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8+7+2 is equivalent to 7+8+2 which is equivalent to 7+10 which equals 17.Clarifications
Clarification 1: Within this benchmark, the expectation is to apply the associative and commutative properties of addition. It is not the expectation to name the properties or use parentheses. Refer to Properties of Operations, Equality and Inequality (Appendix D).Clarification 2: Instruction includes emphasis on using the properties to make a ten when adding three or more numbers.
Clarification 3: Addition is limited to sums within 20.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Associative Property of Addition
- Commutative Property of Addition
- Equation
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to explore addition and think flexibly when it comes to adding three numbers together such as rearranging addends, looking for doubles, making a ten, etc. In Kindergarten, students find ways to make a ten when given a 1 to 9 digit. Students also find ways to represent a given number from 0 to 10 as the sum of two numbers (MTR.2.1, MTR.5.1).- Instruction includes use of manipulatives to model addition problems within 20 (MTR.5.1).
Common Misconceptions or Errors
- Students may not understand that when three numbers are rearranged the sum will still be the same. In this case, open a class discussion by showing the following expressions A. 3 + 9 + 4 and B. 9 + 4 + 3 and ask students what they notice about the expressions. Once a student notices that they both expressions have the same exact numbers but that the numbers are arranged in a different order ask, “Do you think they will have the same sum?” Have students share how they could solve the expressions using a strategy. Then discuss the sums of both equations being 16 and when one adds the same numbers together but in a different order it will always have the same total.
Strategies to Support Tiered Instruction
- Instruction provides opportunities to use a set of three number cards and make multiple equations with three addends. Students solve all equations and then discuss how they are similar and different.
- For example, students choose three numbers from a set of number cards and create the equations below. After students have finished solving the equations, they answer and discuss the following questions: How are the equations different? Students should discuss how the order of the addends is different in each equation. How are the equations the same? Students should conclude that the sum is always the same no matter the order in which the addends are added. Would the same thing happen if we used three different number cards? Would we be able to create equations in which the addends are in different orders? Would the sum be the same no matter the order in which we add the addends?
- Instruction provides opportunities to build equations with three addends in multiple orders to explore the concept of the commutative property.
- For example, the teacher provides the expression 3 + 2 + 4. Students build each addend using snap cubes and determine the sum. Teacher records the student work on chart paper. Teacher gives the students another expression 2 + 4 + 3. Students build each addend using snap cubes and determine the sum. Teacher adds the student work to the chart paper. Teacher gives the students a final expression 4 + 3 + 2. Students build each addend and determine the sum. Teacher adds the students work to the chart paper. Teacher asks “How are these equations similar? How are they different? What do you think would happen if we solved 3 + 4 +2?”
Instructional Tasks
Instructional Task 1 (MTR.2.1)
Provide students with three different colors of manipulatives (six of each color), three dice and a recording sheet.- Part A. Student rolls three dice and set out that many one color manipulatives per die that they rolled. Student arranges the manipulatives to create an addition sentence then records it.
- Part B. Student rearrange their manipulatives to create a new addition sentence and records it. Student thinks of another way they could get to their sum by creating a true equation.
Instructional Task 2 (MTR.5.1, MTR.6.1)
Melonie is working on solving an addition problem with three numbers. She says that she can make a ten with two of her numbers then add the third number. What could two of Melonie’s numbers be that would make a ten?
Instructional Items
Instructional Item 1
Using three digits, create an addition sentence that would have a sum of 18.
Instructional Item 2
The total of three numbers is eleven. What could the three numbers be?
Instructional Item 3
How many different ways can you get a total of seventeen when you toss three six-sided dice? Record each way.
Instructional Item 4
Which of the following addition problems will get the same sum asa. 2 + 6 + 2 + 4?
b. 2+4+8
c. 4+8+2
d. 8+6
e. 10+3+1
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
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Formative Assessments
Lesson Plans
Perspectives Video: Teaching Idea
Problem-Solving Task
Tutorial
STEM Lessons - Model Eliciting Activity
This MEA focuses on students' problem solving skills. After reading a story about what is in a piñata, students are asked to help a company find the best way to fill a piñata. It focuses on math skills, including counting and adding three numbers to make 20.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
In the story Curious George and the Pizza Party (by Rey, H.A., and Margret Rey), Curious George attends a pizza party for a friend. Now the man with the yellow hat wants to plan his own pizza party for Curious George, but he needs the students' help. Help the man with the yellow hat use the data about the different pizza companies in his area to rank the options from best to worst, considering the toppings offered, crust options, prices, and customer satisfaction ratings. Then the students will use the special promotions from each pizza company and their math skills to figure out which pizza place offers the best deals. Each team of students will write letters to the man with the yellow hat explaining how they ranked the companies and why they chose their rankings to help him choose the best pizza for George's party.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students are asked to solve word problems that call for addition of three addends.
Students are asked to solve word problems that call for addition of three addends.
Students are given pairs of word problems that can be solved using the Commutative (and/or Associative) Property of addition.
Student Resources
Tutorial
Parent Resources
Problem-Solving Task
The language for this task is written above a 1st grade reading level, so it will need to be introduced verbally by the teacher. This problem helps students to practice adding three numbers whose sum are 20 or less. It is an open-ended problem with many solutions.
Type: Problem-Solving Task
