9 fingers and says "nine makes ten". Then Student B shows 2 fingers and says "two plus" and Student A follows by showing 8 fingers and says "eight makes ten." The it's Student B's turn to start the next round, continuing this way until they have gone through all the ways to make 10. (NOTE: The goal here is for students to become very smooth and fluent with these facts.) Ten Frame Choral -- Activity: Show students "within 10" ten-frame cards (with blue and red dots) and ask them to use subtraction to find how many red dots (e.g., 10-3=?). (NOTE: Ask individual students to share how they are seeing the quantities on the cards.)

Routine (C-R): Ten in the Bed (10-0, 10-1, 10-2, 10-3, ..., 10-10) Pairs Practice (C): Ten in the Bed Hand Song

Routine (C-R): Ten in the Bed (10-0, 10-1, 10-2, 10-3, ..., 10-10) Pairs Practice (C): Ten in the Bed Hand Song


Routine (R): Part-Whole Grid Choral (10-0, 10-1, 10-2, 10-3, ..., 10-10) Pairs Practice (C): Ten in the Bed Hand Song

Routine (R): Part-Whole Grid Choral (10-0, 10-1, 10-2, 10-3, ..., 10-10) Pairs Practice (C): Ten in the Bed Hand Song

Ten in the Bed (PPT or ten-frame on board) - see powerpoint for ways to adapt the activity to the board. Ten in the Bed Hand Song - Activity: Have pairs of students sing the modified song "There were ten in the bed and the little one said 'roll over, roll over'. So three rolled over and then fell out. There were seven in the bed and the little one said 'Again!'" While the students are singing, also have them use their hands to model each subtraction situation. Part-Whole Grid Choral – show students part-whole grids for “Within 10” (available on CD -Blackline Masters folder) and have students state both the addition and subtraction relationships while you write them on the board

Routine (A): Snap Facts (10-0, 10-1, 10-2, 10-3, ..., 10-10) Pairs Practice (A): Goal 3 Pairs Practice Tent Begin Assessing Goal 3 -

Routine (A): Snap Facts (10-0, 10-1, 10-2, 10-3, ..., 10-10) Pairs Practice (A): Goal 3 Pairs Practice Tent






Goal 4 Addition -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample) Monday Tuesday Wednesday Thursday Friday Routine (C-C): Abacus Choral (1+10, 2+10, 3+10, ..., 10+10) Pairs Practice (C): With Tens Hand Chant

Routine (C-C): Abacus Choral (1+10, 2+10, 3+10, ..., 10+10) Pairs Practice (C): With Tens Hand Chant

Routine (C-C): Snap Cube Student Leaders (1+10, 2+10, 3+10, ..., 10+10) Pairs Practice (C): With Tens Hand Chant



Abacus Choral – use Slavonic abacus (or applet of Slavonic abacus) to model with 10 problems such as 3+10. Students can work in pairs to show the same problem on their hands. Write each problem on the board so that students can continue to develop the understanding that the 1 in a teen number (such as 13) stands for 1 ten.

With Tens Hand Chant - Subtraction -- Activity: Student A shows 10 fingers and says "ten plus" and then Student B shows 1 finger and says "one makes ten-one". Then both students chorally say "eleven!". Then Student B shows 10 fingers and says "ten plus" and Student A follows by showing 2 fingers and says "two makes ten-two." They then chorally say "twelve!". Continue until 10+10.

Snap Cubes Student Leader -- have one or more students use snap cubes (unifix, multilink, …) to model “with 10s” addition problems and lead students in choral responses such as “10+8 makes?” Each pair of students can model with their hands.

Routine (C-R): Ten-Frame Choral (1+10, 2+10, 3+10, ..., 10+10) Small Group Practice (R-A): With Tens "War" Card Game

Routine (C-R): Ten-Frame Choral (1+10, 2+10, 3+10, ..., 10+10) Small Group Practice (R-A): With Tens "War" Card Game

Routine (C-R): Arrow Cards (1+10, 2+10, 3+10, ..., 10+10) Small Group Practice (R-A): With Tens "War" Card Game



Ten Frame Choral (cards can be found on CD - Blackline Masters folder) – show students “With 10s” ten-frame cards and use choral response, such as “10+7 makes” and “17-10 makes”. Pairs of students can model the problems with their hands.

Arrow Cards - show students a 10 arrow card and any 1-digit arrow card (CD - Blackline Masters folder). Have students respond chorally as you slide the two arrow cards together. Consider having the students respond in two different ways: 1) in “place value order” (e.g., 10+8 makes “ten eight”) and 2) in standard number language (e.g., 10+8 makes eighteen).

Hundred Chart Choral – use the first two rows of a hundreds chart. a) Point to a single-digit number such as 8 and ask students to add 10. Move your finger down to 18.

With Tens "War" Card Game (regular deck of cards with the face cards removed) -- Have students place one 10 face up in the middle of the table. The remaining cards are dealt to the students and they place their stacks face down. Each student turns up a card and says the addition problem and the sum (e.g., 3+10 makes 13). The student who has the largest sum takes all of the turn cards, but leaves the 10 out for the rest of the game.

Small Group Practice (R): Hundred Chart Choral (1+10, 2+10, 3+10, ..., 10+10) Pairs Practice (A): Pairs Practice Tents Begin Goal 4+ Assessments

Small Group Practice (R): Hundred Chart Choral (1+10, 2+10, 3+10, ..., 10+10) Pairs Practice (A): Pairs Practice Tents

Small Group Practice (A): Snap Facts (1+10, 2+10, 3+10, ..., 10+10) Small Group Practice (R-A): With Tens "War" Card Game

Small Group Practice (A): Snap Facts (1+10, 2+10, 3+10, ..., 10+10) Pairs Practice (A): Pairs Practice Tents

Small Group Practice (A): Snap Facts (1+10, 2+10, 3+10, ..., 10+10) Pairs Practice (A): Pairs Practice Tents




Goal 4 Subtraction -- 5-10 Minutes Every Day! -- A Sample Calendar (every class is different, so this is just a sample) Monday Tuesday Wednesday Thursday Friday Routine (C-C): Abacus Choral (11-10, 11-1, 12-10, 12-2, ..., 20-10) Pairs Practice (C): With Tens Hand Chant

Routine (C-C): Abacus Choral (11-10, 11-1, 12-10, 12-2, ..., 20-10) Pairs Practice (C): With Tens Hand Chant

Routine (C-C): Snap Cube Student Leaders (11-10, 11-1, 12-10, 12-2, ...) Pairs Practice (C): With Tens Hand Chant



For these routines and practices, read the suggestions for Goal 4 Addition and then reverse for subtraction.

Routine (C-R): Ten-Frame Choral (11-10, 11-1, 12-10, 12-2, ...) Pairs Practice (C): With Tens Hand Chant

Routine (C-R): Ten-Frame Choral (11-10, 11-1, 12-10, 12-2, ...) Pairs Practice (C): With Tens Hand Chant

Routine (C-R): Arrow Cards (11-10, 11-1, 12-10, 12-2, ...) Pairs Practice (A): Pairs Practice Tents



For these routines and practices, read the suggestions for Goal 4 Addition and then reverse for subtraction.

Routine (R): Hundred Chart Choral (11-10, 11-1, 12-10, 12-2, ...) Pairs Practice (A): Pairs Practice Tents Begin Goal 4- Assessments

Routine (R): Hundred Chart Choral (11-10, 11-1, 12-10, 12-2, ...) Pairs Practice (A): Pairs Practice Tents

Routine (R): Snap Facts (11-10, 11-1, 12-10, 12-2, ...) Pairs Practice (A): Pairs Practice Tents



... Continue to work on Goal 4 subtraction as needed, using these or other routines and practice activities ...



Goal __________________________________________ Monday Tuesday Wednesday Thursday Friday Routine ( ): Practice ( ):

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Section 11: Common Core State Standards related to Addition and Subtraction Facts Fluency Solving Word Problems Part-Whole Thinking

on the way to Memorization Tens-Based Thinking

K Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). Fluently add and subtract within 5.

For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Apply properties of operations as strategies to add and subtract. Examples: If 8+3=11 is known, then 3+8=11 is also known (Commutative property of addition) To add 2+6+4, the second two numbers can be added to make a ten, so 2+6+4=2+10=12 (Associative property of addition) Understand subtraction as an unknown-addend problem. For example, subtract 10-8 by finding the number that makes 10 when added to 8.

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

2 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem.

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.



Common Core State Standards Building on Addition/Subtraction Facts Flexibility & Fluency

Solving Word Problems Part-Whole Thinking on the way to Memorization

Tens-Based Thinking

2 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem.

Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Add up to four two-digit numbers using strategies based on place value and properties of operations. Mentally add 10 or 100 to a give number 100-900, and mentally subtract 10 or 100 from a give number 100-900.

Explain why addition and subtraction strategies work, using place value and the properties of operations.

3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Apply properties of operations as strategies to multiply and divide. Examples: If 6x4=24 is known, then 4x6=24 is also known (Commutative property of multiplication). 3x5x2 can be found by 3x5=15, then 15x2=30 or by 5x2=10, then 3x10-30 (Associative property of multiplication) Knowing that 8x5=40 and 8x2=16, one can find 8x7 as 8x(5+2) =(8x5)+(8x2)=40+16=56 (Distributive property). Understand division as an unknown factor problem. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9x80, 5x60) using strategies based on place value and properties of operations.

4 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, ... Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.



Principles for Teaching Basic Facts (Addition and Subtraction)

1. Focus on accuracy, fluency, and part-whole thinking (encouraging students to move from counting to strategies as well as memorization)

o Focus part-whole strategies on fives & tens, rather than doubles-related strategies

o Avoid tricks, focus on relationships

o Use ten-based models (e.g., ten-frames, slavonic abacus)

2. Teach New Material in small chunks, in a Hierarchical Order

3. Teach subtraction facts just after related addition facts

o Teach two part-whole subtraction strategies: Taking from Ten Breaking to Make a Ten

4. Ongoing whole-class instruction & practice (every 24-48 hours)

o Elaborative Rehearsal

o Immediate Feedback

5. Ongoing one-on-one assessment

o Continuing press to move beyond counting o Avoid timed tests until after student has

"graduated" from Goal 9. The evidence is mounting that timed tests encourage reliance on counting for many students.

6. Systematic homework


adding & subtracting with fluency, flexibility & number … · adding & subtracting...

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