Whos in the Fact Family
Unit: Macaroni Math
PreK to 2nd
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
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.
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
Move on to the last lesson, What's the Difference?
Questions for Students
1. 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.]
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.]
3. Suppose you make two sets, each with three pasta shapes. What sentences does this suggest?
[3 + 3 = 6, 6 - 3 = 3.]
4. 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.]
5. Name one addend pair for a sum of nine. What subtraction sentences do they suggest?
[Example: 3 + 6 = 9.]
6. What is missing when I say 2 + "something" = 5? Can you write the complete subtraction sentence?
[3; 2 + 3 = 5.]
Recording Two Ways
Grade: PreK to 2nd
How Many Left?
Where Will I Land?
What's the Difference?