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Adding in Any Order. Unit of Study: Addition and Subtractions Concepts Global Concept Guide: 4 of 5. Content Development.

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adding in any order

Adding in Any Order

Unit of Study: Addition and Subtractions Concepts

Global Concept Guide: 4 of 5

content development
Content Development
  • According to John Van De Walle (2010),“Although the commutative property may seem obvious to us (simply reverse the two piles of counters on the part-part-whole mat), it may not be as obvious to children. Because this property is quite useful in problem solving, mastering basic facts, and mental mathematics, there is value in spending some time helping children construct relationships” (p 153).
  • SMP 7 and 8 – students need to self discover
  • It is not essential for students to be able to specifically name the Commutative Property or to recite a definition. Allow students to express their own definitions of the property and document their findings on an anchor chart.
content development1
Content Development
  • Discuss with students how you can reverse the addends, but to be sure to identify what they represent.
  • Consider the following scenario:
    • There are 3 boys in the class. There are also two girls. How many student in all?



The 3 (boys) and 2 (girls) represent the same parts in the first model.

The 3 (boys) and 2 (girls) represent different parts in the second model and reverse their meaning.





day 1
Essential Question: Why can you add addends in any order?
  • During Day 1, engage students with hands-on activities that will allow them to explore the Commutative Property.
    • Use GO Math Lesson 1.6, On Your Own on p. 35 #4-9 to identify addition sentence that use the commutative property, Problem Solving on p. 36 #10-13 students can make connections between picture and numbers sentences.
  • Start students off with a problem solving scenario such as:
    • Jose has 3 lollipops and 2 candy bars. Julian has 2 lollipops and 3 candy bars. Who has more candy?
  • Students can record related addition sentences in their journal.

Turn Around Trains– Build snap cube trains as a

Hands-on alternative on this day.

Day 1
day 1 continued
Essential Question: Why can you add addends in any order?
  • Provide examples of addition sentences with two addends on each side and practice reading the equal sign as “is the same as”
  • This can be demonstrated on the iTools balance in order for students to make a connection with equal values.
  • By the end of Day 1, students will be able to add addends in any order.
  • Number Balance:
Day 1 Continued…

3+2 is the same as 2+3. Both sides have a value of 5.


day 2
Essential Question: How can the Commutative Property help me solve a problem?
  • Day 2 will continue with the use of manipulatives and problem scenarios to model the Commutative Property.
  • Commutative Property Lesson – Part One steps 1-5 on pages 2-3 to be used as an engage. The Commutative Property lesson has several applicable parts. Choose the lesson features that would address your students specific needs.
  • Providing exploration time and probingwith the Commutative Property and subtractions with HOT Questions such as:
    • Dante says that if 8-2=6 is true, then 2-8=6 must also be true. Do you agree or disagree with Dante’s thinking? Why or why not?
Day 2
day 2 continued
Day 2 Continued…

Essential Question: How can the Commutative Property help me solve a problem?

  • Go Math Lesson 1.7 Essentials: Listen & Draw on p. 37 use snap cubes to explore all the different ways to make 5, On Your Ownon p. 39 #11-21 to help students make an organized list and connect to the commutative property, Problem Solving on p. 40 #22-23 to demonstrate higher order thinking.
  • Make connections among the student discoveries by asking questions such as:
    • Which number sentences illustrate the Commutative Property that we discussed yesterday?
      • Go Math questions: 11, 21; 12, 20; 13, 19; 14, 18; 15, 17
  • Conversations about why question #16 doesn’t have a “partner” because it is a double fact.
  • By the end of Day 2, students will be able to use the Commutative Property to solve a problem and explain .
enrich reteach intervention
    • GO Math Chapter 1 Enrich Activity p. 33B utilizing graph paper
  • Reteach
    • GO Math Chapter 1 RtIActivity p. 33B
    • GO Math Reteach p. R6
    • Part Three – commutative link
  • Intervention/Small Group
    • GO Math Grade 1 RTI Intensive Intervention Skill 5