€¦ · web view2017-06-21 · the mathematics curriculum provides sequential and comprehensive...

District OverviewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.

Grade 4 DescriptionIn grade 4, instructional time should focus on the following mathematical core domains:

Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Geometry

In grade 4, instructional time should focus on the following mathematical practices: Make sense of problems and persevere in solving them (MP. 1) Reason abstractly and quantitatively (MP. 2) Construct viable arguments and critique the reasoning of others (MP. 3) Model with mathematics (MP. 4) Use appropriate tools strategically (MP. 5) Attend to precision (MP. 6) Look for and make use of structure (MP. 7) Look for and express regularity in repeated reasoning (MP. 8)

Grade 4 Units: Topic 1: Generalize Place Value Understanding Topic 2: Fluently Add and Subtract Multi-Digit Whole Numbers Topic 3: Use Strategies and Properties to Multiply by 1-Digit Numbers Topic 4: Use Strategies and Properties to Multiply by 2-Digit Numbers Topic 5: Use Strategies and Properties to Divide by 1-Digit Numbers Topic 6: Use Operations with Whole Numbers to Solve Problems

Topic 7: Factors and Multiples Topic 8: Extend Understanding of Fraction Equivalence and Ordering Topic 9: Understand Addition and Subtraction of Fractions Topic 10: Extend Multiplication Concepts to Fractions Topic 11: Represent and Interpret Data on Line Plots Topic 12: Understand and Compare Decimals Topic 13: Measurement: Find Equivalence in Units of Measure Topic 14: Algebra: Generate and Analyze Patterns Topic 15: Geometric Measurement: Understand Concepts of Angles and Angle Measurement Topic 16: Lines, Angles, and Shapes

Subject: Math Grade: 4 Suggested Timeline: 5 DAYS

Unit Title: Topic 1: Generalize Place Value UnderstandingUnit Overview/Essential Understanding:

Our number system is based on groups of ten. Whenever we get 10 in one place value, we move to the next greater place value. In a multi-digit whole number, a digit in one place represents ten times what it would represent in the place immediately to its right. Place value can be used to compare numbers. Rounding whole numbers is a process for finding the multiple of 10, 100, and so on closest to a given number. Good math thinkers use math to explain why they are rights. They can talk about the math that others do, too.

Unit Objectives: At the end of this topic, students will be able to independently use their learning to:

read and write numbers in expanded from, with numerals, and using number names recognize the relationship between adjacent digits in a multi-digit number use place value to compare multi-digit numbers use place value to round multi-digit numbers use previously learned concepts and skills to construct arguments about place value

Focus Standards Addressed in this Unit: CC.2.1.4.B.1 – Apply place value concepts to show an understanding of multi-digit whole numbers

Important Standards Addressed in this Unit:N/A

Misconceptions: Some students may call the ones period the hundreds period. Show them that the least place value in a period is the same name as the

period. Students may transpose the inequality symbols when comparing numbers. Both symbols will always open toward the greater number.

Concepts/Content: Place Value Whole Numbers Structure of Our Numeration

System

Competencies/Skills: Represent Multi-Digit Whole

Numbers Understand Place-Value

Relationships Compare Multi-Digit Whole

Description of Activities: Problem-Solving Reading Mat Center Games Online Math Tools (www.pearsonrealize.com) Videos (www.pearsonrealize.com) Quick Check

http://www.pearsonrealize.com/


Numbers Round Whole Numbers Understand the Structure of Our

Numeration System

Practice Buddy Math and Science Activity Problem-Solving Reading Activity Vocabulary Cards and Activity

Assessments: Practice Buddy Quick Check Online Topic Assessment Topic Assessment Basic Facts Timed Test Computation Assessments (created)

Interdisciplinary Connections:Problem-Solving Reading Mats – Reading (TE p. 1H)Problem-Solving Reading Activity – Reading (TE p. 1H)Math and Science Project – Science (TE p. 1)

Additional Resources: https://www.pearsonrealize.com/index.html#/ https://www.ixl.com/math/grade-4 https://xtramath.org/#/home/index https://www.sumdog.com/ Pearson, enVisionmath2.0


https://www.sumdog.com/

https://xtramath.org/#/home/index

https://www.ixl.com/math/grade-4

https://www.pearsonrealize.com/index.html#/

Unit Title: Topic 2: Fluently Add and Subtract Multi-Digit Whole NumbersUnit Overview/Essential Understanding:

Representing numbers and numerical expressions in equivalent forms can make some calculations easy to do mentally. There is more than one way to do a mental calculation.

There is more than one way to estimate a sum or difference. Estimation gives a way to replace numbers with other numbers that are close and easier to compute with mentally.

The standard addition algorithm for multi-digit numbers breaks the calculation into simpler calculations using place value. The standard addition and subtraction algorithms for multi-digit numbers break the calculation into simpler calculations using place

value starting with the ones, then the tens, and so on. The standard addition and subtraction algorithms for multi-digit numbers break the calculation into simpler calculations using place

value starting with the ones, then the tens, and so on. Good math thinkers know how to think about words and numbers to solve problems.


add and subtract whole numbers mentally using a variety of methods round greater whole numbers to estimate sums and differences add numbers to one million with and without regrouping using the standard algorithm use place value and an algorithm to subtract whole numbers use number sense and regrouping to subtract across zeros use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations

Focus Standards Addressed in this Unit: CC.2.1.4.B.2 – Use place value understanding and properties of operations to perform multi-digit arithmetic CC.2.2.4.A.1 – Represent and solve problems involving the four operations


Misconceptions: If students did not get a reasonable estimate, ensure that they understand it is important to check that they have correctly rounded the

numbers to the same place to get a reasonable result.

If students cannot explain how to regroup, show them that 5+5=10. The 0 is in the ones place and the 1 is in the tens place. The extra ten needs to be regrouped where it will be added to the other tens.

Watch for students who may have trouble regrouping. In Step 2, for example, some students may forget to add 10 tens to the 8 tens. Remind students that addition and subtraction have an inverse relationship. To check the answer to a subtraction problem, they can add

the difference to the lesser number. If the answer is the same as the greater number, they subtracted correctly.Concepts/Content:

Place Value Addition of Whole Numbers Subtraction of Whole Numbers Properties of Operations Number Sense

Competencies/Skills: Fluently Add and Subtract Whole

Numbers Develop Fluency with the

Standard Algorithm Understand Place Value and

Properties of Operations Use Number Sense to Estimate Develop Fluency in Adding and

Subtracting Multi-Digit Whole Numbers

Description of Activities: Problem-Solving Reading Mat Center Games Online Math Tools (www.pearsonrealize.com) Videos (www.pearsonrealize.com) Quick Check Practice Buddy Math and Science Activity Problem-Solving Reading Activity Vocabulary Cards and Activity


Interdisciplinary Connections:Problem-Solving Reading Mats – Reading (TE p. 43H)Problem-Solving Reading Activity – Reading (TE p. 43H)Math and Science Project – Science (TE p. 43)

Additional Resources: https://www.pearsonrealize.com/index.html#/ https://www.ixl.com/math/grade-4 https://xtramath.org/#/home/index https://www.sumdog.com/ https://www.teacherspayteachers.com/ Pearson, enVisionmath2.0


https://www.teacherspayteachers.com/







Unit Title: Topic 3: Use Strategies and Properties to Multiply by 1-Digit NumbersUnit Overview/Essential Understanding:

Basic facts and place-value patterns can be used to find products when one factor is 10, 100, or 1,000. Rounding is one way to estimate products. The properties of multiplication can be used to simplify computation and to verify mental math and paper and pencil algorithms. Properties of multiplication and place-value understanding can be used to multiply without paper and pencil. The expanded algorithm for multiplication can be represented with arrays. In the algorithm, numbers are broken apart using place

value, and the parts are used to find partial products. The expanded algorithm for multiplication breaks numbers apart using place value, and the parts are used to find partial products. The

partial products are then added together to find the product. The standard multiplication algorithm is a shortcut for the expanded algorithm. Regrouping is used rather than showing all the partial

products. The standard algorithm for multiplication involves breading apart numbers using place value, finding partial products, and then adding

partial products to get the final product. The process is the same regardless of the size of the factors. The standard algorithm for multiplication involves breaking apart numbers using place value, finding partial products, and then adding

partial products to get the final product. The process is the same regardless of the size of the factors. Good math thinkers choose and apply math they know to show and solve problems from everyday life.


multiply multiples of 10, 100, and 1,000 using mental math and place-value strategies use rounding to estimate products and check if answers are reasonable use the Distributive Property to multiply larger numbers use place value and properties of operations to multiply mentally use arrays and partial products to multiply 3- and 4-digit numbers by 1-digit numbers use place value and partial products to multiply 3- and 4-digit numbers by 1-digit numbers use place value and the standard algorithm to multiply 2- and 3-digit numbers by 1-digit numbers use the standard algorithm to multiply 4-digit numbers by 1-digit numbers use the standard algorithm to multiply 2-, 3-, and 4-digit numbers by 1-digit numbers. Estimate to check if answers are reasonable use previously learned concepts and skills to represent and solve problems


Important Standards Addressed in this Unit:N/AMisconceptions:

Be aware that students may be confused if the product of a basic fact ends with a 0. Have students underline the product of the basic fact and then include zeros after the basic fact as needed: 8 x 50 = 400.

Some students might think that because the addition symbol is inside the parentheses in the equation where 1,842 is broken apart, it goes inside the parentheses wen multiplying the products of all 4 parts. Point out that the 6 is multiplied by the sum of 1,000 + 800 + 40 + 2. The 6 must be multiplied by 1,000, 800, 40, and then by 2, and the products are added together. Use the model to help students see this.

In Step 2, students may think they should add the regrouped tens to the tens digit of the 2-digit factor before multiplying. Connect to what they already know about partial products. First you multiply, then you add.

Some students may think that they do not need to multiply the digit in a place if it is a 0 or that they do not have to record a partial product of 10. Demonstrate how making these errors results in unreasonable answers.

Concepts/Content: Place Value Multiplication of Whole Numbers Properties of Operations Number Sense

Competencies/Skills: Multiply by 1-Digit Whole

Numbers Develop Number Sense Use Number Sense to Estimate Understand Place Value and

Properties of Operations



Interdisciplinary Connections:Math and Science Project – Science (TE p. 91)

Additional Resources: https://www.pearsonrealize.com/index.html#/ https://www.ixl.com/math/grade-4





https://xtramath.org/#/home/index https://www.sumdog.com/ https://www.teacherspayteachers.com/ Pearson, enVisionmath2.0


Unit Title: Topic 4: Use Strategies and Properties to Multiply by 2-Digit NumbersUnit Overview/Essential Understanding:

Basic facts and place-value patterns can be used to mentally multiply a 2-digit number by a multiple of ten.




Place-value blocks, area models, and arrays provide ways to visualize and find products. Products of 2-digit by 2-digit multiplication problems can be estimated by replacing each factor with the closest multiple of ten. Products can be estimated by replacing factors with other numbers that are close and easy to multiply mentally. The expanded algorithm for multiplying with 2-digit numbers is an extension of the expanded algorithm for multiplying with 1-digit

numbers. The Distributive Property can be used to multiply two 2-digit numbers by breaking the computation down into 4 simpler products and

adding the partial products together. The expanded algorithm for multiplication ca be represented with arrays. In the algorithm, numbers are broken apart using place value,

and the parts are used to find partial products. The standard algorithm for multiplying a 2-digit number by a multiple of 10 is an extension of the algorithm for multiplying multi-digit

numbers by a 1-digit number. The standard multiplication algorithm involves breaking the calculation into simpler ones using place value and properties of operations.

Regrouping is used rather than showing all partial products. The standard multiplication algorithm involves breaking the calculation into simpler ones using place value and properties of operations.

Regrouping is used rather than showing all partial products. Good math thinkers make sense of problems and think of ways to solve them. If they get stuck, they don’t give up.


use mental-math strategies to multiply 2-digit by 2-digit multiples of ten use models and properties of operations to multiply 2-digit numbers by multiples of ten estimate products for 2-digit by 2-digit multiplication problems by rounding the factors to multiples of ten use compatible numbers to estimate products of 2-digit by 2-digit multiplication problems use arrays, place value, partial products, and properties of operations to multiply two 2-digit numbers use the Distributive Property and an area model to multiply two 2-digit numbers use place value and partial products to calculate products of 2-digit by 2-digit multiplication problems use area models and place value strategies to multiply by 2-digit numbers by multiples of 10 use the expanded and the standard algorithm to multiply 2-digit by 2-digit numbers. Estimate to check if products are reasonable use models and algorithms to solve 2-digit by 2-digit multiplication problems make sense of problems and persevere in solving them



Misconceptions: If two factors when rounding are both greater than the original factors, the product is an overestimate. If two factors when rounding are

both less than the original factors, the product is an underestimate. If, when rounding, one factor is greater than the original factor, and the other is less than the original factor, the product may be either an overestimate or an underestimate.

Some students may have difficulty understanding the first application of the Distributive Property. Underlining the zeros in each factor and counting the zeros at the same time can help students remember to include all of the zeros.

Concepts/Content: Place Value Multiplication of Whole Numbers Properties of Operations Number Sense

Competencies/Skills: Multiply by 2-Digit Whole

Numbers Develop Number Sense Use Number Sense to Estimate Understand Place Value and














Unit Title: Topic 5: Use Strategies and Properties to Divide by 1-Digit NumbersUnit Overview/Essential Understanding:

Basic facts and place-value patterns can be used to divide multiples of 10 and 100 by 1-didigt divisors. There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients. There is more than one way to estimate a quotient. Using place=value patterns and compatible number are efficient techniques for

estimating quotients. When dividing, the remainder must be less than the divisor. When solving a real-world problem, the kind of questions asked determines

how to interpret the remainder. Sharing is one way t think about division. Division with partial quotients involves breaking apart the dividend, dividing the parts, and adding the partial quotients. The standard division algorithm breaks the calculation into simpler calculations using basic facts place value, the relationship between

multiplication and division, an estimation. Good math thinkers choose and apply math they know to show and solve problems from everyday life.


use mental-math and place-value strategies to divide multiples of 10 and 100 by 1-digit divisors use compatible numbers to estimate quotients use place-value patterns and division facts to estimate quotients for 4-digit dividends solve division problems and interpret remainders use place value and drawings to divide 2- and 3-digit numbers by 1-digit numbers use partial quotients to divide use partial quotients and place-value understandings to divide with greater dividends divide 2- and 3-digit numbers by 1-digit numbers using the standard division algorithm divide 4-digit numbers by 1-digit numbers using the standard division algorithm use previously learned concepts and skills to model and solve problems



Misconceptions: Students may look at the dividend (300), see 2 zeros, and think the quotient should also have 2 zeros. Remind students that they are not rounding 1,320 to the nearest 100. Instead they are trying to find a number close to 13, the first two

digits of 1,320, that is divisible by 6. Concepts/Content:

Place ValueCompetencies/Skills:

Divide by 1-Digit Whole Numbers Description of Activities:

Problem-Solving Reading Mat

Division of Whole Numbers Properties of Operations Number Sense

Develop Number Sense Use Number Sense to Estimate Understand Place Value and


Center Games Online Math Tools (www.pearsonrealize.com) Videos (www.pearsonrealize.com) Quick Check Practice Buddy Math and Science Activity Problem-Solving Reading Activity Vocabulary Cards and Activity





Unit Title: Topic 6: Use Operations with Whole Numbers to Solve ProblemsUnit Overview/Essential Understanding:

Both addition and multiplication can be used to make comparisons. Bar diagrams and equations can be used to show both situations and to distinguish between them.

Bar diagrams and equations can be used to solve problems involving multiplicative comparison. Sometimes there is a hidden question that must be answered before solving a problem. Bar diagrams and equations can represent

problems and are helpful in answering both parts of a problem.








Good math thinkers make sense of problems and think of ways to solve them. If they get stuck, then don’t give up.Unit Objectives: At the end of this topic, students will be able to independently use their learning to:

interpret comparisons as multiplication or addition equations use multiplication and division to compare two quantities solve two-step problems by finding and solving the hidden question first solve multi-step problems by finding and solving the hidden questions first make sense of a multi-step problem and keep working until it is solved



Misconceptions: Some students may have difficulty understanding. Show them the relationship with basic facts.

Concepts/Content: Multi-Step Word problems Properties of Operations Multiplication as Comparison

Competencies/Skills: Understand the Meanings of

Multiplication Understand Operations and Find

Hidden Questions Use Understanding of Operations

and Procedural Skills to Solve Multi-Step Word Problems








Unit Title: Topic 7: Factors and MultiplesUnit Overview/Essential Understanding:

Factors of a number n can be shown by arranging n counters into rows with the same number of counters in each row. The number of rows and the number of counters in each row are factors of n.

Factors of a number can be found in pairs by thinking about multiplication. Good math thinkers look for things that repeat, and they make generalizations. Prime numbers have exactly 2 factors and composite numbers have more than 2. The product of any nonzero whole number and a given nonzero whole number is a multiple of both. Factors and multiples are closely






related.


use arrays to find the factors of a given whole number use multiplication to find all the factor pairs for a whole number use repeated reasoning to generalize how to solve problems that are similar use factors to determine whether a whole number greater than 1 is prime or composite use multiplication to find multiples of a given number

Focus Standards Addressed in this Unit: CC.2.1.4.B.2 – Use place value understanding and properties of operations to perform multi-digit arithmetic CC.2.2.4.A.2 – Develop and/or apply number theory concepts to find factors and multiples


Misconceptions: Some students may think that 2 groups of 8 and 8 groups of 2 give 4 factors, since there are two factor pairs. Point out that this is really

only one factor pair and two factors. Some students may find multiples of 8 beyond 60. Remind them that the problem asks how many times the car will return to the

starting point in one hour.

Concepts/Content: Factors and Multiples Prime and Composite Numbers

Competencies/Skills: Understand Factors Find Factors and Factor Pairs Use Factors to Find Prime and

Composite Numbers Use Understanding of Factors to

Find All Factors


Assessments: Practice Buddy



Quick Check Online Topic Assessment Topic Assessment Basic Facts Timed Test Computation Assessments (created)




Unit Title: Topic 8: Extend Understanding of Fraction Equivalence and OrderingUnit Overview/Essential Understanding:

Two fractions that represent the same part of the same whole are equivalent. The two fractions are different names for the same number.

The same fractional amount can be represented by an infinite set of different but equivalent fractions. When the numerator and denominator of a fraction are multiplied by the same whole number greater than 1, it is the same as

multiplying the fraction by 1. This gives an equivalent fraction because multiplying by 1 does not change the value of a number. When the numerator and denominator of a fraction are divided by a common factor, the result is an equivalent fraction. One way to compare two fractions that are parts of the same whole is by comparing each to a benchmark fraction such as ½. When two fractions have the same denominator, the fraction with the greater numerator is greater. When two fractions have the same






numerator, the fraction with the lesser denominator is greater. Good math thinkers use math to explain why they are right. They can talk about the math that others do, too.


use area models to recognize and generate equivalent fractions use a number line to locate and identify equivalent fractions use multiplication to find equivalent fractions use division to find equivalent fractions use benchmarks, area models, and number lines to compare fractions use models or rename fractions to compare construct arguments about fractions

Focus Standards Addressed in this Unit: CC.2.1.4.C.1 – Extend the understanding of fractions to show equivalence and ordering


Some students may wonder why a circle can be used then the pizza above is in the shape of a rectangle. Others may thing the rectangle and circle could be sued together to show the fractions are equivalent.

Students may think that the fractions they see written on the number lines are the only fractions there are. Ask them to name a fraction that is not shown and decide where it would be on one of the number lines.

Students may wonder why they can multiply the numerator and denominator of a fraction without changing its value. Explain that multiplying both the numerator and denominator of a fraction by the same number is the same as multiplying the fraction by 1 because 4/4, for example is equal to 1.

Some students may try to divide the numerator and denominator by two different factors. Explain that dividing by 1, like multiplying by 1, does not change the value of a number. So, students must divide the numerator and denominator by the same whole number so they are dividing by 1.

Some students may have difficulty understanding why 3/8 < ½ and 2/3 > ½ implies that 3/8 < 2/3. It may help to write the inequalities as 3/8 < ½ and ½ < 2/3 or show all three fractions on a number line.

Remind students that the open part of an inequality sign faces the greater fraction and the small, pointed part faces the lesser fraction.

Concepts/Content: Fraction Equivalence and

Ordering Fractions

Competencies/Skills: Use Visual Models Use Multiplication and Division Compare Fractions by Creating

Description of Activities: Problem-Solving Reading Mat Center Games Online Math Tools (www.pearsonrealize.com)


Benchmark Fractions Equivalent Fractions Use Common Numerators or

Denominators Understand the Procedure for

Finding Equivalent Fractions Use Multiplication and Division to

Find Equivalent Fractions Use Number Sense to Compare

Fractions

Videos (www.pearsonrealize.com) Quick Check Practice Buddy Math and Science Activity Problem-Solving Reading Activity Vocabulary Cards and Activity











Unit Title: Topic 9: Understand Addition and Subtraction of FractionsUnit Overview/Essential Understanding:

Models can be used to show addition of fractions as joining parts of the same whole. A fraction a/b, where a>1, can be decomposed into the sum of two of more unit or non-unit fractions in one or more ways where the

sum of the fractions is equal to the original fraction. Two fractions can be joined or added to find the total. There is a general method for adding fractions with like denominators. Models can be used to show subtraction of fractions as separating a part from the same whole. The difference between two fractions with like denominators can be found by separating one fractional amount from the other. There is

a general method for subtracting fractions with like denominators. Fraction addition and subtraction can be thought about as joining and separating segments on the number line. They can also be

thought about as counting forward or counting backward on the number line. Fraction sums and differences can be estimated by thinking about how each fraction relates to other fractions that are easy to add and

subtract mentally. Adding and subtracting mixed numbers is an extension of the ideas and procedures for adding and subtracting fractions. Two procedures for adding mixed numbers both involve changing the calculation to a simpler equivalent calculation. Two procedures for subtracting mixed numbers both involve changing the calculation to a simpler equivalent calculation. These are

extensions of the same procedures used for adding mixed numbers with like denominators. Good math thinkers choose and apply math they know to show and solve problems from everyday life.


use fraction strips and number lines to add fractions decompose a fraction or mixed number into a sum or fractions in more than one way solve problems involving joining parts of the same whole by adding fractions use tools such as fraction strips, area models, and number lines to subtract fractions solve problems involving separating parts of the same whole by subtracting fractions count forward and backward on a number line to add or subtract use number lines and benchmark fractions to estimate fraction sums and differences use models and equivalent fractions to add and subtract mixed numbers use equivalent fractions and properties of operations to add mixed numbers with like denominators use equivalent fractions, properties of operations, and the relationship between addition and subtraction to subtract mixed numbers

with like denominators use previously learned concepts and skills to represent and solve problems

Focus Standards Addressed in this Unit: CC.2.1.4.C.1 – Extend the understanding of fractions to show equivalence and ordering CC.2.1.4.C.2 – Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers


Misconceptions: Some students may want to add the denominators. While working with the models, point out that after joining the 5 segments and the

2 segments, there are still 10 segments or 10 equal parts between 0 and 1. Some students may not understand there are several ways to decompose 5/6. Remind them of making ten in many different ways.

Explain to students that another way to decompose 5/6 is to use what they know about unit fractions, 5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6. Ask students if the number of equal parts changes after taking away 2/8. Pointing out that the result is 6/8 and the denominator is still

eighths will help students make the transition to subtracting fractions symbolically in later lessons without subtracting the denominators. Emphasize the similarity between the generalization of how to subtract fractions with like denominators, to the generalization for how

to add fractions with like denominators. The denominator stays the same in both. This can help prevent students from subtracting the denominators.

Some students may still add the denominators. Ask them how many equal segments the number line is divided into and if that changes after they add. Point out that the number of equal segments on the number line stays the same when parts of the same whole are combined or separated.

Remind students to use equivalent fractions to subtract 1 – ¼. Some students will recognize that 6/12 and ½ are equivalent fractions. Remind students that, because they are equivalent, neither is

more or less mathematically precise.

Concepts/Content: Addition of Fractions Subtraction of Fractions Multiplication of Fractions Decomposition of Fractions

Competencies/Skills: Add and Subtract Fractions Understand Why the Procedure

for Adding and Subtracting Fractions Works

Use Number Sense to Estimate Fraction Sums and Differences

Make Sense of Multiplying a Whole Number by a Fraction or Mixed Number

Join and Separate Fractions Decompose Fractions Solve Problems Involving Fraction

Addition, Subtraction, and Multiplication

Connect Addition and Multiplication

Multiply with Unit Fractions Multiply with Other Fractions








Unit Title: Topic 10: Extend Multiplication Concepts to FractionsUnit Overview/Essential Understanding:

Any fraction a/b can be written as a times the unit fraction 1/b. Models and equations can be used to represent problems and compute products of whole numbers and fractions. Models and equations can be used to represent problems and compute products of whole numbers and a mixed number. The standard algorithms for adding, subtracting, multiplying, and dividing can be used to solve time problems. Good math thinkers choose and apply math they know to show and solve problems from everyday life.

Unit Objectives:At the end of this topic, students will be able to independently use their learning to:

use a model to understand a fraction as a multiple of a unit fraction use models to multiply fractions by whole numbers use symbols and equations to multiply a fraction by a whole number use drawings and equations to represent and solve problems involving multiplying a whole number and mixed number use the four operations to solve problems involving time use previously learned concepts and skills to represent and solve problems

Focus Standards Addressed in this Unit: CC.2.1.4.C.2 – Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers






CC.2.4.4.A.1 – Solve problems involving measurement and conversions from a larger unit to a smaller unit


Misconceptions: Students see the convention of multiplying the whole number by the numerator and putting the result over the denominator. Some

students may want to also multiply the denominator by 3. Remind them that multiplying both the numerator and denominator by the same nonzero number gives an equivalent fraction. It is the same as multiplying by 1, not by 3.

Some students may have difficulty seeing the result of 10 x ¼ as 10/4. Remind them that in the precious lesson, they wrote 10/4 as 10 x ¼. If 10/4 = 10 x ¼, then 10 x ¼ = 10/4.

Some students may want to multiply both the numerator and denominator by 2. Emphasize that you are finding how many 1/4s there are altogether. You multiply the whole number times the numerator of the fraction and the product tells how many 1/4s in all, not 1/8s.

Concepts/Content: Addition of Fractions Subtraction of Fractions Multiplication of Fractions Decomposition of Fractions

Competencies/Skills: Add and Subtract Fractions Understand Why the Procedure

for Adding and Subtracting Fractions Works

Use Number Sense to Estimate Fraction Sums and Differences.

Make Sense of Multiplying a Whole Number by a Fraction or Mixed Number

Join and Separate Fractions Decompose Fractions Solve Problems Involving Fraction

Addition, Subtraction, and Multiplication

Connect Addition and Multiplication

Multiply with Unit Fractions Multiply with Other Fractions


Assessments: Practice Buddy



Quick Check Online Topic Assessment Topic Assessment Basic Facts Timed Test Computation Assessments (created)




Unit Title: Topic: 11: Represent and Interpret Data on Line PlotsUnit Overview/Essential Understanding:

A line plot organizes data on a number line and is useful for showing how data are distributed. Data from line plots can be used to solve problems. Good math thinkers use math to explain why they are right. They can talk about the math that others do, too.


read and interpret data using line plots represent data using line plots and interpret data in line plots to solve problems solve problems involving line plots and fractions critique the reasoning of others using an understanding of line plots

Focus Standards Addressed in this Unit: CC.2.1.4.C.1 – Extend the understanding of fractions to show equivalence and ordering CC.2.1.4.C.2 – Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers CC.2.4.4.A.4 – Represent and interpret data involving fractions using information provided in a line plot

Important Standards Addressed in this Unit: CC.2.4.4.A.2 – Translate information from one type of data display to another






Misconceptions: Make sure students understand that the number of dots refers to the number of pencils that are of a given length and not to the length

itself. Some students may think the heaviest water balloon is the one with the most dots above it on the line plot, that is, they may think the

heaviest water balloon Alma filled weighed 1 3/8 pounds.Concepts/Content:

Reading and Making Line Plots Using Line Plots to Solve Problems

Competencies/Skills: Read Line Plots Make Line Plots Use Data in Line Plots













Unit Title: Topic 12: Understand and Compare DecimalsUnit Overview/Essential Understanding:

A decimal is another way to represent a fraction. Points on a number line can represent fractions and decimals. A fraction and a decimal tell the distance a point is from 0 on the number

line. Place value can be used to compare decimals. Fractions with denominators of 10 can be written as equivalent fractions with denominators of 100. Fractions with like denominators

can be added. Fractions and decimals can be used to represent amounts of money. Pictorial models and equations can represent problems involving

money. Good math thinkers look for relationships in math to help solve problems.


relate fractions and decimals with denominators of 10 and 100 locate and describe fractions and decimals on number lines compare decimals by reasoning about their size add fractions with denominators of 10 and 100 by using equivalent fractions use fractions or decimals to solve word problems involving money use the structure of the place value system for decimals to solve problems

Focus Standards Addressed in this Unit: CC.2.1.4.C.3 – Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100) CC.2.4.4.A.1 – Solve problems involving measurement and conversions from a larger unit to a smaller unit


Misconceptions: Students may erroneously write 6/10 as the decimal 0.06. The value of the first place to the right of the decimal point is tenths. If

needed, draw a place-value chart to illustrate the place values to the right of the decimal point. Some students may count tick marks instead of spaces. Remind students that they are showing distances on the number line. A unit is

the distance between two tick marks, which can be called a space. Some students may confuse lesser decimals with greater ones because of the value of the digits when looking from right to left. Remind students that although the monetary value of the total will remain the same, there are multiple combinations of bills and coins

that can be used.

Concepts/Content: Decimals Equivalent Fractions Fraction Addition

Competencies/Skills: Relate Fractions and Decimals Locate Decimals on the Number

Line Understand Decimal Comparison Add Fractions with Denominators

of 10 and 100. Understand Decimals Understand Decimal Comparison Compare Decimals Add Fractions








Unit Title: Topic 13: Measurement: Find Equivalence in Units of MeasureUnit Overview/Essential Understanding:

To convert from a larger unit of length to a smaller unit of length, multiply the number of larger units by the conversion factor, that is, the number of smaller units in each larger unit.

To convert from a larger unit of capacity to a smaller unit of capacity, multiply the number of larger units by the conversion factor, that is, the number of smaller units in each larger unit.

To convert from a larger unit of weight to a smaller unit of weight, multiply the number of larger units by the conversion factor, that is, the number of smaller units in each larger unit.

Some problems can be solved by applying the formula for the perimeter of a rectangle or the formula for the area of a rectangle. Good math thinkers are careful about what they write and say, so their ideas about math are clear.


recognize the relative size of customary units of length and convert from a larger unit to a smaller unit recognize the relative size of customary units of capacity and convert from a larger unit to a smaller unit recognize the relative size of customary units of weight and convert from a larger unit to a smaller unit recognize the relative size of metric units of length and convert from a larger unit to a smaller unit recognize the relative size of metric units of capacity and mass, and convert from a larger unit to a smaller unit rind the unknown length or width of a rectangle using the known area or perimeter be precise when solving measurement problems

Focus Standards Addressed in this Unit: CC.2.1.4.B.2 – Use place value understanding and properties of operations to perform multi-digit arithmetic CC.2.1.4.C.2 – Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers






CC.2.4.4.A.1 – Solve problems involving measurement and conversions from a larger unit to a smaller unit


Some students may have difficulty multiplying 7 ¾ x 12. Remind them that they can use the Distributive Property to break apart a mixed number. 7 ¾ x 12 = (7 + ¾) x 12 = (7 x 12) + (3/4 x 12) = 84 + 9 = 93.

Some students may think the units for the answer should be ounces. Point out that 54 ounces divided into servings with 9 ounces in each serving gives the number of servings, not the number of ounces.

Make sure students make the connection that 200 cm is greater than 175 cm means that 2 meters is greater than 175 centimeters. Check that students understand that when finding perimeter, they add the length and width twice, but when finding area, they only use

the length and width once when multiplying. Some students may want to add the area of the top or bottom of the fish tank. Explain that the plastic is only going around the sides, so

Piper does not need enough plastic to cover the top or the bottom.Concepts/Content:

Equivalent Measurements Customary Units Metric Units Area and Perimeter Relative Sizes of Units

Competencies/Skills: Understand Customary and

Metric Units Understand Area and Perimeter Convert Measurements Use Formulas



Interdisciplinary Connections:Math and Science Project – Science (TE p.671)

Additional Resources: https://www.pearsonrealize.com/index.html#/ https://www.ixl.com/math/grade-4





https://xtramath.org/#/home/index https://www.sumdog.com/ https://www.teacherspayteachers.com/ Pearson, enVisionmath2.0


Unit Title: Topic 14: Algebra: Generate and Analyze PatternsUnit Overview/Essential Understanding:

Rules can be used to create or extend number sequences that form a pattern. Those patterns sometimes have features not described by the rule.

Rules can be used to create or extend patterns in tables. Patterns sometimes have features not described by the rule. It is possible to predict a shape in a repeating pattern of shapes. Good math thinkers look for relationships in math to help solve problems.


create or extend a number sequence based on a rule. Identify features of the pattern in the sequence that are not described by the rule use a rule to extend a number pattern and solve a problem identify features of the pattern generate a shape pattern that follows a given rule and predict a shape in the pattern solve problems by using patterns

Focus Standards Addressed in this Unit: CC.2.2.4.A.4 – Generate and analyze patterns using one rule


Some students might think all number patterns must increase. Another Example! Is an example of a number pattern that decreases. Some students may think the tables are the same. Make sure they understand that with the first table they know the number of

cloverleaves and with the second table they know the number of leaflets. As they will learn in Grade 6, in one table the number of cloverleaves is the independent variable and in the other table, the number of leaflets is the independent variable.

Some students may have trouble understanding why the 49th shape is a triangle. Ask guiding questions to help them understand.Concepts/Content: Competencies/Skills: Description of Activities:




Algebra: Generating and Analyzing Patterns

Addition, Subtraction, Multiplication, and Division Rules

Repeating Number Patterns Repeating Shapes

Understand Relationships Understand Types of Patterns Generate Values Use Addition, Subtraction,

Multiplication, and Division Rules

Problem-Solving Reading Mat Center Games Online Math Tools (www.pearsonrealize.com) Videos (www.pearsonrealize.com) Quick Check Practice Buddy Math and Science Activity Problem-Solving Reading Activity Vocabulary Cards and Activity












Unit Title: Topic 15: Geometric Measurement: Understand Concepts of Angles and Angle MeasurementUnit Overview/Essential Understanding:

Line segments and rays are sets of points that describe parts of lines and angles. Angles are classified by their measure. The measure of an angle depends upon the fraction of a circle that the angle turns through. The unit for measuring angles is 1 degree, the unit angle. The unit for measuring angles is 1 degree, the unit angle. A protractor can be used to measure angles. Angle measures can be added and subtracted. Good math thinkers know how to pick the right tools to solve math problems.


recognize and draw lines, rays, and angles with different measures find the measure of an angle that turns through a fraction of a circle use know angle measures to measure unknown angles use a protractor to measure and draw angles use addition and subtraction to solve problems with unknown angle measures use appropriate tools, such as a protractor and ruler, to solve problems

Focus Standards Addressed in this Unit: CC.2.3.4.A.1 – Draw lines and angles and identify these in two-dimensional figures CC.2.4.4.A.6 – Measure angles and use properties of adjacent angles to solve problems


An angle’s vertex is the shared endpoint of two rays. Some students may think the size of an angle depends on the lengths of the rays. Draw two circles that are obviously different sizes on

the board. Draw angles in the circles that both turn through 2/6 or 1/3 of the circle. They are the same size because they are open the

same amount and turn through the same part of the circle. The rays go on forever, so it does not matter how long the rays are. Remind students that just as you can add the parts to find the whole (n + 60 = 90), you can also subtract a part from the whole to find

the other part (n = 90 - 60).Concepts/Content:

Angle Concepts Measuring Angles Protractor Usage

Competencies/Skills: Identify Points, Lines, Line

Segments, and Rays Identify Angles Measure Angles Use Known Angles to Measure

Angles Use a Protractor Add and Subtract Angle Measures Understand Angle Measure Understand Unit Angles













Unit Title: Topic 16: Lines, Angles, and ShapesUnit Overview/Essential Understanding:

Lines can be classified as parallel, intersecting, or perpendicular. Triangles are classified by their sides and by their angles. Quadrilaterals are classified by their sides and by their angles. A shape that can fold along a line into matching part is line symmetric. Good math thinkers use math to explain why they are right. They can talk about the math that others do, too.


draw and identify perpendicular, parallel, and intersecting lines classify triangles by line segments and angles classify quadrilaterals by lines and angles recognize and draw lines of symmetry. Identify line symmetric figures draw figures that have line symmetry use understanding of two-dimensional shapes to critique the reasoning of others

Focus Standards Addressed in this Unit: CC.2.3.4.A.1 – Draw lines and angles and identify these in two-dimensional figures CC.2.3.4.A.2 – Classify two-dimensional figures by properties of their lines and angles CC.2.3.4.A.3 – Recognize symmetric shapes and draw lines of symmetry


Since all the quadrilaterals shown have at least one set of parallel lines, students may think that all quadrilaterals have a set of parallel lines. The only rule for a quadrilateral is that it is a four-sided closed shape.

Some students may think that any line is a line of symmetry if it divides a figure in half. Have them fold a rectangle sheet of paper on one of its diagonals. Guide them to see that while the halves are the same shape and size, they do not fit exactly on top of each other when the rectangle is folded along the diagonal. The diagonal is not a line of symmetry.

Some students may draw a translation of the figure instead of a reflection. Have them trace their figure on dot paper, cut it out, and fold it to see if the two sides match.

Some students may think that because a counterexample shows that a statement is false, that examples can show that a statement is

true. Concepts/Content:

Lines Plane Shapes Lines of Symmetry Points, Lines, Line Segments,

Rays, and Angles

Competencies/Skills: Classify Plane Shapes Identify Lines, Line Segments,

Rays, and Angles Fold and Draw Lines of Symmetry












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