Illuminations: Macaroni Math

Macaroni Math

Recording Two Ways

The students make sets of pasta shapes and count some away, then record the subtraction in vertical and horizontal formats. They draw a set and cross out some shapes, then write in both formats the subtraction that the drawing represents.

Learning Objectives
 
Students will:
  • model numbers to 10
  • identify sets to 10 and write the numeral for the set
  • find differences from numbers to 10 by counting back
  • record differences in vertical and in horizontal format

Materials
 
Pasta
Paper plates
Paper
Crayons
Index cards with numerals 0 to 10 written on them
Number cubes
Electronic Abacus Tool

Instructional Plan

Display the NCTM Electronic Abacus and demonstrate how to create a set of up to 10 counters on the top line (by clicking on the beads on the left).

Electronic Abacus Tool Electronic Abacus Tool

Then select a student to count one bead away from the set that you made. (By clicking on the beads, they will move from the left side of the abacus to the right side.) Call on a volunteer to write on the board the number sentence that shows what happened. (Example: 5 – 1 = 4.) Repeat and have other students take turns counting away one bead and writing the number sentence. Then repeat counting back more than one.

Give each student 10 to 12 pasta shapes and a paper plate. Then tell a story that involves counting back one such as, there were six pieces of pasta on the plate and Jerry took one. How many are left? Ask the students to model with pasta shapes what is happening as they listen to the story. Then ask them to write the numeral for the whole set, for what was taken away, and for what was left. Repeat with other stories. Check to see that all the students are able to write the numerals that correspond to each set.

Next, hold up an index card displaying a number (for example, 4), and ask the students to make a set with that many pasta shapes, place them on the plate, and record the number of pasta shapes on the plate. Then ask the students to count three pieces of pasta from the plate and record the number remaining on the plate. Now write the appropriate equation in horizontal format, and ask them to copy it. Now show another number and ask the students to make a set with that many pasta shapes, then call on a volunteer to tell how many pieces should be taken away this time. As the students model the subtraction, introduce the vertical subtraction format and ask them to also record the subtraction in this way. Ask them to compare the two formats.


Now put the students into pairs and give each pair a number cube. Assign one student in each group to roll the number cube twice, recording both numbers that come up. Tell the other student to model a subtraction by counting away the smaller number from the larger number. Tell the first student to record the subtraction in two different ways. Have them reverse their roles and repeat several times.

When the students are ready, ask each pair to read one of their subtraction examples and show the two ways they recorded it. Then ask the students to draw one subtraction situation of their choosing and record it in both vertical and horizontal formats.

Questions for Students
 

How many pasta shapes are in this set? (Show a set with eight pasta shapes.) Can you write that number? Now count three pieces of pasta away. Can you write that number? How many are left? Can you write that number?

[8; 3; 5]

What number sentence would show that you started with 10 pasta shapes and took 3 away? How could you show that in another way?

[10 - 3 = 7; Students should be able to show this vertically.]

What is alike between the two ways we recorded the differences? What was different?

[Both ways showed the same subtraction equation; One format was vertical, while the other format was horizontal.]

How could you help a younger student model 7 - 2?

[Student responses may vary.]

Suppose you started with eight pasta shapes and took four pieces of pasta away. What would the number sentence look like? What would a recording in the vertical format look like?

[8 - 4 = 4; Students should be able to write this in a vertical format.]

If the same number came up on both tosses of the number cube, what is the answer to the subtraction equation?

[0]

What two symbols did you use to mean "equals"?

[The equal (=) symbol; the bar in the vertical format functions as an equals sign.]

Assessment Options
 
  1. As you observe the students completing the activities in this lesson, you will be able to gather data about their growth in understanding. To help you document information on the individual needs and strengths of your students, a recording format, Class Notes recording sheet, is provided. The information you record at the end of each lesson may be useful when you discuss the students' progress toward learning targets with the students themselves and with their parents.
  2. Collect the subtraction situations created by the students at the conclusion of the lesson. Reviewing these situations will help you assess the students' level of understanding thus far.

Teacher Reflection
 
  • Which students were able to recognize sets up to 10 and write the numeral for the set?
  • Which students could record subtraction in the horizontal format? Which could record it in the vertical format?
  • What mathematical ideas need clarification?
  • What adjustments will I make 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. Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
  4. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  5. Connect number words and numerals to the quantities they represent, using various physical models and representations.
  6. Count with understanding and recognize "how many" in sets of objects.
  7. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
  
1 period   

NCTM Resources

Navigating through Number in preK‑2

 Activities
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