Illuminations: Do It with Dominoes

Do It with Dominoes

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5

Lesson 6

Hopping on the Number Line

In this lesson, students generate sums using the number line model. This model highlights the measurement aspect of addition and is a distinctly different representation of the operation from the model presented in the previous lesson. The order (commutative) property is also introduced. At the end of the lesson, students are encouraged to predict sums and to answer puzzles involving addition.

Learning Objectives

Students will:

use the number line model to find sums
investigate the order (commutative) property of addition
solve and create puzzles using the number line

Materials

Dominoes
Number lines
Counters

Instructional Plan

Tell the students that they will find sums using the number line model. Then display a large number line and a 5+4 domino, that is, a domino with 5 spots on the left side and 4 spots on the right. Then demonstrate with a counter how a hop of 5 is taken on the number line. You may wish to encourage students to count aloud as the hop is made. Then make a hop of 4, starting at the place the counter landed. You might choose to have them record what happened using the equation notation 5 + 4 = 9, or to informally describe the moves this way: “If you take a hop of 5 spaces and then a hop of 4 spaces, you land on 9.” You may wish to highlight the fact that in this model, spaces are counted, not points on the number line.

After several trials, put the students in pairs and give each pair some dominoes, a counter, and individual number lines.

Number Lines Activity Sheet

Ask the students to take turns moving the counter on the number line to find the sum shown on the domino and recording the hops in pictures and in equation form. Ask them to draw the first hop and write the first numeral in green and the second hop and numeral in red. Encourage the students to predict the sums and to verify their predictions by moving a counter on the number line.

After allowing time for exploration, ask the students to predict the answers to questions such as “If I take a hop of 3 and then a hop of 5, where will I land?” [8] Now have students make up 2 similar problems on a piece of paper and trade them with a friend. Students should then solve their partners’ problems using the number line. When the pairs have finished, call them together to discuss what they did. Encourage them to use the number line in their explanation. Then ask “If I take a hop of 5 and then a hop of 4, where will I land?" [9] "How about if I take a hop of 4 and then a hop of 5?" [9] "Will this work every time?" [Yes] Encourage them to explore the order property by writing each first addend in green and each second one in red.

Be sure to lead a discussion about the order (commutative) property. You may need to use other examples to illustrate this important property of addition.

As a concluding activity, pose puzzles such as “I am the number you land on when you take a hop of 5 and then a hop of 1. Who am I?” [6] You may wish to encourage students to create and share similar problems. One or more of these puzzles could be added to their unit portfolios.

Questions for Students

What number did you land on when you made a 5-hop, then a 3-hop?

[8]

Could you land on the same number if you took a 3-hop first, then a 5-hop? How do you know?

[Yes; 5 + 3 = 8, and 3 + 5 = 8.]

What sums did you model with hops? How did you record them?

[Student responses will depend upon the "hops" they performed.]

Were any of the sums the same? Why?

[Student responses will depend upon the "hops" they performed.]

How would you find the sum of 2 and 5?

[Make a hop of 2, and then a hop of 5, to reach 7.]

How would you tell a friend to add on the number line?

[Student responses may vary.]

Assessment Options

The Questions for Students help students focus on the mathematics and aid you in understanding the students’ current level of knowledge and skill with the mathematical concepts of this lesson. You may want to add others that conversations with the students suggest.
A teacher’s resource, Class Notes, is provided to document your observations about student understanding and skills. You may find the information useful when planning additional learning experiences for individual students or for documenting progress for students with mandated instructional plans.

Extensions

Ask students, "How is using a number line like measuring? How is it different?"

Teacher Reflection

Which students counted as they took hops and which moved directly to the number?
What activities would be appropriate for students who met all the objectives?
Which students had trouble using the number line? What instructional experiences do they need next?
Did any children notice a connection with measurement?
What adjustments would you make the next time that you teach this lesson?

NCTM Standards and Expectations

Number & Operations Pre-K-2

Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
Develop fluency with basic number combinations for addition and subtraction.
Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
Understand the effects of adding and subtracting whole numbers.
Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.

This lesson prepared by Grace M. Burton.