Wrapping Up the Unit

Pre-K-2
1

During this final lesson in the unit, the students use the mathematical knowledge and skills developed in the previous lessons as they visit five stations to review comparative subtraction.

Assign groups of four students each to work at one of the five stations. If you need more than five stations, you might choose to provide an extra computer for a sixth station.]

Station 1: High versus Low

Materials: Twelve index cards, numbered 0 through 11

Place the cards upside down in a stack in the center of the group and ask each student to draw one and place it face up where all can see it. To play, the students should order the cards from least to greatest, then find the difference of the highest and lowest card. The students who drew the highest and lowest cards record a tally mark, and all players return their cards to the deck that is then shuffled. Play continues until one student has five tally marks or time is up.

Station 2: How Many More?

Materials: fish-shaped crackers, paper, paper plates, number cubes

Each student rolls the dice and makes a plate that has as many fish-shaped crackers as the sum of the numbers thrown on the dice. Then the students compare the plates. The player with the plate with the most crackers finds the difference between the number of crackers on his or her plate and those of each of the other three plates, then makes a tally mark on a piece of paper. When time is up, the student with the most tallies wins the game.

Station 3: Spin, Spin, Spin

Materials: Adjustable Spinner, paper

[Before class, divide the Adjustable Spinner into 12 parts.] Direct the group to take turns spinning the spinner twice and recording the numbers. When all have recorded two numbers, ask them to subtract the smaller from the greater number. Then ask them to see whether anyone got a difference larger than everyone else. If so, that student wins a point. The student who has earned the most points when time is called wins the game.

Station 4: Heads or Tails?

Materials: 20 pennies, cup

Divide the group of four into teams of two. Give each team a cup containing 10 pennies. Assign one team to count heads and the other to count tails. Have the teams empty their cups onto the table. Then the teams count how many of the 20 pennies came up with their assigned side. The team with more announces how many more heads or tails in their set of coins and records that amount on a score sheet. The first team to reach or pass 25 wins the game.

Station 5: What a Difference

Materials: Four number cubes, Number Lines Activity Sheet, fish-shaped crackers

Divide the group of four into two teams of two. Give each team of players some crackers, a number line, and two dice. Tell the teams to take turns rolling the 2 dice and place a cracker on the number line that matches the larger number rolled. Have students place a cracker on the smaller number rolled. Then ask students to compare the places they landed on by finding the difference. Ask them to record the differences they found and repeat the activity. When time is nearly up, ask the teams to tally the total of differences from each play.

After each 10-minute interval has passed, assign the students to new stations. When time is up, call them together and ask students to record in their journals which station they liked most and why. Explain to students that they should focus on the mathematics they learned from each station rather than on other aspects of the activity.

Assessment Option

You may wish to review the completed Class Notes recording sheets completed throughout this unit. These can guide the summative comments you make for individual students.

Question for Students

1. What addends less than 10 have differences of 2? Of 5?
2. What subtraction sentence shows that we have compared a set of seven red pencils with a set of five blue pencils?
3. A balance has three crackers of the right side and five on the left side. Which side needs more crackers? How many more?
4. How could you use a number line to compare a plate of eight fish-shaped crackers with a plate of five fish-shaped crackers?
5. If you subtract 0 from a number, what happens?
6. What are the addition facts and the subtraction facts in one family where the sum is 6? When the sum is 8?
7. How did you use subtraction in the games that you played? What activity did you like most? Which was hardest for you? Why?

Teacher Reflection

• With what meanings of subtraction were the majority of the students most comfortable?
• Did all the students display understanding of the subtraction meanings?
• Can the students explain how to compare to find differences?
• Which students met all the objectives of this unit? What extension activities are appropriate for those students?
• Which students are still having difficulty with the objectives of this unit? What additional instructional experiences do they need?
• What were the greatest challenges for the students?
• What will I do differently the next time that I teach this unit?
• What other learning situations would extend their experiences with comparison subtraction?
• How might I connect the essential ideas of this unit with lessons about related mathematics content? (Data is an area that is a logical extension of this unit.)

Counting Back

Pre-K-2
Students count back to compare plates of fish-shaped crackers, and then they record the comparison in vertical and horizontal format. They apply their skills of reasoning and problem solving during this lesson in several ways. [Because students have associated the word "more" with addition, the comparative approach to subtraction is typically more challenging for the students to understand.]

How Many More?

Pre-K-2
Students write subtraction problems, model them with sets of fish-shaped crackers, and communicate their findings in words and pictures. They record differences in words and in symbols. The additive identity is reviewed in the context of comparing equal sets.

Hopping Backward to Solve Problems

Pre-K-2
In this lesson, students determine differences using the number line to compare lengths. Because this meaning is based on linear measurement, it is a distinctly different representation from the meanings presented in Lessons One and Two. At the end of the lesson, the students use reasoning and problem solving to predict differences and to answer puzzles involving subtraction.

Balancing Equations

Pre-K-2
This lesson encourages the students to explore another meaning for operations of subtraction, the balance. This meaning leads naturally into recording with equations. The students will imitate the action of a pan balance and record the modeled subtraction facts in equation form.

Fact Family Fun

Pre-K-2
In this lesson, the relation of addition to subtraction is explored with fish-shaped crackers. The students search for related addition and subtraction facts for a given number and also investigate fact families when one addend or the difference is 0.

Learning Objectives

Students will:

• Review the meanings for subtraction.
• Practice comparative subtraction in a variety of formats.

NCTM Standards and Expectations

• Count with understanding and recognize "how many" in sets of objects.
• Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.
• Use multiple models to develop initial understandings of place value and the base-ten number system
• 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.
• Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
• Develop fluency with basic number combinations for addition and subtraction.
• Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Common Core State Standards – Mathematics

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.A.2
Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.B.5
Count to answer ''how many?'' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

-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.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.5
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

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 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.5
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

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.

Grade 2, Number & Operations

• CCSS.Math.Content.2.NBT.B.9
Explain why addition and subtraction strategies work, using place value and the properties of operations.

Grade 2, Measurement & Data

• CCSS.Math.Content.2.MD.B.6
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.