fourth grade math pacing guide 2015-2016

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Sunflower County Consolidated School District

Fourth Grade Math Pacing Guide

2015-2016

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Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their

students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of

these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second

are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic

competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in

carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as

sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

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

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They

analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution

pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the

original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older

students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing

calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal

descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.

Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students

check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand

the approaches of others to solving complex problems and identify correspondences between different approaches.

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2. Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary

abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it

symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and

the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.

Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to

the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

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

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing

arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to

analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them

to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the

context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments,

distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students

can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be

correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an

argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions

to clarify or improve the arguments.

4. Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply

proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a

design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can

apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may

need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as

diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They

routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving

the model if it has not served its purpose.

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5. Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and

paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry

software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each

of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high

school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically

using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to

visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at

various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to

pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their

own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are

careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately

and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students

give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit

use of definitions.

7. Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven

more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later,

students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2

+ 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and

can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see

complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 –

3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

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8. Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary

students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a

repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with

slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x

– 1) (x + 1), (x – 1) (x2 + x + 1), and (x – 1) (x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work

to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually

evaluate the reasonableness of their intermediate results.

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Sunflower County Consolidated School District Fourth Grade Math Pacing Guide

First Nine Weeks

August

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

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

September


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

October


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 30

30 31

Nine Weeks Exams: October 6-9

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Math Pacing Guide: Fourth Grade First Nine Weeks

STANDARDS ARE NOT NECESSARILY WRITTEN IN THE SEQUENCE THEY SHOULD BE TAUGHT.

Date Taught

Envision/Ready Lessons

Suggested Vocabulary

Common Core State Standards “I Can” Statements Mathematical Practices

Resources

NUMBER AND OPERATIONS IN BASE TEN (NBT)

August 10 to October 6

3-1 3-2 3-6 10-3 Ready Lessons 1 & 2

Digits place value standard form expanded form word form

4. NBT.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

I can recognize through division that a multi-digit whole number in a given place is 10 times the value of the place to the right (4 thousand=______ tens, 4, 0000/40=10.

1,2, and 7 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources


3.1 3-2 3-3 3-4 Ready Lessons 1 & 2

Digits place value standard form expanded form word form compare

4. NBT.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

I can read and write a multi-digit whole number in standard, word, and expanded form. I can compare two-multi-digit numbers using >, <, or = symbols.

1,2, and 7 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

August 10 to October

1-5 4-2

4. OA.3: Solve multi-step word problems posed with whole

I can apply the four basic operations to

MP 1,2,3,4,6, and 7

Envisions Math Common Core Kit

8

6 4-6 7-4 Ready Lessons 9 & 10

Compatible numbers

numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. 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.

solve multi-step word problems. examine, analyze, and compose a variable to determine an unknown quantity I can estimate and infer reasonableness using rounding

Pearsonsccessnet.com Achievethecore.org PARCC Practice Test


3.5 4-1 4-2 5-4 5-5 5-6 6-5 7-3 7-4 Ready Lesson 4

Breaking apart Compensation Counting on Commutative Property of Addition Associative Property of Addition Identity Property of Addition Compensation Compatible numbers

4. NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

I can calculate by rounding a multi-digit whole number to any place.

MP 1,2,7 EnVision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

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4-2 4-3 4-4 4-5 4-6 Ready Lessons 3

Inverse operations

4.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models of drawing and strategies based on place value, properties of operation, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

I can fluently add and subtract multi-digit whole numbers using a standard algorithm.

MP 1,2,3,4,5,6,7,8

EnVision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

OPERATIONS AND ALGEBRAIC THINKING (OA)


1-1

Array Product Factors

4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35=5x7 as a statement that is 5

I can interpret multiplication equations using the Commutative

MP 1,2,4 EnVision Math Common Core Kit pearsonsuccessnet.com

10

1-3 1-7 Ready Lesson 5

Commutative Property of Multiplication Zero Property of Multiplication Identity Property of Multiplication Inverse operations Fact family

times as many as 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Property.

achievethecore.org PARCC Practice Test items Questar sample items Ready Resources


1-8 1-9 1-10 2-6 5-4 5-6 6-2 6-3 6-5 6-6 7-2 thru 7-3 7-4 7-5 8-5 9-1to 9-3 9-6 10-8 Ready Lessons 9 & 10

Compensation Compatible numbers

4. OA.3 Solve multi-step word problems with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity.

I can solve for the unknown using multiplicative comparisons examine and I can apply four basic operations to solve multi-step word problems. Examine, analyze, and compose a variable to determine an unknown quantity.

MP 1,2,3,4,6, and 7

Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

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1-4 11-1 11-2 11-3 Ready Lesson 7

Distributive Property Prime number Composite number

4. OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range of 1-100 is prime or composite.

I can list all factor pairs for whole numbers 1-100 (ex.25-1,5,25) I can state and show that a whole number is a multiple of its factors (ex. Ski counting by 5s-5,10,15, 20)

8 MP 1,2,3,4,5,6,7,8



1-2 1-5 2-1 2-2 thru 2-6 11-3 16-11 Ready Lesson 8

Multiple Repeating pattern

4. OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1 generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

I can create a number or shape pattern which follows a given rule. I can identify and explain other patterns that go beyond the given rule.

MP 1,2,3,4,5,6,7,8



5-1 5-2 5-3

Partial product

4. NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and

I can multiply a whole number up to four digits by a one

1,2,3,6, and 7

Envision Math Common Core Kit

12

5-4 5-5 5-6 6-1thru 6-6 7-1 7-2 7-4 7-5 8-1 thru 8-5 9-5 10-8 Ready Lesson 11

Compensation Compatible numbers

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.

digit whole number. I can multiply 2 two-digit whole numbers using properties of operations (Zero Property, Identity Property, Distributive Property, Associative Property, Commutative Property) I can illustrate my calculations by using a written equation, rectangular array, and/or area model.

pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources


9-1 9-2 9-3 9-4 9-5 9-6 10-1 10-2 10-3 10-4 10-5 10-6 10-7

Remainder

4. NBT.6 Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on the place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

I can divide four -digit dividends by one-digit divisors. I can find quotients and remainders in a given division problem. I can apply the inverse operation to demonstrate the relationship between multiplication and division.

MP 1,2,3,6,7, and 8

Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items

13

Ready Lesson 12

I can illustrate my calculations by using a written equation, rectangular array, and/or area models.

Ready Resources

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Second Nine Weeks

October


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 30

30 31

November


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

December


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

Nine Weeks Exams: December 15-18

15

Fourth Grade Second Nine Weeks

Date Taught

Envision Topic(s)



Resources

NUMBERS AND OPERATIONS IN BASE TEN (NBT)

October 14th-December 15th

Topic 9.1-9.6 and 10.1-10.7 Ready Lessons 12

Quotient Dividend divisor remainder Inverse operations equation array area model

4. NBT.6 Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on the place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

I can divide four -digit dividends by one-digit divisors. I can find quotients and remainders in a given division problem. I can apply the inverse operation to demonstrate the relationship between multiplication and division. I can illustrate my calculations by using a written equation, rectangular array, and/or area models.

MP 1, 2,3,4,6, and 8



1-1 1-6 1-8 1-9 1-10

Array Product factors

4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawing equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive

I can multiply to solve word problems involving multiplicative comparison

MP 1,2,3,4,5,6,7,8

EnVision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test

16

Ready Lesson 6

comparison items Questar sample items Ready Resources


Topic 1.4 and 11.1-11.3 Ready Lesson 7

Factor Prime number Composite number

4. OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range of 1-100 is prime or composite

I can list all factor pairs for whole numbers 1-100 (ex.25-1,5,25) I can state and show that a whole number is a multiple of its factors (ex. skip counting by 5s-5,10,15, 20)

MP 1,2,7,8 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

NUMBER AND OPERATIONS –FRACTIONS (NF)


11.4 11.5 11-8 Ready Lesson 13

fraction equivalent fractions numerator denominator

4. NF.1 Explain why a fraction a/b is equivalent (n x a)/(n x b) by using visual fraction b models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use the principle to recognize and generate equivalent fractions.

I can recognize equivalent fractions by using visual models. I can generate equivalent fractions using visual models or pictures. I can explain why two fractions are equivalent using visual models.

MP 1,3,4,5,6,7


October 14th-December

11-5 11-6

Benchmark

4NF.2 Compare two fractions with different numerators and denominators, e.g., by creating

I can find common denominators to compare two

MP 2,3,5,6,7

EnVision Math Common Core Kit

17

14th 11-7 11-8 Ready Lesson 14

fractions common denominators or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, <, or = and justify the conclusions, e.g., y using a visual fraction model.

fractions with unlike numerators and denominators. I can compare two given fractions by comparing them to benchmark fractions (1/2, ¾, 2/3, ¼).



12.1 Ready Lessons 15, 16, & 17

Mixed number Improper fraction Equivalent fraction Reduce/simplest form

4.NF.3 Understand a fraction a/b with a 1 as a sum of fractions 1/b.

I can add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction (ex. Improper fractions and/or simplest form).

MP 1,2,3,4,5,6,7,8



12.1 12-2 12-3 12-4 12-5 12-11 Ready Lessons 15 & 16

Addition Subtraction Fraction Part/whole relationship

4. NF.3a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

I can add and subtract fractions with the same denominators (part of the same whole). I can explain the multiples of fractions by using visual models.

MP 1,2,3,,5,6,7,8


18


12-6 12-7 12-10 Ready Lessons 15 & 17

fraction decompose equation model

4. NF.3b. Decompose a fraction in to a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8=1/8+1/8+1//8; 3/8=1/8+2/8; 2 1/8 =1+ 1 +1/8.

I can decompose (break –apart) a fraction into a sum of fractions with the same denominators. I can decompose a fraction and record it as a fraction. I can justify my decomposition by using a fraction model.

MP 1,2,3,4,5,6,7,8


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12-6 12-7 12-8 12-9 Ready Lesson 17

Mixed numbers Improper fraction

4.NF.3c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

I can add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction (ex. Improper fractions and/or simplest form.

MP 1,2,3,,5,6,7

Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

20

October

14th-

Decemb

er 14th

12-2 12-3 12-4 12-5 12-10 12 Ready Lessons 15 & 17

fractions numerator denominator

4. NF.3d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

I can solve word problems involving multiplication of fractions involving a whole number. I can solve word problems using visual fraction models. I can solve word problems using equations to represent the topics.

MP 1,2,3,4,5,6


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Fourth Grade Math Pacing Guide

Third Nine Weeks

January


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

February


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

March


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

Nine Weeks Exams: March 8-11

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FOURTH GRADE THIRD NINE WEEKS

Number and Operations-Fractions (NF)

Jan. 6th – Mar. 7th

Topic 12 Lessons 12.1 Ready Lessons 15 - 17

Fraction Numerator Denominator Mixed number Improper fraction Equivalent fraction Simplest form

4.NF.3 Understand a fraction a/b with a .1 as a sum of fractions 1/b.

I can add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction (ex. Improper fractions and/or simplest form).



Topic 12 Lessson12.2-12.4 Ready Lessons 15 & 16

Like Fraction Part Numerator denominator Whole model

4. NF.3a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole

I can add and subtract fractions with the same denominators (part of the same whole). I can explain the multiples of fractions by using visual models.

MP 1,2,3,5,6,8 EnVision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources


Topic 12 Lesson 12.10

Decompose Fraction model

4. NF.3b. Decompose a fraction in to a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.

I can decompose (break –apart) a fraction into a sum of fractions with the same denominators.

MP 1,2,3,4,5,6,7,8

EnVision Math Common Core Kit pearsonsuccessnet.com

24

Ready Lessons 15 & 17

Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8=1/8+1/8+1//8; 3/8=1/8+2/8; 2 1/8 =1+ 1 +1/8.

I can decompose a fraction and record it as a fraction. I can justify my decomposition by using a fraction model.

achievethecore.org PARCC Practice Test items Questar sample items Graphic organizer Ready Resources


Topic 12 Lesson 12.6-12.9 Ready Lesson 17

4.NF.3c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

I can add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction (ex. Improper fractions and/or simplest form.

EnVision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Graphic organizer Ready Resources


Lesson 12.5 Lesson 12.11 Ready Lessons 16 & 17

4. NF.3d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

I can solve word problems involving multiplication of fractions involving a whole number. I can solve word problems using visual fraction models. I can solve word problems using equations to

MP 1.2.3.4.5.6 EnVision Math Common Core Kit pearsonsuccessnet.com achievethecore.org Graphic organizer PARCC Practice Test items Questar sample items Ready Resources

25

represent the topics.


13-2 Fraction Unit fraction multiple

4. NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

PARCC Practice Test items Questar sample items Ready Resources



Unit fraction 4. NF.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5x (1/4), recording the conclusion by the equation 5/4 = 5x (1/4).

I can explain why a/b=ax1/b by using visual models to show how to decompose fractions into unit fractions and represent it as a multiple of unit fractions (.g., ¾=1/4+1/4+1/4+1/4=3x1/4). (R)

MP 3,4,7 PARCC Practice Test items Questar sample items


Lesson 13-2 13-3 Ready Lesson 18

4. NF.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3x (2/5) as 6x (1/5), recognizing this product as 6/5. (In general, nx(a/b=(nxa)/b.)

I can decompose a fraction (a/b) into a multiple of unit fractions (ax1/b) in order to show why multiplying a whole number by a fraction (nx(a/b)) results in (nxa)/b (e.g., 5x3/8= (5x3)x1/8=15/8).

MP Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Graphic organizer Ready Resources


Lesson 13.3 Ready Lesson 19

Fraction Unit fraction multiple

4. NF.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there

I can solve word problems that involve multiplying a whole number and fraction with visual models and equations.

MP Common Core Kit pearsonsuccessnet.com achievethecore.org Envision Math Graphic organizer PARCC Practice Test items

26

will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Questar sample items Ready Resources


Lesson 13.4-13.5 13-6 Ready Lesson 20

Fraction Equivalent fraction Numerator denominator

4. NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 34/10 as 30/100, and add 3/10+ 4/100=34/100.

I can rewrite a fraction with a denominator 10 as an equivalent fraction with denominator 100. I can add two fractions with denominators 10 and 100.

MP Envision Math Common Core Kit(Decimal model/Teaching Tool 17) Pearsonsuccessnet.org achievethecore.org PARCC Practice Test items Questar sample items


13-4 To 13-6 13-10 Ready Lesson 21

decimal notation convert denominator

4. NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters: locate 0.62 on a number line diagram.

I can explain the relationship between a fraction and the decimal representation. I can represent fractions with denominators of 10 and 100 as a decimal. I can identify tenths and hundredths I can show the placement of a decimal on a number line.

MP Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Graphic organizer

27


13-7 13-8 13-9 Ready Lesson 22

Tenth Hundredth Decimal point

4. NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols

I can compare two decimals to hundredths by reasoning about their size using a visual model. I can determine that the comparisons are true when the two decimals refer to the same whole. I can compare two decimals using >, <, or= symbols. I can justify the comparison/conclusion using visual models (ex. Charts, base-ten blocks).

MP 1,2,3,4,5,6,7

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MEASUREMENT AND DATA (MD)


Convert/conversion 4. MD Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.


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13-10 14-1 14-2 14-3 14-4 14-5 14-6 14-7 14-8 14-9 14-10 14-11 Ready Lesson 23

Inch Foot Yard Mile Capacity Weight Ounce Pound Ton Millimeter Centimeter Decimeter Meter Kilometer Milliliter Liter Mass Gram Kilogram

4MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min, sec. within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a

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4.MD Solve problems involving measurement and conversion



Inch Foot Yard mile

4. MD.1 Know relative sizes of measurement units within one system of units including km, m, cm: kg, g; lb., oz. l, ml: hr., min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1ft is 12 times as 1 in. express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), 2, 24), 3, 36),…

I can describe the relative size of measurement units(e.g., km,m,cm;kg,g;lb,oz.;l,ml;hr,min,sec). I can represent a larger unit as a multiple of smaller units within the same system of measurement and record the equivalent measures in a two-column table (e.g., 1 feet=12 inches, 2 feet=24 inches, 3 feet=36 inches).

MP 1,2,3,4,5,6,7,8

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13-9 13-10 14-10 14-11 15-2 15-3 15-4 15-5 Ready

Tenth Hundredth Decimal point Line plot

4. MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams that feature a measurement scale.

I can represent measurements using diagrams and correct measurement scale. I can use the four operations to solve measurement and word problems. I can solve word problems involving various measurements

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30

Lessons 24 & 25

expressed by whole numbers, fractions, and decimals. I can convert a measurement given in a larger unit into an equivalent measurement in smaller units in order to solve a problem



4. MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width f a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

I can explain the formula for area and perimeter. I can use the formulas for area and perimeter to solve real world problems.

1,2,3,5 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org Gr PARCC Practice Test items Questar sample items Ready Resources Graphic organizer



Line plot fraction

4MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line-plot, find and interpret the difference in length between the

I can create a line plot with a given data set of measurements using fractions as a unit. I can use the information on the line plot to solve

2,4,5 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items

31

longest and shortest specimens in an insect collection.

addition and subtraction problems.

Questar sample items Ready Resources Graphic organizers

32


Fourth Nine Weeks

March


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

April


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

May


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

Nine Weeks Exams: May 23-26

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Fourth Grade Fourth Nine Weeks

Date Taught

Envision Topic(s)/Lesson(s)



Resources

MEASUREMENT AND DATA (MD)

Mar.21- May

14.1 14-2 14-3 14-4 14-5 14-6 14-7 14-8 14-9 14-10

Inch Foot Yard Mile Capacity Weight Ounce Pound ton millimeter centimeter decimeter meter kilometer milliliter liter mass gram kilogram

4MD.1 Know relative sizes of measurement units within one system of units including km, m, cm: kg, g: lb., oz.; l, lm; hr., min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft. is 12 times as long as 1 inch. Express the length of a 4 ft. sake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …

I can relate measurement sizes within the metric system. I can relate measurement sizes within the customary system. I can convert measurements from a larger unit to a smaller unit in the metric system. I can convert measurements from larger units to smaller units in the customary system.

MP 1,2,3,,6

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14-11 Ready Lesson 23

March 16 to May 20

Topic 13 and 15 Lesson13.9 Lesson 14.11, Lesson15.2- 15.3 Lesson 15.5 Ready Lessons 24 & 25

Distance Intervals of time Volume mass

4MD2.Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

I can solve word problems involving intervals of time. I can solve word problems involving volume and mass. I can solve word problems involving money.

MP 1,2,3,6,8


March 16 to May 20

Topic 15 Lesson 15.1 Ready Lesson 26

Area Perimeter Formula Length Width

4. MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

I can apply the formula for area of a rectangle to solve real world and mathematical problems using an unknown factor (variable). I can apply the formula for perimeter of a rectangle to solve real world and mathematical problems using an unknown factor (variable)

MP 1,2,4

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March 16 to May 20

Topic 15 Lesson 15.4

fraction line plot

4MD.4 Make a line plot to display a data set of measurements in

I can create a line plot with a given

MP 3,5,6 EnVision Math Common Core Kit

35

Ready Lesson 27

data data set unit compare analyze interpret

fractions of a unit (1/2, ¼, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line-plot, find and interpret the difference in length between the longest and shortest specimens in an insect collection.

data set of measurements using fractions as a unit. I can use the information on the line plot to solve addition and subtraction problems.


March 16 to May 20

16-3 16-4 16-5 Ready Lesson 28

Degree Unit angle Angle measure protractor

4. MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint and understand concepts of angle measurement.

I can identify and recognize angles as geometric shapes with specific attributes (vertex, end point, and ray).

MP 1,2,3,7 EnVisin Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

March 16 to May 20

16-3 16-4 16-5 Ready Lesson 28

degree unit angle angle measure protractor

4. MD.5a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

I can describe a circle as a figure that has 360 degrees. I can recognize an angle as a fraction of a 360 degree circle. I can identify the

MP 1,2,3,7 Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

36

measure of an angle in terms of degrees.

March 16 to May 20


4. MD.5b An angle that turns through n 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

I can identify the measure of an angle in terms of degrees. I can calculate the measure of an angle using 360 degrees of a circle. I can use a 1 degree angle to measure other angles.

MP 3,5,6 Common Core Kit (pattern blocks/Teaching Tool 25) pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

March 16 to May 20

Topic 16 Lesson 16.5 Ready Lesson 29

protractor 4. MD.6 Measure angles in whole number degrees using protractor. Sketch angles of specified measure.

I can measure angles in whole number degrees using a protractor. I can sketch angles as a specified measure using a protractor.

MP 2,3,5 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources Graphic organizers

37

March 16 to May 20


4. MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

I can classify angles by their measurement (obtuse, straight, right, acute) I can add the sum of the parts to equal the whole (90°+90°=180°). I can subtract the sum of the parts to equal the whole (180°-90°=90°). I can solve addition and subtraction equations using a variable to find the unknown angle (180°+q=360°; q=180°)

2, 4, 5, 7 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources Graphic organizers

GEOMETRY(G)

March 16 to May 20

16-1 16-2

Point Line Plane Parallel lines Intersecting lines Perpendicular lines Line segment Ray Angle Right angle Acute angle Obtuse angle Straight angle

4. G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

I can draw points, lines, line segments, rays, angles (right, acute, obtuse). I can identify these as parallel or perpendicular lines.

MP 2,3,4,5 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources Graphic organizers

38

16-3 16-4 16-5 Ready Lesson 31

Degree Unit angle Angle measure protractor

March 16 to May 20

16-7 16-8 16-9 16-11 Ready Lesson

Polygon Side Vert3ex Triangle Quadrilateral Pentagon Hexagon Octagon Equilateral triangle Isosceles triangle Scalene triangle Right triangle Acute triangle Obtuse triangle Rhombus Trapezoid Parallelogram Rectangle Square

4. G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

I can classify two-dimensional figures by identifying parallel or perpendicular lines. I can classify two-dimensional shapes into categories based on the presence or absence of acute, obtuse, or right angles. I can recognize right triangles as a category. I can identify right triangles.

1, 2, 3, 4, 7, 8

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39

32

March 16 to May 20


Symmetric Line of symmetry

4. G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line symmetric figures and draw lines of symmetry.

I can identify line symmetric figures. I can define line of symmetry, explain how to identify it in a two-dimensional figure, and explain how folding along a line of symmetry results in matching parts.

MP 2,3,7 Envision Math Common Core Kit pearsonsuccessnet.com achievethecore.org PARCC Practice Test items Questar sample items Ready Resources

40

I can draw a line on a figure to create two symmetric figures.

fourth grade math pacing guide 2015-2016

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