Any Order

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The students will be able to use the commutative property to find sums of related addition facts.

Big Idea

The numbers in an addition number sentence (addends) can be added in any order and the sum remains the same.


10 minutes

The lesson begins by asking the students to explain what they know about addition problems.  The hope is they would acknowledge that there are two addends, which when added together equal the sum.  Then ask the students to make a train of 4 with one color cube and a train of 5 of another color.  Ask the children to demonstrate how they would show that they were adding those two trains together.

Develop the Concept

20 minutes

Have the students use their individual white boards to write a number sentence for how many cubes they have in all.  Have the students show their white boards and have students look around at each other’s boards.  Does everyone have the same number sentence?  Have the students compare boards with a classmate, and turn and talk with their classmate about if there is more than one number sentence that could be written for the cube train they made with both colors.  If necessary, remind the students about the order of addends.  Once they have had ample time to discuss, have the students share their thinking.  Remind the students of the No Matter the Order... chant that we use about addend order.  “No matter the order the addends are in, the sum remains the same. Cha, Cha!”

Practice the Concept

20 minutes

Have students work in partners to create another cube train with two different colors.  Have each partner use the Large Graph Paper and color the squares to represent the cube train they have created.  Ask students to turn and talk to discuss how they could use the same cube train to represent two addition number sentences. 

Following the student discussion, glue the graph paper “train” to construction paper and write the number sentences below the Adding in Any Order model.  Have the students complete as many of these examples as you see necessary. 

When students have demonstrated understanding with 3 or 4 examples, have them independently complete the Any Order Practice page to demonstrate understanding.


10 minutes

Have students come back together as a class.  Encourage students to turn and talk about what they learned about adding in any order.  Ask the students “How do you think this strategy could help you build your math fact fluency?”