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Pyramid Power

Number and OperationsAlgebra
Grace M. Burton
Location: unknown

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.

Have the students each pick one picture of food. Now call out the name of a food group and ask all the students holding a picture of a food that is in that group to stand together. Repeat with each of the other food groups. Ask the students to tell how many students are in their group. Then ask for a volunteer to write that number on the board.

404 Fruit kids

In the example above, there are 3 fruits shown.

Now call out the names of two food groups, and ask the students holding pictures of foods from those groups to form a single group. Ask the rest of the students to tell how many are in the new combined group. Have a volunteer write the number on the board.

Ask for volunteers to write the numbers up to 10 on index cards. Then pull out one of the cards at random, and call on that many students to place their food picture in a group. Display a number that is either larger or smaller than the one you just displayed, and invite the students to tell how the group of pictures should be changed so that the new number describes the group (by adding or subtracting from the total number of pictures in the group). Call on a volunteer to choose the card with the appropriate number on it from the stack of numbered index cards. Repeat several times.

Next, put the students into groups and give each group a large assortment of food pictures. Display a numbered card (or number-word cards, if appropriate for your students), and ask the students to make a set with that many food pictures. When they are ready, ask the students to classify the food pictures in the set by arranging them according to the food groups to which they belong. Then have the students count each small set and label the set with a number describing the number of food pictures in each small set and in all the sets together. Then call on several volunteers to report what food groups were represented in their sets, how many were in each group, and how many there were in all.

Next, put the students into pairs and give each pair two number cubes. Ask the students to write "One More" and "One Less" on index cards. Then give one student in each pair the two file cards. Give the other student the number cubes and the food pictures. Ask the student who received the number cubes to roll them and make a set of food pictures with the number rolled. Then have the other student make sets of one more or one less and label each set with the correct index card. When they have done so, call on various groups to describe what they did. Have the partners switch roles and repeat this activity several times. Then ask them to record and label a set of six, a set of one more, and a set of one less.

  • Crayons
  • Index cards
  • Number cubes
  • Paper
  • Pictures of food

Assessment Options

  1. You may wish to add notes to the Class Notes recording sheet used in previous lessons or make a new record just for this lesson.
  2. Keeping a portfolio of student work provides evidence to support the students' understanding and allows you to interpret their level of performance.
Move on to the next lesson, Combining Foods.

Questions for Students 

  1. How many of your food pictures belonged to the dairy group? The meat group? How many pictures were in both groups together?
  2. What number words did we use that tell "how many"?
  3. Make a set of nine food pictures. How many food pictures would be in a set with one more? With one less? (Repeat with other numbers.)
  4. Here is a set of food pictures. How many are in this set? Make sets of one more and one less. How many are in a set with one more? How do you write that number? With one less? Write that number.
  5. What number comes after 6? After 11? Write those numbers.
  6. What number comes before 3? Before 10? Write those numbers.
  7. What number comes before 1? After 1? Write those numbers.
  8. How many food pictures will there be in a set of one less than six? In a set of one less?

Teacher Reflection 

  • Which cardinal (counting) number words were the students familiar with when the lesson began?
  • Were all the students able to recognize the numerals up to 12? If not, which numerals caused them trouble?
  • Were they able to make sets that corresponded to each numeral?
  • Could they write all the numerals up to 12? If not, which numerals were they not able to write?
  • Were all the students able to make sets of one more and one less for each number up to 12?
  • What adjustments would I make 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.
Number and Operations

Combining Foods

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.
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:

  • Create sets that correspond to a given number up to 12.
  • Count the elements in a set up to 12 members.
  • Record the number of elements in sets up to 12.
  • Decompose sets of numbers up to 12.
  • Construct sets of one more and one less than a given number.

NCTM Standards and Expectations

  • Connect number words and numerals to the quantities they represent, using various physical models and representations.
  • Count with understanding and recognize "how many" in sets of objects.
  • Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
  • Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.
  • Illustrate general principles and properties of operations, such as commutativity, using specific numbers.

Common Core State Standards – Mathematics

-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, 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.