Topic 5: Work with Addition and Subtraction Equations

Pacing (Duration of Unit): 7 Lessons

Desired Results

Transfer:
1. Makes sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

Established Goals:

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

1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.3 Apply properties of operations as strategies to add and subtract.Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.

Student "I Can" Statements:

I can tell if addition or subtraction number sentences are true because I understand what an equal sign means.

I can figure out what a missing number is in an addition or subtraction problem

I can use different strategies for addition to solve word problems (within 20).

I can use different strategies for subtraction to solve word problems (within 20).

I can use solve word problems where I have to add 3 whole numbers.

I can use fact families to help me solve addition problems (commutative).

I can use addition facts I know well to help me solve problems where there are more than two numbers (associative).

Prerequisite Standards:

K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

K.CC.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

K.CC.7: Compare two numbers between 1 and 10 presented as written numerals.

K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

K.OA.2Solve addition and subtraction word problems and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

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

K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

K.OA.5Fluently add and subtract within 5.

Big Ideas:

Equivalence Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.

Operation Meanings & Relationships There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers and each operation is related to other operations.

Properties For a given set of numbers there are relationships that are always true, called properties, and these are the rules that govern arithmetic and algebra.

Variables, Expressions, and Equations
Letters and symbols, called variables, can be used to stand for a number or any number from a particular set of numbers. Some mathematical and real-world situations can be represented using variables, operations, and numbers in expressions and equations.

Solving Equations and Inequalities
Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.

Practices, Processes, and Proficiencies Mathematics content and practices can be applied to solve problems.

Essential Questions:

How can adding and subtracting help you solve or complete equations?

Students will know...

Models and the relationship between addition and subtraction can be used to solve equations with an unknown part.

An addition or subtraction equation is true if the values on each side of the equal sign are the same. An addition or subtraction equation is false if the values on each side of the equal sign are not the same.

An addition or subtraction equation is true if the values on each side of the equal sign are the same. Models, addition facts, and subtraction facts can be used to solve equations with an unknown part.

Numbers can be grouped in different ways to solve word problems with three addends.

Three numbers can be grouped and added in any order.

Objects, drawings, diagrams, and equations can help you solve different types of word problems.

Mathematicians are careful about what they write and say, so their ideas about math are clear.

Vocabulary:

Students will be skilled at...

Finding the unknown number in an equation.

Determining if addition and subtraction equations are true or false.

Finding the missing numbers in equations to make them true.

Using different strategies to solve word problems with 3 addends.

Using different strategies to add three numbers.

Solving word problems involving comparisons.

Using precision to determine the missing number or symbol in an equation.

Assessment Evidence

Performance Assessment:

Other Evidence:

Formative Assessments:

Learning Plan

Learning Activities:

5-1 Models and the relationship between addition and subtraction can be used to solve equations with an unknown part. 5-2 An addition or subtraction equation is true if the values on each side of the equal sign are the same. An addition or subtraction equation is false if the values on each side of the equal sign are not the same. 5-3 An addition or subtraction equation is true if the values on each side of the equal sign are the same. Models, addition facts, and subtraction facts can be used to solve equations with an unknown part. 5-4 Numbers can be grouped in different ways to solve word problems with three addends. 5-5 Three numbers can be grouped and added in any order. 5-6 Objects, drawings, diagrams, and equations can help you solve different types of word problems. 5-7 Mathematicians are careful about what they write and say, so their ideas about math are clear.

## Topic 5: Work with Addition and Subtraction Equations

Pacing (Duration of Unit): 7 Lessons## Desired Results

Transfer:1. Makes sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

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

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Established Goals:1.OA.1Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.1.OA.2Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.1.OA.3Apply properties of operations as strategies to add and subtract.Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)1.OA.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.1.OA.8Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.Student "I Can" Statements:Prerequisite Standards:K.CC.2:Count forward beginning from a given number within the known sequence (instead of having to begin at 1).K.CC.6:Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.K.CC.7:Compare two numbers between 1 and 10 presented as written numerals.K.OA.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.K.OA.2Solve addition and subtraction word problems and add and subtract within 10, e.g., by using objects or drawings to represent the problem.K.OA.3Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).K.OA.4For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.K.OA.5Fluently add and subtract within 5.Big Ideas:EquivalenceAny number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.

Operation Meanings & RelationshipsThere are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers and each operation is related to other operations.

PropertiesFor a given set of numbers there are relationships that are always true, called properties, and these are the rules that govern arithmetic and algebra.

Variables, Expressions, and EquationsLetters and symbols, called variables, can be used to stand for a number or any number from a particular set of numbers. Some mathematical and real-world situations can be represented using variables, operations, and numbers in expressions and equations.

Solving Equations and InequalitiesRules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.

Practices, Processes, and ProficienciesMathematics content and practices can be applied to solve problems.

Essential Questions:Students will know...Vocabulary:Students will be skilled at...## Assessment Evidence

Performance Assessment:Other Evidence:Formative Assessments:## Learning Plan

Learning Activities:5-1Models and the relationship between addition and subtraction can be used to solve equations with an unknown part.5-2An addition or subtraction equation is true if the values on each side of the equal sign are the same. An addition or subtraction equation is false if the values on each side of the equal sign are not the same.5-3An addition or subtraction equation is true if the values on each side of the equal sign are the same. Models, addition facts, and subtraction facts can be used to solve equations with an unknown part.5-4Numbers can be grouped in different ways to solve word problems with three addends.5-5Three numbers can be grouped and added in any order.5-6Objects, drawings, diagrams, and equations can help you solve different types of word problems.5-7Mathematicians are careful about what they write and say, so their ideas about math are clear.Resources:Problem of the Month:Centers:SmartBoard Resources/Games:*