Illuminations: Macaroni Math

Macaroni Math

Who's in the Fact Family?

In this lesson, the exploration of the relation of addition to subtraction is continued as the students use problem-solving skills to find fact families, including those in which one addend is zero or in which the addends are alike.

Learning Objectives
 
Students will:
  • find missing addends
  • generate fact families given two addends or given one addend and the sum

Materials
 
Pasta shapes
Paper
Crayons

Instructional Plan

Give each student a paper plate. Ask the students to divide their plate down the middle. Tell them to put four pasta shapes on one side and two pasta shapes on the other side. (The purpose of this lesson is to explore the relationship between addition and subtraction.) Have the students record the number of pieces on each side, and then cover one side. Ask what subtraction sentence they could write to describe the "take away" situation. Have them repeat the exercise by covering the other side.

Then ask what addition sentences describe how the two sets can be joined. Finally, ask the students to write the four sentences these two sets suggest. [4 + 2 = 6; 2 + 4 = 6; 6 – 2 = 4; 6 – 4 = 2.] Have volunteers tell stories that fit each of the equations. This activity will help them focus on the relation of subtraction to addition. Now have them put four pasta pieces on one side of their plates and zero pieces on the other side.

 

 

Call on a volunteer to tell each of the appropriate subtraction and addition stories. Then call on another student to record the two addition and subtraction sentences.

4 + 2 = 6 2 + 4 = 6 6 – 2 = 4 6 – 4 = 2

If the students seem comfortable with this process, distribute pasta shapes to pairs of students and have them take turns making two sets, covering one group of pasta shapes, and writing equations. Then call the students together and ask a volunteer to make two sets and write the four number sentences (two addition and two subtraction) that the sets of pasta suggest. You may wish to repeat this with other volunteers. Invite one of the students to make two sets, each with five pasta shapes, and write the related addition and subtraction sentences. [There will be only one of each.] Finally, ask the students to write the set of number sentences that would be appropriate if one set had six pieces of pasta and the other had zero.

Tell the students that you are thinking of a piece of paper that has eight pieces of pasta in all, and two are on the left side. Ask them to determine how many are on the right side of the paper. Invite the students to consider the equation: 2 + _ = 8. Remind students that eight is the sum and that the other two numbers are addends. Ask: What is the missing addend? [Six] Repeat with other examples. Ask the students to record one of the examples and to illustrate it with a picture.

Questions for Students
 

If one side has seven pasta shapes and the other side has two pasta shapes, what subtraction sentences can you write?

[7 - 2 = 5 or 7 - 5 = 2]

How many addition and subtraction facts can you write if you put four pasta shapes on one side and five pasta shapes on the other? How are the subtraction facts alike? How are they different?

[Facts include:
4 + 5 = 9
5 + 4 = 9
9 - 4 = 5
9 - 5 = 4
They include the same numbers, but the order of the subtrahend and minuend are reversed.]

Suppose you make two sets, each with three pasta shapes. What sentences does this suggest?

[3 + 3 = 6, 6 - 3 = 3]

How could you help a friend find a subtraction fact related to 5 + 4 = 9? To 5 + 0 = 5?

[9 - 5 = 4 or 9 - 4 = 5; 5 - 0 = 5]

Name one addend pair for a sum of nine. What subtraction sentences do they suggest?

[Example: 3 + 6 = 9]

What is missing when I say 2 + "something" = 5? Can you write the complete subtraction sentence?

[3; 2 + 3 = 5]

Assessment Options
 
  1. The Questions for Students help the students focus on their current level of understanding.
  2. This is a good time for you to record on the Class Notes recording sheet which students are still having difficulty with the challenging concept of missing addends and plan remediation activities for them.

Teacher Reflection
 
  • Did most students remember the effects of adding or subtracting zero?
  • Which students met all the objectives of this lesson? What extension activities are appropriate for those students?
  • Which students are still having difficulty with the objectives of this lesson? What additional instructional experiences do they need?
  • What will I do differently the next time that I teach this lesson?

NCTM Standards and Expectations
 
Number & Operations Pre-K-2
  1. Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  2. Develop fluency with basic number combinations for addition and subtraction.
  3. Understand the effects of adding and subtracting whole numbers.
  4. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  
1 period   

NCTM Resources

Navigating through Number in preK‑2

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