# MA.K.AR.1.2

Given a number from 0 to 10, find the different ways it can be represented as the sum of two numbers.

### Clarifications

Clarification 1: Instruction includes the exploration of finding possible pairs to make a sum using manipulatives, objects, drawings and expressions; and understanding how the different representations are related to each other.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

• Equation
• Expression

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is to allow students to continue to flexibly discover various sums as they work towards procedural reliability in Kindergarten, and automaticity in grade 1 (MTR.2.1, MTR.5.1).
• Instruction allows students to see multiple ways to add numbers to make a given number, such as 1 + 3, 2 + 2, and 3 + 1 are all ways to make 4 (MTR.2.1).
• Instruction includes the use of manipulatives and pictorial representations.
• Instruction includes the use of context to provide a purpose for adding (MTR.7.1).
• Instruction includes making connections to subtraction equations related to addition equations (MTR.5.1).
• Items include equations with one or both addends unknown.
• Though there is no expectation that students name the commutative property, they should begin to discover the connections and patterns and recognize that if a + b = 10, then b + a = 10.

### Common Misconceptions or Errors

• Students may not connect pairs of addends through the commutative property. Though there is no expectation that students name the commutative property, they should begin to discover the connections and patterns and recognize that if a + b = 10, then b + a = 10.
• Students may not recognize that multiple pairs of addends represent the same sum.
• Students may not recognize that the two numbers don’t have to be different.
• For example, if the given number is 8 a student may not think to represent it as 4+4.

### Strategies to Support Tiered Instruction

• Teacher provides opportunities to solve multiple expressions with the same sum using snap cubes (representing each addend with a different color).
• For example, students use snap cubes to build 3 + 4, 2 + 5, and 1 + 6 to represent a sum of seven.

• Instruction provides opportunities to build multiple pairs of addends to represent given numbers 1 – 10 using snap cubes, two-color counters, hands, etc.
• For example, given the number 6, students model 1 + 5, 2 + 4, and 3 + 3 using snap cubes. Process repeats with multiple numbers, including odd numbers, so students begin to recognize that some numbers have repeating addends and others do not. Discussion should focus on the fact that the two addends can be the same number.

• Instruction includes the opportunity to build sets of five using two-color counters to represent the commutative property.
• For example, students build 3 + 2 and 2 + 3 and 4 + 1 and 1 + 4. Students should write an equation to represent the counters. Teacher asks: How is the set of 3 + 2 and 2 + 3 the same? How are they different? Does it matter which addend comes first? Do you get the same sum if you add them in a different order? Students should use the models to develop the understanding that the order of the addends does not change the sum.

• Teacher provides instruction for using two-color counters to decompose a number into multiple addends that represent the same sum.
• For example, students decompose a group of 7 counters into 6 red/1 yellow, 5 red/2 yellow, and 3 red/4 yellow. They write an equation for each representation to show that multiple pairs of addends can make the same sum.

• Instruction includes the opportunity to use addend cards to build equations that represent doubles facts. Alternatively, math racks, dot cards, ten frames, etc... can be used in place of addend cards.
• For example, students are provided with array cards that represent multiple numbers. Students will need more than one of each card. Students use the cards to build equations for doubles facts and record the equation in writing.

Show a student a number of counters from 0 to 10. Cover some of the counters and ask the student how many counters are hidden. Give the student an opportunity to record an equation for the situation. Repeat the task by covering different amounts of counters and/or starting with a different amount of counters.

Write as many equations as you can to get to a sum of 9, a sum of 5, a sum of 6 and a sum of 7.

### Instructional Items

Instructional Item 1

Find three different ways to get to 8 by adding 2 numbers together.

Instructional Item 2

Complete the equations to show different ways to make 7.
5+___= 7
___+4 = 7
7 = ___ + ___

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
5012020: Grade Kindergarten Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712015: Access Mathematics - Grade Kindergarten (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012005: Foundational Skills in Mathematics K-2 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.K.AR.1.AP.2: Given a number from 0 to 5, find the different ways it can be represented as the sum of two numbers.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Vanilla and Chocolate Cupcakes:

Students are asked to find all possible pairs of numbers that sum to six in the context of a word problem.

Type: Formative Assessment

Planting Rose Bushes:

Students are asked to find all possible pairs of numbers that sum to nine in the context of a word problem.

Type: Formative Assessment

## Lesson Plans

Students will play a fun game using paper cups and counters to "roll" out combinations to make a ten.

Type: Lesson Plan

Go Fish! Ways to make 10.:

Go Fish is a really fun and interactive way to teach kindergartners about the number pairs that equal ten. This hands-on lesson will give students the engaging practice that they need to not only build number bonds to ten but also to find the missing addend and count up to ten. Students will love the Go Fish game and want to play it over and over again!

Type: Lesson Plan

Wow! That's Ten!:

This activity will show students how exciting it can be to find groups of ten. The students must be able to recognize the number that is given as the first addend. They must then be able to work, using counters and a ten frame, toward creating another group that they can add to the first group to total one group of ten. They will work first with a partner using counters and during the assessment they would be expected to work on their own. Their completion of the assessment would show just how much of the skill they have or have not mastered.

Type: Lesson Plan

An Amazing Sunny Day Story- Ways to Make 10:

In this lesson, students are shown a picture of a beach scene. They are asked to identify groups of ten within the picture. There are three pre-determined groups of ten with noticeable parts (people, starfish, coconuts). Using the picture, students will identify a group of ten, create an addition equation for the parts, and transfer the equation into sentences to tell the story.

Type: Lesson Plan

Ten to Win!:

While playing Ten to Win, children represent numbers on a ten frame & determine how many more are needed to make ten. The game reinforces the number partners that make ten and supports fluency of addition and subtraction within ten.

Type: Lesson Plan

Number Pairs to Ten:

In this lesson, the students will create and write equations for all of the ways to make ten on a ten-frame.

Type: Lesson Plan

Quacking Addition – Sums within Ten:

This activity deepens the students' understanding of addition and recording addition sentences by using an engaging story about ducks in a pond.

Type: Lesson Plan

Shelves of Shells!:

In this lesson students will help the teacher organize seashells on two shelves. Students will represent the number ten as the sum of two numbers and then create an addition sentence to match their "shelves of seashells." Students will also be asked to create all the ways to make ten.

Type: Lesson Plan

Balancing Equations:

This is an engaging, hands-on lesson to help the students understand the meaning of the equal sign. The lesson is written using a pan/equal arm balance but may be done with just connecting cubes.

Type: Lesson Plan

Decomposition with Cheerios:

In this lesson, students will use Cheerios as manipulatives for decomposing numbers 5-10. Students will be encouraged to decompose numbers in as many different ways as possible. Students will also record their decompositions as addition equations.

Type: Lesson Plan

Sums of Ten Pyramid:

In this lesson, students will play a card game to practice finding pairs of numbers that make 10 when added.

Type: Lesson Plan

Popsicle Math:

This lesson explores ways to represent 10. The students will use two sided counters to investigate the ways that 10 can be broken apart and put back together. The students will also work in pairs to collaborate and expand their understanding of the concept.

Type: Lesson Plan

Monster Math - Composing and Decomposing the Number 10:

This activity will have students finding ways to make ten. Students use two colors of linking cubes to make and record equations of ten.

Type: Lesson Plan

Disc Drop - Decomposing Ten:

In this lesson, students will use two-sided colored counters (discs) to decompose the number ten.

Type: Lesson Plan

Students will use number bracelets to practice representing numbers less than or equal to ten as a sum of two numbers. They will manipulate beads to find all possible combinations of making one number. This lesson required students to work with partners.

Type: Lesson Plan

Five Little Ducks - Decomposing Number 5:

In this activity students will recite the Five Little Ducks poem to decompose numbers using manipulatives and equations to represent the math.

Type: Lesson Plan

Making Numbers in More Than One Way:

In this lesson, students will find the different ways a given number can be represented as the sum of two numbers. Students will use linking cubes, colored squares of construction paper, and written expressions.

Type: Lesson Plan

Making Tens with Caterpillars:

In this lesson, students create caterpillars using two different colored circles to emphasize the addends that make 10. Students then write the equation they create, and do a gallery walk to record the other combinations that make 10.

Type: Lesson Plan

Math Sticks:

In this activity, students practice decomposing numbers one through five, using fuzzy sticks and beads, and recording the equation for each decomposition.

Type: Lesson Plan

## Perspectives Video: Teaching Ideas

The Van de Walle Dot Matrix: A tool to support concepts from counting to multiplying polynomials:

Unlock an effective teaching tool that can help students all the way from basic counting principles to multiplying polynomials.

Type: Perspectives Video: Teaching Idea

Connecting Geometry to Numbers:

Unlock an effective teaching strategy for connecting geometry and numbers in order to build number sense in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Equations on the Math Balance:

Unlock an effective teaching strategy for teaching inequalities and equations with the math balance in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Boys and Girls, Variation 2:

This task represents the Put Together/Take Apart with both addends unknown context for addition and subtraction. Once a student finds one correct answer, he/she can be encouraged to find another. Ask the student to use objects, pictures, or equations to represent each answer.

## MFAS Formative Assessments

Planting Rose Bushes:

Students are asked to find all possible pairs of numbers that sum to nine in the context of a word problem.

Vanilla and Chocolate Cupcakes:

Students are asked to find all possible pairs of numbers that sum to six in the context of a word problem.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Boys and Girls, Variation 2:

This task represents the Put Together/Take Apart with both addends unknown context for addition and subtraction. Once a student finds one correct answer, he/she can be encouraged to find another. Ask the student to use objects, pictures, or equations to represent each answer.