work in progress grade 2 - 1.cdn.edl.io file2nd!grade!mathematics!sequence! 201462015!! trimester!...

Lake Elsinore Unified School District

Instructional Module To Enhance the Teaching of Envision Math – CA Edition

WORK IN PROGRESS

Grade 2

Module 4 Envision Topic 5

Place Value to 100

Revised June 2015

2nd Grade Mathematics Sequence

2014-‐2015

Trimester Module/Topic Envision Lessons Approximate Days

1st Trimester

Understanding Addition and Subtraction

Topic 1 10 days

Addition/Subtraction Strategies Topics 2 and 3 20 days

Working with Equal Groups Topic 4 25 days

2nd Trimester

Place Value to 100 Topic 5 12 days

Addition/Subtraction Strategies with Two-‐

Digit Numbers Topics 8 and 9 35 days

Place Value to 1,000 Topic 10 12 days

3rd Trimester

Three-‐Digit Addition/Subtraction Topic 11 10 days

Geometry Topic 12 10 days

Counting Money Topic 13 10 days

Money Topic 14 10 days

Measuring Length Topic 15 5 days

Time, Graphs and Data Topic 16 5 days

** Topics 6, 7 and 16 (Mental Addition/Subtraction and Time, Graphs and Data) should be embedded into Instructional Routines.

2nd Grade Module 4 at a Glance

Topic: Place Value to 100

Some lessons may take more than one day.

Lesson Number Lesson Focus

4-1 Counting and Grouping Items

4-2 Place Value using Tens and Ones

4-3 Using Symbols to Compare Double Digit Numbers

4-4 Ten More/Ten Less with Hundreds Chart

4-5 Ten More/Ten Less with Hundreds Chart

4-6 Missing Numbers on a Hundreds Chart

4-7 Even and Odd Numbers

Connecting Mathematical Practices and Content Grade 2

Connecting Mathematical Practices and Content – Grade 2

The Standards for Mathematical Practice (MP) are developed throughout each grade and, together with the content standards, prescribe that students experience mathematics as a rigorous, coherent, useful, and logical subject that makes use of their ability to make sense of mathematics. The MP standards represent a picture of what it looks like for students to understand and do mathematics in the classroom and should be integrated into every mathematics lesson for all students. Although the description of the MP standards remains the same at all grades, the way these standards look as students engage with and master new and more advanced mathematical ideas does change. Below are some examples of how the MP standards may be integrated into tasks appropriate for Grade 2 students.

Standards for Mathematical Practice

Explanation and Examples from Mathematics Framework

MP.1. Make sense of problems and persevere in solving them.

In second grade, students realize that doing mathematics involves reasoning about and solving problems. Students explain to themselves the meaning of a problem and look for ways to solve it. They may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They make conjectures about the solution and plan out a problem-solving approach.

MP.2. Reason abstractly and quantitatively.

Younger students recognize that a number represents a specific quantity. They connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities. Students represent situations by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 25 children in the cafeteria, and they are joined by 17 more children. How many students are in the cafeteria? ” Students translate the situation into an equation, such as: 25 + 17 = __ and then solve the problem. Students also contextualize situations during the problem solving process. Teachers might ask, “How do you know” or “What is the relationship of the quantities?” to reinforce students’ reasoning and understanding.

MP.3. Construct viable arguments and critique the reasoning of others.

Second graders may construct arguments using concrete referents, such as objects, pictures, math drawings, and actions. They practice their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” “Explain your thinking,” and “Why is that true?” They not only explain their own thinking, but also listen to others’ explanations. They decide if the explanations make sense and ask appropriate questions. Students critique the strategies and reasoning of their classmates. For example, to solve 74 – 18, students might use a variety of strategies and discuss and critique each other’s reasoning and strategies.

MP.4. Model with mathematics.

In early grades, students experiment with representing problem situations in multiple ways including writing numbers, using words (mathematical language), drawing pictures, using objects, acting out, making a chart or list, creating equations. Students need opportunities to connect the different representations and explain the connections. Students model real-life mathematical situations with an equation and check to make sure that their equation accurately matches the problem context. They use concrete manipulative and/or math drawings to explain the equation. They create an appropriate problem situation from an equation. For example, students create a story problem for the equation 43 + □ = 82 such as “There were 43 gumballs in the machine. Tom poured in some more gumballs. There are 82 gumballs in the machine now. How many did Tom pour in?” Students should be encouraged to answer questions, such as “What math drawing or diagram could you make and label to represent the problem?” or “What are some ways to represent the quantities?”

Connecting Mathematical Practices and Content Grade 2

Connecting Mathematical Practices and Content – Grade 2

MP.5. Use appropriate tools strategically.

In second grade, students consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be better suited than others. For instance, second graders may decide to solve a problem by making a math drawing rather than writing an equation. Students may use tools such as snap cubes, place value (base ten) blocks, hundreds number boards, number lines, rulers, virtual manipulatives, diagrams, and concrete geometric shapes (e.g., pattern blocks, three-dimensional solids). Students understand which tools are the most appropriate to use. For example, while measuring the length of the hallway, students can explain why a yardstick is more appropriate to use than a ruler. Students should be included to answer questions such as, “Why was it helpful to use…?”

MP.6. Attend to precision.

As children begin to develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and when they explain their own reasoning. Students communicate clearly, using grade-level appropriate vocabulary accurately and precise explanations and reasoning to explain their process and solutions. For example, when measuring an object, students carefully line up the tool correctly to get an accurate measurement. During tasks involving number sense, students consider if their answer is reasonable and check their work to ensure the accuracy of solutions.

MP.7. Look for and make use of structure.

Second graders look for patterns and structures in the number system. For example, students notice number patterns within the tens place as they connect counting by 10s to corresponding numbers on a 100s chart. Students see structure in the base-ten number system as they understand that 10 ones equal a ten, and 10 tens equal a hundred. Teachers might ask, “What do you notice when…?” or “How do you know if something is a pattern?” Students adopt mental math strategies based on patterns (making ten, fact families, doubles). They use structure to understand subtraction as an unknown addend problem (e.g., 50 – 33 = __ can be written as 33 + __ = 50 and can be thought of as “How much more do I need to add to 33 to get to 50?”).

MP.8. Look for and express regularity in repeated reasoning.

Second grade students notice repetitive actions in counting and computation (e.g., number patterns to count by tens or hundreds). Students continually check for the reasonableness of their solutions during and after completing a task by asking themselves, “Does this make sense?” Students should be encouraged to answer questions, such as “What is happening in this situation?” or “What predictions or generalizations can this pattern support?”

Instructional Strategies Used in K-7 Instructional Modules

Taken from the CA Mathematics Framework and 5 Practices for Orchestrating

Productive Mathematics Discussions by Peg Smith and Kay Stein

POSE THE PROBLEM

Simply pose the problem, without suggesting or allowing other students to suggest any particular mathematical strategy to solve the problem.

INDEPENDENT Students work independently and quietly, often for the purpose of letting students think about their own reasoning and informal assessment.

THINK-PAIR-SHARE Students get time to think quietly, then share their thoughts with a partner and listen to their partners’ thinking.

TABLE TALK THINK-PAIR-SHARE with more than 2 students.

WHOLE GROUP Focus is on pulling the whole class together.

CONSENSUS Students share their individual ideas and come to an agreement within the group to share with the whole class.

MONITOR

Teacher pays close attention to students’ mathematical thinking and solution strategies as they work on a task, for the purpose of using their observations to decide what and whom to focus on during the class discussion that follows.

SELECT The teacher, through monitoring, selects student work samples or strategies to display or have students present.

SEQUENCE

The teacher purposefully chooses the order in which student strategies are displayed and/or discussed, often beginning with the more concrete strategies moving to more abstract.

CONNECT

The teacher helps students draw connections between their solutions/strategies and others’ solutions/strategies for the purpose of connecting their thinking to the mathematics we want them to learn

DISPLAY The teacher shows student work to the rest of the class for the purpose of allowing students to analyze the students’ strategies.

CAROUSEL-MUSEUM WALK

Each group posts sample work on the wall while students rotate around the room to analyze other students’ work. A leader from each group may, but does not need to stand near his/her own group’s work.

Hundreds Chart With Missing Numbers

115

2 7

4433

19

372621

1130

80

60

73

91 100

6851

89

Fill in the missing numbers.

Name: __________________________________ Date: ______________________

Leap 3 tens

Leap 2 tens

Leap 2 tens

Leap 2 tens

Leap 2 tens

Leap 2 tens

Leap 1 ten

Leap 1 ten

Leap 1 ten

Grade 2 Module 4, Lesson 1

Lesson Focus Models for tens and ones up to 100 PLC Notes

Lesson Purpose

Develop concept of groups of tens with ones left over to determine the total number of items in the collection. Also, understanding that ten tens is called a “hundred”.

Content Standards

2 NBT.1.a 100 can be thought of as a bundle of ten tens-called a “hundred” 2 NBT a. Base –ten numerals in standard form (e.g., 6 hundreds, 3 tens, and 7 ones)

Practice Standards

☒ Make sense of problems and persevere in solving them. ☒ Reason abstractly and quantitatively. ☒ Construct viable arguments and critique the reasoning of others. ☒ Model with mathematics.

☒ Use appropriate tools strategically. ☒ Attend to precision. ☒ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials

Countable items: Beans, linking cubes,

shoes in classroom,

crayons etc.

Find a collection of things that children might be interested in counting. The quantity should be countable, somewhere between 25 and 100. Do not use manipulatives that are already in groups of ten such as base ten blocks. POSE THE PROBLEM: What strategy could we use to count our collection of items?

Investigate

Materials

Countable

items: Beans, linking cubes,

shoes in classroom,

crayons etc.

Optional IPAD Tools

Explain

Everything App:

Square Tiles

INDEPENDENT/MONITOR- Allow students to work independently and quietly, for the purpose of letting students think about their own reasoning. As students work, teacher observes students’ methods of counting and selects 3 -4 students to demonstrate. It is acceptable if the students count by ones as the purpose of the lesson is for students to discover that counting by 10s is a more efficient way to count. THINK-PAIR-SHARE/SELECT- Selected students take turns demonstrating how they counted their collection of items. Try to start the discussion with a student who has counted by ones. Ask another student to explain how the first student is counting. The following are some questions to facilitate the discussion.

• What do you notice is happening in this strategy? (counting each item, counting by ______.)

• What does each counting number represent in this strategy? (counting by ______.)

• Why do you think he/she circled/put that over here? • Do you agree or disagree with this strategy? Why or why not? • How is this strategy like the one that we just saw? • How is this strategy different from the one we just saw?

Investigate

Materials

Countable items: Beans, linking cubes,

shoes in classroom,

crayons etc.

POSE THE PROBLEM: Now, can you find a different way to count the items? We are trying to find a strategy that makes counting the objects easier and faster? INDEPENDENT/MONITOR- Allow students to work independently and quietly, for the purpose of letting students think about an easier way to count the items. The teacher will look for students who have grouped items for counting. Look for students who have grouped the items into unequal groups. This will provide an opportunity for students to discover that grouping into equal groups makes counting easier. Also look for students who have grouped by 2s, 3s, 5s, and 10s. Select students to show several different strategies for counting the items. WHOLE GROUP Teacher pulls the whole class together to discuss the grouping displayed and how to use skip counting and counting on to find the total amount in the collection. Have selected students bring the display to the elmo one at a time to show how they counted the collection of objects. Do not have the selected student explain the thinking. Other students should be preparing to explain the thinking. THINK-PAIR-SHARE Students get time to think quietly about what is displayed then share their thoughts with a partner about how each collection of items are grouped and counted. WHOLE GROUP Other students will explain the thinking of the selected student. Use the following questions to facilitate a discussion of the different counting strategies.

• What do you notice is happening in this strategy? (counting groups of items, counting by ______.)

• What does each counting number represent in this strategy? (counting by ______.)

• Why do you think he/she circled/put that over here? • Do you agree or disagree that this strategy is fast and easy for

counting the objects? Why or why not? • How is this strategy like the one that we just saw? • How is this strategy different from the one we just saw? • Which strategy do you think is faster and easier for counting the

objects? Why? * Misconceptions:

• Students believe that they can make unequal groups when making sets.

• Students may not separate groups when collection is displayed.

• Students may count all groups by ten even when they do not contain ten ones.

Optional Practice

* For students that initially group by tens (advanced) pose the following questions as extensions focusing on the idea that ten tens is called a “hundred”. POSE THE PROBLEM: Would you also group by tens if you had 154 items? Can we make new groups from the groups of ten? *TE122, enVision, Topic Opener Game Bridge to Lesson 2 Create a large place value board on the floor (using butcher paper, masking tape, or you could even draw it on the sidewalk with chalk and play the game outside). Make sure that the area that you create has a column for both the ones and tens that can hold at least 9 students (or objects) comfortably in each. Also draw a smaller place value chart with tens and ones on a whiteboard to use for recording the number of students standing. POSE THE PROBLEM How can we use the “counting on by tens” strategy to count the students (or objects) in our classroom? We will be using a place value mat to help us organize the students so we can count them. What do you notice about the place value chart that is on the floor? [There are two columns. There is a place for ones and a place for tens.] With a large die, or a deck of cards with the numbers 1 – 9, roll/draw a number. Ask the class for volunteers and have that many students stand on the place value mat. Use the smaller place value mat to record the number students standing. Select students to talk about the number of students standing on the place value mat. Ideally, students should verbalize that there are ____ tens and ____ ones. Point out that there are no students in the tens column now. Roll/draw another number. Ask for more volunteers and add that many more students to the ones area. The area might be getting a little more crowded now. Students should realize to move a group of 10 students to the “tens column.” Continue with the game by rolling the die/drawing cards until all the students are standing on the board. Have students explain to a partner what is happening and why groups are moving. *Encourage them to use the terms place and value as they are explaining the answers to the questions!

Summarize

34T

WHOLE GROUP After discussing and displaying several methods, have a class discussion of what worked well and what did not emphasizing that grouping by tens is an efficient method of counting. THINK PAIR SHARE- Would you also group by tens if you had 100? Monitor and listen for students that you’ll want to share out. If grouped by tens, how many tens would that be? Students make connections to the idea that ten tens is called a “hundred”.

Homework enVisionMath Common Core Interactive Homework Workbook, Reteaching 5-1 and Practice 5-1

Tens Ones

Tens Ones

Place Value Mat

Copyright © 2014 Pearson Education, Inc. All rights reserved.

BLM 15 Place-Value Mat (with Double Ten-Frames)

ON

ES

TE

NS


Lesson Focus Models for tens and ones up to 100 PLC Notes

Lesson Purpose

Arranging countable items into groups of tens with ones left over to determine the total number of items in the collection. Also, understanding that ten tens is called a “hundred”.

Content Standards

2 NBT.1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

a. 100 can be thought of as a bundle of ten tens-called a “hundred”

2 NBT 3. Read and write numbers to 1000 (100) using base-ten numerals, number names, and expanded form.

Practice Standards


☒ Use appropriate tools strategically. ☒ Attend to precision. ☒ Look for and make use of structure. ☒ Look for and express regularity in repeated reasoning.

Introduce

Materials

Optional IPAD Tools

Explain

Everything App:

Square Tiles

Set up bags of different types of objects such as toothpicks, buttons, beans, counters, linking cubes, popsicle sticks or other countable items. Make one of the bags with 99 items inside. Place the bags at stations around the room. Provide students with ways to make groups of ten such as ten frames, small cups, or rubber bands. Also provide a small whiteboard for the group to make a place value mat. POSE THE PROBLEM Work with your group to count how many items are inside each bag?

Investigate

Materials

12 - Items to use for making

groups of 10 such as ten

frames, small paper cups,

rubber bands.

Small Whiteboard

and a dry erase marker

INDEPENDENT Before the group starts to count, each student will get a small piece of paper and write down an estimate of how many items are in the bag. TABLE TALK Students are given about 5-7 minutes to count the items. They will work in a table groups to make groups of ten for the purpose of counting the items in the bag. The table group will record the total number of items using the place value mat on the small whiteboard. As they work, students should use base ten language to describe the number of items in the bag. (ie: There are 3 tens and 8 ones in the bag.) Students should also use standard language to talk about the number of items in the bag. (ie: There are 38 beans in the bag.) Have groups return all the items to the bag and rotate to the next table. Begin the process of counting and grouping the items at the new table. Repeat the process until students return to the original table.

Materials Cont.

Plastic Bags

Countable

items: such as beans, linking cubes, straws,

counters crayons etc

4 small pieces of paper per student to

record estimates.

Pencils

MONITOR/SELECT As the students are working during the last rotation, the teacher will pay close attention to students’ mathematical thinking for the purpose of deciding what and whom to focus on during class discussion. At the end of the rotation, choose groups to share their displays one at a time on the elmo. Students to explain the thinking and decide how many items were in the bag. Ask students to vote if they agree or disagree. Choose 2 -3 students to explain why they agree or disagree. Encourage the students to use both standard and base ten language when giving the explanation. Note: For the final discussion, choose the group that has the bag with 99 items. Discuss in the same way that you have done with the previous bags, but at the end, ask the students: THINK-PAIR-SHARE How would the display change if we added one more item to the bag? Allow students to discover that the tens column would have ten groups of ten. Guide the students to discover that ten groups of ten is the same as 100. Allow them to discover that they need to add the hundreds place to the place value chart to show 100.

Optional Practice

Repeat the Optional practice Activity from Lesson 4.1 using the floor sized place value chart with students working together to count the total number of fingers for all the students. This will allow students to count groups of ten, practice making higher numbers, and regrouping 10 groups of ten to make 100. You can also have each student hold groups of items to count as they stand on the place value mat.

Summarize

34T

Math Journal- Students write a math journal entry that explains how grouping items can help them to count 38 items. Look for journal entries that can be used for discussion to reflect upon these main ideas.

• Making groups of 10 makes counting easier because we can count by 10s.

• 38 has 3 groups of ten and 8 ones. • Three groups of 10 is the same as 30 items. • We can count the groups of 10 by skip counting by tens. We

can count on by 1s to find 38. • Eight ones is not enough to make a group of ten.

Homework enVisionMath Common Core TE, Lesson 5-1, page 126, Problem Solving and Journal enVisionMath Common Core TE, Lesson 5-1, page 124, Problem Guided Practice


Lesson Focus Using symbols to compare numbers. PLC Notes

Lesson Purpose Using place value to compare and order two-digit numbers using symbols

Content Standards

2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Practice Standards


☒ Use appropriate tools strategically. ☒ Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials

Give each child a set of number cards from 0-9, and a set of symbol cards (>, <, =). Ask each student to select two number cards and create a double digit number. Have each student use base ten model blocks to display their number using tens and ones. Students will work in pairs to compare both double digit numbers.

Investigate

Materials

Number Cards (0-9), Symbol Cards (<, >, =)

Vocabulary >(greater than) <(less than) =(equal) Digit Compare Base Ten Blocks

Optional IPAD Tools

Explain

Everything App: Base Ten Blocks

POSE THE PROBLEM/ THINK-PAIR-SHARE – Students get time to think quietly about which number is the greater number between their partner’s double digit number and their double digit number. Then, students prove their thinking to their partner about how they know which of their double digit numbers is greater. MONITOR/SELECT As students work, the teacher listens to student reasoning and selects 3 – 4 students to display their double digit numbers and comparing sign (>, <, =). Other students will explain the thinking. Ex: [34 > 24] WHOLE GROUP – Students share their thinking and strategies.

• How did you decide in which order to place the cards?

• What would happen if you changed the order of the cards?

• How did you decide which player had the greater number?

• How did you decide which player had the lesser number?

• When you compared these two digit numbers, which place value did you compare first? Why? [If students say to compare the ones first, then ask them if this strategy works when comparing 42 and 29.]

• What if you compare the numbers 64 and 64, what could you

say about those two numbers? [they are equal]

• How would you compare the numbers 78 and 73? [First compare the tens to see they are equal. Then compare the ones.

• Could we use a number line to help compare numbers? How?

• Could we use a hundreds chart to help compare numbers? How?

*Misconceptions:

• Students believe that there must be a (+) or (–) sign inside of the circle.

• Students do not understand that the place value position of the digits affects the value of the number. They may think that 64 and 46 are equal since they both have the digits 6 and 4.

• Students do not understand the concept of the equal sign.

Optional Practice

• Envision. Ready-Made Centers for Differentiated Instruction. Center Activity 5-3.

• Use pattern block shapes to represent numbers. Have

students compare groups of patterns blocks to find if they are less than, equal to, or greater than the other group. Example: Note that the circle is where the symbol is inserted.

= 6 = 2 = 9 Compare +

• Prepare a plastic bag with 2 different pattern block shapes. Create a bar graph to compare the two pattern block shapes such as 12 triangles and 21 squares. Point out that the bar representing the 12 triangles is shorter than the bar representing the 21 squares. Students will write a number sentence using symbols to show that 21 is greater than 12. Use the graph to find how much greater.

• Students play a matching game to compare two double digit numbers using the “greater than”, “less than”, and “equal to” symbols. Place a stack of double digit cards face down and have the symbol cards available for the players to choose. Player A and B draw a card from double digit stack and place them face up. Player A chooses a symbol card to correctly compare the two double digit numbers. Then, justifies their thinking to Player B. Player B must agree or disagree. If Player B disagrees, they explain why and fix the number sentence. The student who makes the true number

sentence, gets to keep the equation and sets it aside. The process begins again with Player B. At the end of the game, the player with the most equations wins.

Summarize

Symbol Cards

WHOLE GROUP – Teacher displays the following two double digit numbers. Students hold up the correct symbol card in order to compare the two digit numbers. Students explain their reasoning.

• 90 19

• 27 72

• 33 33

• 46 60

• 23 15

Homework enVisionMath Common Core TE, Lesson 5-3, page 134, Problem Solving and Journal enVisionMath Common Core TE, Lesson 5-3, pages 132 and 133, Guided Practice and Independent Practice

< less than

< less than

< less than

< less than

< less than

< less than

> greater than

> greater than

> greater than

> greater than

> greater than

> greater than

= equal to

= equal to

= equal to

0 1 2 3

0 1 2 3

4 5 6 7

4 5 6 7

8 9 8 9

27 10 12

12 92 72

43 56 98

17 5 29

61 75 61

10 9 20

46 57 13

88 92 53

70 35 28

92 3 23


Lesson Focus 10 More/10 Less, Counting to 100(Before/After) PLC Notes

Lesson Purpose

The place value number system makes it easy to name the number that is 10 more or 10 less than any other given number by simply adjusting the digit in the tens place. The position words before and after are used to explain and understand number relationships.

Content Standards

2.NBT.2 Count within 1000; skip-count by 5’s, 10’s and 100’s. 2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Practice Standards



Introduce Materials

Hundreds

Chart

Yellow Crayon

Optional IPAD Tools

Explain

Everything App:

120 Chart

Pass out a hundreds chart and crayons to each student. Today we will be using a hundreds chart to help us think about adding 10 more and subtracting 10 less. We will look for patterns on the hundreds chart to help us predict 10 more or 10 less. We will also be using the hundreds chart to think about other addition and subtraction problems. POSE THE PROBLEM – On Monday, Jake starts reading on page 29 in his book. He reads 10 more pages. What page will Jake be on when he stops reading? In our problem, on what page does Jake start reading? We can use the hundreds chart to model this problem. Where would you start on the hundreds chart? [29] Put your finger on number 29 and color it yellow. Using the hundreds chart, how can we find the number that is 10 more than 29?

Investigate

THINK-PAIR-SHARE – Students get time to think quietly, then, share their thoughts with a partner and listen to their partner’s thoughts. WHOLE GROUP – Ask for volunteers to share out the ways that they found the number that is ten more than 29. [counted ten more boxes on the hundreds chart]

Investigate

Vocabulary

Before After

Compare

Color in number 39. Look at the hundreds chart. We see that 39 comes after 29 when we are counting on the hundreds chart. If we are counting by ones, we would need to count 10 more boxes to get to 39. How can we use words to compare 39 and 29? What equation can we write to show that 39 is ten more than 29? [29 + 10 = 39 or 39 = 29 + 10] We can also say that 29 is 10 less than 39. We see that 29 comes before 39 when we are counting on the hundreds chart. How can we use words to compare 29 and 39 . We can say that 29 is 10 less than 39. What equation can we write to show that 29 is ten less than 39? [39 - 10 = 29 or 29 = 39 - 10] Now, put your finger on 39. On Tuesday, Jake starts reading on page 39 and reads 10 more pages. On what page will Jake stop reading? [49] Color 49 yellow on the hundreds chart. THINK-PAIR-SHARE – Students get time to think quietly, then, share their thoughts with a partner and listen to their partner’s thoughts. Select students to display the hundreds chart on the elmo and use their finger to trace the path they took to find ten more. Have other students explain the thinking and decided if they agree or disagree. Ask them to explain why they agree or disagree. What number did you find that is 10 more than 39? [49] Color 49 yellow on the hundreds chart. What number sentence can we write to show that 49 is ten more than 39? [39 + 10 = 49 or 49 = 39 + 10] What if Jake reads 10 more pages? Predict what number we would be on if we added ten more to 49? Color yellow the number that is ten more than 49. [59] MONITOR/SELECT The teacher observes student thinking and selects students to demonstrate their path on the elmo. Try to select a student (student A) who has counted by ones to reach number 59. Also select a student (student B) who has discovered that moving one box down the column will show 10 more. Have student A demonstrate first. Then ask: Did anyone get to number 59 in a different way? [down one] Explain how student A had to count 10 boxes and you only went down one box? [going down one is the same as counting 10 more boxes] Continue to have the students add 10 more until they reach 99. WHOLE GROUP – Compare the numbers in yellow. Do you see any patterns with the numbers that are colored in yellow? What is the same about the numbers in this column? What is different about the numbers in this column?

Note: Students should recognize that the ones place remains the same and the 10’s place increases by one group of ten as they move down the column. Students should realize that moving down a column is the same as adding ten more. How do you think I would use the hundreds chart to find the number that is 10 less than 29? [19] THINK-PAIR-SHARE – Students get time to think quietly, then, share their thoughts with a partner and listen to their partner’s thoughts. MONITOR/SELECT The teacher observes student thinking and selects students to demonstrate their path on the elmo. Try to select a student who has continued to add 10 more to arrive at 39. Have the student trace the path on the elmo. Have other students explain the thinking and decided if they agree or disagree. Ask them to explain why they agree or disagree. THINK-PAIR-SHARE What pattern do we see when we move down the column on this hundreds chart? [We are counting 10 more.] What pattern do we see when we move up the column on this hundreds chart? [We are counting 10 less.] Now, let's look for a pattern when we move to the right on a row. Place your finger on number 41. Move your finger across the row to the right. Compare the numbers as you move across the row.

• What is the same about the numbers? [The tens digit is the same until the end.]

• What is different about the numbers in this row? [The ones digit is increasing.]

• How do the numbers change as you move across the row to the right? [We are counting one more. The numbers are getting bigger, It is like we are counting by 1s]

• Why do you think that the number at the end of the row is different from the other numbers in the row? [ When we have 9 ones and add one more, we can make a new group of ten]

THINK-PAIR-SHARE What patterns do you see if your finger moves backward or to the left on this row? [We are counting one less. The numbers decrease. We are counting backward by 1s] Now put your finger on 41 again. Use your hundreds chart to find the number that is one more than 41. How did your finger move on the chart? THINK-PAIR-SHARE – Students get time to think quietly, then, share their thoughts with a partner and listen to their partner’s thoughts.

WHOLE GROUP – Ask for volunteers to share out what they did to arrive at that number that is one more than 41 [ moved to the right one box on the row.] We can say that 42 is after 41 or 42 is one more than 41. What number sentence can we write to show that 42 is one more than 41? [41 + 1 = 42 or 42 = 41 + 1 ] THINK-PAIR-SHARE How can I use the hundreds chart to find the number that is one less than 45? [Put my finger on 45 and move to the left on the row one box. What number is one less than 45?

Optional Practice

Simon Says- Students practice finding one more/one less and ten more/ten less by playing a game of "Simon Says". The teacher chooses a number for a starting point on the hundreds chart. The teacher give 3 directions to the students using one more/less and 10 more/less and the students move their finger to arrive at the final destination. Students must then guess the secret number. ie: Place your finger on number 24. Now move your finger to the number that is ten more than 24. [34] Next move your finger to the number that is one more. [35] Last move your finger to the number that is ten less. What number is your finger touching? [25]

• As student become comfortable with finding one more/one less and ten more/ten less using the hundreds chart, begin to ask them to move in multiples of ten (30 more/less) or multiples of one. (3 more/less) Make sure to give instructions that require students to add or subtract across rows. ie Put your finger on 42. Now find the number that is 3 less than 42. Students must know to move backward to the end of the row and return to the right side of the row above.

• Students use calculators to enter a double digit number. They then predict what ten more than that number would be. They can check by adding ten on the calculator. Have them continue to predict and check ten more so they can realize the pattern. This also works for ten less, one more, and one less.

• Use the hundreds chart inside of a page protector. Assign a starting point and an ending point for the students to circle with a dry erase marker. (start at 58 and end at 65) Students must trace a path with their marker and use ten more/less and one more/less words to the path from the starting point to the ending point. ie: ten more than 58 is 68. Three less than 68 is 65. Have students show other possible paths to get to the ending point.

• enVision Math Common Core, Ready-Made Centers for

Differentiated Instruction, Listen and Learn, Center Activity 5-5 (One - attached).

Summarize: WHOLE GROUP – What patterns have you noticed while working with the Hundreds Chart? What is happening to the numbers when I move my finger across a row? [The ones digit increases. The numbers are getting bigger by 1 more.] What happens when I get to the end of the row? [I move down to the next column and begin on the right side to keep counting one more.] What happens to the numbers if I move backward on a row? [The ones digit decreases. The numbers are getting smaller by 1 less.] What happens to the number if I move down a column? [The tens digit increases. The numbers are getting bigger by 10 more.] What happens to the number if I move up a column? [The tens digit decreases? The numbers are getting smaller by 10 more.] THINK-PAIR-SHARE – Students get time to think quietly, then, share their thoughts about each question with a partner. They also listen to their partner’s thoughts. Note: [Help students should recall the following patterns:]

• The number that is 1 more is 1 box to its right • The number that is 1 less is more 1 box down • The number that is 10 more is 1 box down • The number that is 10 less is 1 box up • When adding 10 more/10 less, the tens number

increases/decreases by 1 group of 10 and the ones number stays the same

• When adding 1 more/1 less, the ones number increases/decreases by 1 and the tens number stays the same

Homework enVisionMath Common Core TE, Lesson 5-4, pages 136 & 137, Guided Practice and Independent Practice enVisionMath Common Core TE, Lesson 5-5, pages 142 Problem Solving and Journal

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Grade 2 Module4, Lesson 5

Lesson Focus Ten more or Ten Less, Counting to 100 (one before/one after) PLC Notes

Lesson Purpose

Students will identify and write numbers that are 10 more and 10 less than given numbers. Students will also identify and write numbers that are 1 before and 1 after given numbers. They will also count on and count back to identify missing numbers to 100.

Content Standards

2. NBT.2 Count within 1,000; skip-count by 5’s, 10’s and 100’s. 2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations and/ or the relationship between addition and subtraction.

Practice Standards


☒ Use appropriate tools strategically. ☐ Attend to precision. ☐ Look for and make use of structure. ☐ Look for and express regularity in repeated reasoning.

Introduce

Materials

Bubble Hundreds

Chart, pencil

Optional IPAD Tools

Explain

Everything App:

Blank Hundreds

Chart

Pass out Bubble Hundreds Chart and 2 blank pieces of paper to each student.

Using one piece of paper horizontally, cover up all but two rows, How many tens are shown? [Two tens, called twenty.] Students write the number 20 in the correct bubble. Can you show me 40? What did you have to do to get to forty? CONSENSUS- Students share their individual ideas and come to an agreement within the table group to share with the whole class. [Students cover up all but 4 rows and notice they slide down to add 2 more groups of ten ] Students write the number 40 in the correct bubble.

Ask students to use the second piece of paper horizontally over the first one. Can you show me 53? What did you have to do to get 53? CONSENSUS- Students share their individual ideas and come to an agreement within the table group to share with the whole class. [Students cover up all but 6 rows then slide the second piece of paper over counting by ones to expose 3 showing 53] Students write the number 53 in the correct bubble. What is ten more than 53? Write the number in the bubble. [63] THINK-PAIR-SHARE Students get time to think quietly, then share their thoughts with a partner explaining how they figured it out. What is one more than 63? What direction did we move? [64, right] - Write the number in the correct bubble.

One less than 63? What direction did we move? [62, left] - Write the number in the correct bubble.

What is ten more than 63? - Write the number in the correct bubble.

* Misconceptions- Students may not understand that they have to expose another row of ten in order to have ones. They may only expose the number in the tens place. 5 Students must understand that 53 is more 50. Using the Bubble Hundreds Chart and 2 pieces of paper POSE THE PROBLEM- Daniel is 20 years older than his cousin Susie. Susie is 46. How old is Daniel? How would we use our Bubble Hundreds Chart as a tool to solve this word problem? Explain your thinking and write a number sentence. THINK-PAIR-SHARE- Students get time to think quietly about what they would do to solve the problem, then, share their thoughts with their partner and listen to their partners’ thinking. INDEPENDENT- Students work independently and quietly to solve the problem.

Optional Practice

enVision Math Common Core, Ready-made Centers for differentiated Instruction, Listen and Learn Center Activity 5-5 (Two -attached)

Summarize

34T

MONITOR, SELECT, SEQUENCE While students are working select 2 or 3 examples of student work that displays correct and incorrect ways of solving the problem above. Display each and have students THINK-PAIR-SHARE about what is being displayed. MONITOR while students are talking and select students to share out about what they think the student did to solve the problem. (If there is a wide spread common misconception let it come out) [Students start at 46 and move down two entire rows moving both pages.]

Homework Materials

Bubble

Hundreds Chart

See attached Bubble Hundreds Chart and paper to solve word problems.

Name ________________________ Date _____________

Module 4 Lesson 5 Homework Use the Bubble Hundreds Chart and 2 blank pieces of paper to solve the following word problems.

1. Some children were lining up for lunch. 10 children left and then there were 66 children still waiting in line. How many children were there before? Write the number sentence and Explain.

2. Johnny loves playing video games. He scored 42 points on level 1. In order for him to reach Level 2 he needs 62 points. How many more points does he need? Write the number sentence and Explain.


Lesson Focus Students will identify and write numbers that are 10 more and 10 less

than given numbers. Students will also identify and write numbers that are one before and one after given numbers. They will also count on and count back to identify missing numbers to 100.

PLC Notes

Lesson Purpose

Recognizing and using patterns on the hundreds chart to add and subtract 10 more/less and 1 more/less.

Content Standards

2.NBT.2 Count within 1000; skip-count by 5’s, 10’s, and 100’s. 2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Practice Standards

☒ Make sense of problems and persevere in solving them. ☒ Reason abstractly and quantitatively. ☒ Construct viable arguments and critique the reasoning of others. ☐ Model with mathematics.


Introduce

Materials

Hundreds Chart used in

Module 5 Lesson 3

Partial

Number Grid

Pencil

Optional Materials:

Place Value

Blocks

Optional IPAD Tools

Explain

Everything App:

120 Chart

Have students refer to the Hundreds Chart used in Module 5 Lesson 3. We have learned that there are patterns on the hundreds chart that can help us when we are adding and subtracting. Use your hundreds chart to explain to your partner a hundreds chart pattern that can help you add or subtract? [students should recall the following patterns:]

• The number that is 1 more is 1 box to its right • The number that is 1 less is 1 box to its left • The number that is 10 more is 1 box down • The number that is 10 less is 1 box up • When adding 10 more/10 less, the tens number

increases/decreases by 1 group of 10 and the ones number stays the same

• When adding 1 more/1 less, the ones number increases/decreases by 1 and the tens number stays the same

THINK-PAIR-SHARE: Students are given time to recall hundred chart patterns and explain using the hundreds chart to find 10 more/less and 1 more/less. WHOLE GROUP: The teacher will select students to remind the class of hundred-chart patterns learned in module 5 lesson 3.

Investigate

Vocabulary

Partial Horizontal

Vertical Increase Decrease

Above Below

POSE THE PROBLEM: How can we use these patterns to help determine the value of missing numbers on a partial hundreds chart? Students must put away the hundreds chart. Next, pass out the partial number grid page. Explain to the students that the grid sections are a part (explain the term partial) of the hundreds chart, but some of the numbers are missing. Challenge students to be detectives using the clues given to find the missing numbers in the first grid. INDEPENDENT: Students are given time work independently to complete the blank boxes in the grid #1. TABLE TALK: Students compare their answers and explain the strategy they used for determining the remaining numbers. If answers are different, students must reach consensus about which answer is correct and justify the choice. WHOLE GROUP: Teacher pulls the whole class together to discuss the thinking in determining what number should go into the blank boxes. [Possible responses include: The box to the right will be one more.” The ones number increases. The box below is ten more. The tens number increases.] Repeat the activity for the grid #2. [Student responses should also include a discussion of the box “before” or “to the left” being one less. The ones number is decreasing. The box above is ten less. The tens number is decreasing.] Misconceptions: Student may not understand that the partial number grid will not start with the digit 1.

Optional Practice

• enVision Math Common Core, Ready Made Centers for Differentiated Instruction, Center Activity 5-4(one )

• enVision Math Common Core, Teacher’s Resource Masters, Numbers and Operations in Base Ten, Enrichment 5-4 (attached)

• Challenge: enVision Math Common Core, Teacher’s Resource Masters, Numbers and Operations in Base Ten, Enrichment 5-5 (attached)

Summarize

34T

Students will again refer to the hundreds chart from Module 5 Lesson 3. Today we have learned that we can find a missing number on the hundreds chart by thinking about patterns for one more, one less, ten more, and ten less. Now we will use those patterns to be a detective and play an “I Spy” game. Teacher models how to play by giving the first clue. First, I will be the detective, and I will give you a clue to help you to find the “I Spy number”. Here is your clue. I spy a number that is ten more than 27. Choose students to explain how they found the “I Spy number.” Next, allow a student to be the detective and give a clue to the class. Students should be able to use the lesson vocabulary to give clues as well as explain answers.

Homework Partial Number Grid homework

Module 4 Lesson 6

Partial Number Grid

12 36 42

82 50 63

73 5 19

21 77 17

81 52 39

Name _______________________ Date _____________

Module 4 Lesson 6 Homework

Complete the partial hundreds charts by filling in the missing numbers. Think about

the patterns on the hundreds chart.

1.

38

64

27

3.

5.

14

87

73

2.

4.

6.


Lesson Focus Even and Odd Numbers PLC Notes

Lesson Purpose

Understand that some numbers can be divided into two equal parts (even numbers) and some cannot (odd numbers). Students will use this concept to understand doubles/doubles plus one addition facts and decomposing numbers into equal addends.

Content Standards

2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

Practice Standards



Introduce

Materials for each student

Hundreds

Chart

Orange crayon Green crayon

Dot Cards

20 Linking

Cubes

Optional IPAD Tools

Explain

Everything App:

Triple Ten Frame

Square Tiles 120 Chart Base Ten

Blocks

Pass out a dot pattern card to each student. Provide a container of linking cubes for each student group. Each student should also have a hundreds chart and a green and orange crayon. Throughout the lesson, use the hundreds chart to chart whether a number is even or odd. Color orange for the odd numbers and green for the even numbers. Encourage students to look for patterns with even and odd numbers on the hundreds chart. INDEPENDENT PRACTICE Pretend that the dots in each square are cookies. Find the group of dots that show 8 cookies. Use the linking cubes to display the dot pattern. Using the 8 linking cubes, decide if 2 children could share the 8 cookies equally? TABLE TALK/CONSENSUS Students share their individual ideas and come to an agreement within the group to share with the whole class. Explain how you know? WHOLE GROUP Students share ideas and teacher connects the idea that 8 is an even share so the number is even. [Each student will get the same amount of cookies. There are no cookies left over. Both students will get 4 cookies.] Students write the number 8 and the word even in the box by the dots.

• Did each child get the same number of cookies? Are any cookies left?

• How many cookies did each student get? • Can we write a number sentence to show how the children

shared the 8 cookies equally? [4 + 4 = 8] • What can we say about the number 8? [It is even, we can share

equally, we can make a number sentence that is a double]

Vocabulary

Odd Even

Equally

We will be using a hundreds chart to color the even numbers green and the odd numbers orange. Color the number 8 green to show that it is even. INDEPENDENT PRACTICE Find the group of dots that show 7 cookies. Use the linking cubes to display the dot pattern. Using the 7 linking cubes, decide if 2 children could share the 7 cookies equally? TABLE TALK/CONSENSUS Students share their individual ideas and come to an agreement within the group to share with the whole class. Explain how you know? WHOLE GROUP Students share ideas and teacher connects the idea that 7 is an odd share so the number is odd. Students write the number 7 and the word odd in the box by the dots.

• Did each child get the same number of cookies? [Each student will not get the same amount of cookies.] Are any cookies left? [There are cookies left over.]

• How many cookies did each student get? [3] • Can we write a number sentence to show how the children

shared the 7 cookies? [3 + 3 + 1 = 7] • What can we say about the number 7? [It is odd, we cannot

share equally, we cannot make a number sentence that is a double]

• Color the number 7 orange to show that it is odd. THINK-PAIR-SHARE Students get time to think quietly about each remaining number 1 – 9 (one at a time.) Then they share their thoughts with the partner and come to an agreement about if the number is even or odd. Students write the number in the box and write if the number is even or odd. Color the hundreds chart accordingly.

Investigate

Materials

Linking Cubes

Vocabulary

Odd Even Fair

Equal Equally

Unequally

POSE THE PROBLEM - Tell a story about two twin sisters (or brothers). Two twins always share whatever they have equally. If they find stickers, they count them out and share them so that each has the same number of stickers. When their dad gives them cookies for lunch, they make sure that each of them has the same number of cookies. However, sometimes they can’t share things fairly because there is an extra that is left over. If the twins’ mom gave them 13 marbles, would they be able to share the marbles equally? Discuss if the twins could share 13 marbles equally.

THINK-PAIR-SHARE – Students get time to think quietly, then, share their thoughts with a partner and listen to their partners’ thoughts on why 13 would be an odd number.

WHOLE GROUP – Have students share why they determine 13 to be an odd number. [some left over, everyone does not get the same, someone gets too many, it’s no equal] Possible strategies used to determine if they have even or odd numbers:

• Students may count out 13 linking cubes and distribute them one by one to each twin to discover an extra cube.

. • Some students may pair the cubes up to determine if each

twin receives the same number of cubes. Assign three or four numbers from 10 to 20 to pairs of children. Their task is to decide which of their numbers could be shared equally and which would have a leftover. Linking cubes can be provided to help them in their investigation.

WHOLE GROUP/CONSENSUS – Students get time to think quietly, then share their thoughts with others and listen to other students’ thoughts on why or why not the numbers are odd or even [some left over, everyone does not get the same, someone gets too many, not all of them have pairs].

Ask the students to share what they did in order to determine whether the number they have is odd or even. Have all students color the hundreds chart as each number is discussed. When all the numbers from 1 – 20 have been colored, have the following discussion. Did you find any patterns on the hundreds chart when you colored odd and even numbers? [Odd numbers line up in columns and even numbers line up in columns, numbers have a 1,3,5,7,& 9 in the ones place are odd, numbers having a 0, 2,4,6,& 8 in the one place are even, even numbers are counting by 2s numbers] Look at the numbers in each column. What do you see that is the same? [The ones number stays the same] What do you see that is different? [The tens number changes]

Investigate

Materials

Linking Cubes

Vocabulary

Odd Even Fair

Equal Equally

Unequally

Does the digit in the ones place help you to decide if the number is even or odd? [Because the value of the tens place will always be even. If a number is odd, the” left overs” can only be found in the ones place] If needed, have students look at counters on a ten frame to realize that groups of ten counters can always be shared equally and are always even. The only place there could be an extra counter would be in the ones place. Can I use this pattern to help me decide if 46 is odd or even? How?

Summarize

Through the discussion, help them to understand that: • Even numbers is an amount that can be shared fairly or split

into equal parts with no leftovers • An odd number is one that is not even or cannot be split into

two equal parts Extension: Have you noticed any patterns while you are working with the odd and even numbers? [odd numbers end in 1, 3, 5, 7, 9 and even numbers end in 2, 4, 6, 8] Note: “The number endings of 0, 2, 4, 6 and 8 are only an interesting and useful pattern or observation and should not be used as the definition of an even number. ”Teaching Student-Centered Mathematics, John A. Van de Walle, LouAnn H. Lovin, et al.” WHOLE GROUP – Demonstrate that doubles addition facts and decomposing numbers into equal addends can be used to understand the concept of even numbers. Ask students to count out 8 linking cubes and another 8 linking cubes. Write and display the equation 8 + 8 = 16. Help the students realize that adding even numbers will create an even number. Ask students to count out 8 linking cubes and another 9 linking cubes (doubles plus 1 fact). Write and display the equation 8 + 9 = 17. Help the students realize that 8 is even number plus an odd number equals an odd number. Ask students to count out 7 linking cubes and another 7 linking cubes. (doubles fact) Write and display the equation 7 + 7 = 14. Help the students realize that an odd number plus an odd number equals an even number.

Homework enVision Math, Common Core, Teacher’s Resource Masters, Number and Operations in Base Ten, Practice 5-6

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Math Module Assessment Module 4

Name ___________________________

Three-Point Scoring Rubric 1.

The Problem: Sam’s Pet Shop has 36 black puppies. The pet shop gets30 more black puppies. How many black puppies does the pet shop have now?

Make a math drawing using base ten blocks. Make sure to label your model and write an equation.

Explain your thinking.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

2. Three-Point Scoring Rubric

The Problem: Sam’s Pet Shop also has 87 white puppies. Compare the number of black puppies to the number of white puppies using >, <, or = symbols.

How do you know?

___________________________________________________________________

___________________________________________________________________

3.

Three-Point Scoring Rubric

The Problem: Sam’s Pet Shop also has 42 goldfish. A customer visited the shop and bought 30 goldfish. How many goldfish does Sam’s Pet Shop have now?

Make a math drawing using base ten blocks. Make sure to label your model and write an equation.

Explain your thinking.

___________________________________________________________________

___________________________________________________________________

___________________________________________________________________

4. Three-Point Scoring Rubric

Does the pet shop have an even or odd number of goldfish left? _____________

How do you know? __________________________________________________

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