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Combining Foods

Number and Operations
Grace M. Burton
Location: unknown

In this lesson, students explore addition and comparison subtraction by modeling and recording related addition and subtraction facts for a given number. Comparison subtraction is the focus of this lesson because later in the unit, the students will explore the idea of "how many more?" to complete a set. The students also investigate the commutative property and model fact families, including those in which one addend is zero and those in which the addends are alike.

To review the concept of subtraction, name two sections of the food pyramid (vegetables, fruits, meats, cereal and grains, and milk and dairy products). Place the students in pairs and assign one student in each pair to locate three to five pictures of food belonging to the fruit section.

Ask the other student to find three to five pictures of meat. Now ask the pairs to discuss the number of food pictures that they collected all together and to compare the number of pictures each student collected. Call on a volunteer pair to describe the compilation and the comparison of their pictures in words and in addition and subtraction sentences. Repeat with other pairs. Then name a difference, such as two, and have each pair model the meaning of the subtraction sentence by combining all their pictures and making two new sets of food pictures. Call on several groups to explain how they constructed sets with the given difference. Repeat, if you wish, with other differences.

Using six food pictures in one group and one food picture in another group, ask the students to dictate a set of related addition and subtraction sentences that describe the joining and comparison of these groups.

407 six plus one with food

The sentences for these groups will be:

7 – 1 = 6
7 – 6 = 1
6 + 1 = 7
1 + 6 = 7

Ask the students whether the order of the addends changes the sum. [It does not.] Then ask whether the order of the numbers matters in a subtraction sentence. [It does matter. Subtraction is not a commutative operation.]

Next, have the students make two groups of food pictures of any size that they choose as long as the sum of the groups is 12 or less. Then ask them to generate addition and subtraction sentences that can be modeled using the pictures in their groups. If the students seem comfortable with this procedure, encourage them to make other pairs of picture groups with a sum of their choice and then combine and compare the groups, writing equations to describe each action. This activity is designed to help them focus on the commutative property and on the relation of subtraction to addition. When all the students are ready, suggest that they make a set of seven pictures and a set of zero pictures and write the four related addition and subtraction sentences, as shown below:

7 – 7 = 0
0 + 7 = 7
7 – 0 = 7
7 + 0 = 7

Then call the students together and ask a volunteer to make two sets. Call on a second student to write the two addition sentences, and ask a third volunteer to write the two subtraction sentences that the food picture groups suggest. You may wish to repeat this procedure with other trios of volunteers. Finally, invite one of the students to make two sets of food pictures, each containing three pictures. Call on a volunteer to write the related addition and subtraction sentences that use these sets. [These will be: 3 – 3 = 0 and 3 + 3 = 6.]

Finally, ask them to draw two of the groups that they made during this lesson and write number sentences that describe the combination and comparison of the groups. You may wish to add these recordings to their portfolios. These provide evidence of their growth in understanding of the important topics central to this lesson.

  • Crayons
  • Paper
  • Pictures of food


Assessment Options

At this point, you may wish to add more documentation to the Class Notes recording sheet. These notes will be valuable as you plan appropriate remediation and enrichment opportunities.


Move on to the last lesson, Try For Five.

Questions for Students 

  1. If one group has seven food pictures and another group has two pictures, how many will there be in all? How many more pictures are in the larger group?
  2. How many different addition and subtraction facts can I write if I make a group with five food pictures? How are the facts alike? How are they different?
  3. Can you show that 2 + 4 and 4 + 2 have the same sum?
  4. Suppose I make two groups each with four food pictures. What sentences will describe these groups?
  5. How could you help a friend model with pictures of food the number sentence 5 + 4 = 9? How about 5 + 0 = 5?
  6. How many addend pairs can you find for a sum of seven? What subtraction sentences do they suggest?

Teacher Reflection 

  • Which students easily used number sentences to record the combination of groups?
  • Which students easily recorded comparisons with number sentences?
  • Which students have some of the facts memorized?
  • Did most students remember the effects of adding or subtracting zero?
  • Which students were able to find all the members of a fact family?
  • 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?

Sorting Foods

Students sort foods using the categories of the Food Pyramid. They also create sets up to 10 and write numerals up to 10. Finally, students use an Internet-based tool to apply their knowledge of the Food Pyramid. This lesson makes a natural connection to the science of nutrition.

Eating Patterns

Students sort pictures of food and create patterns. They also analyze a partner's patterns and extend those patterns.

Pyramid Power

In this lesson, students make sets of a given number, explore relationships between numbers, and write numbers that name how many elements are in a group. They make and record sets of one more and one less than a given number.
Number and Operations

Try for Five

In this lesson, students explore the many ways to decompose numbers, and they build on their knowledge of addition and subtraction to find missing addends.

Learning Objectives

Students will:

  • Model related addition and subtraction facts up to 12.
  • Model the commutative property.
  • Review the role of the additive identity.
  • Generate fact families when they are given two addends.

NCTM Standards and Expectations

  • Connect number words and numerals to the quantities they represent, using various physical models and representations.
  • 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.

Common Core State Standards – Mathematics

-Kindergarten, Counting & Cardinality

  • CCSS.Math.Content.K.CC.C.6
    Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.1
    Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.2
    Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.5
    Fluently add and subtract within 5.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.B.3
    Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.B.4
    Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.C.6
    Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.D.7
    Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Grade 1, Number & Operations

  • CCSS.Math.Content.1.NBT.C.4
    Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Grade 2, Algebraic Thinking

  • CCSS.Math.Content.2.OA.B.2
    Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.7
    Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP4
    Model with mathematics.
  • CCSS.Math.Practice.MP5
    Use appropriate tools strategically.
  • CCSS.Math.Practice.MP6
    Attend to precision.