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Practice Makes Perfect

Links Away
Grace M. Burton
Location: unknown

During this lesson, students use what they know about fact families to play a concentration game. They will also identify subtraction facts they need to learn.

Ask the children to write a fact family with one fact on each of four file cards. Have them also write their initials on the front of each card. Next collect cards from 5 students to play a round of “Concentration.” To play, shuffle the cards and place them upside down in an array. Then call a child to turn over two cards. If the cards belong to the same fact family, the child keeps the cards. If they do not match, the cards are returned to the array and another child takes a turn. Continue playing until all children have had a chance.

541 concentration

Next put the children into small groups and have them play “Concentration” with their cards. As groups complete the activity, ask the students to list the subtraction facts they know and those they have yet to memorize. Have them make flash cards for some of the facts they still need to memorize.

  • Pencils
  • File Cards

Assessment Options

  1. Observe students as they play "Concentration." Use the Class Notes recording sheet to record which students are able to recognize facts in the same family.
  2. Have students illustrate, then write, a fact family for 10 on a ten frame.


  1. This extension is for students who need extra support recognizing and writing fact families. Place 10 2-color chips in a cup. Have students shake up the cup and spill its contents in a shoe box lid. Then have students write the fact family illustrated by the 2-color chips.
  2. Move on to the last lesson, Looking Back and Moving Forward.

Questions for Students 

1. How do you know if two facts are in the same fact family?

[They have the same numbers.]

2. What do you notice about your “easy” facts?

[Answers will vary.]

3. What do you notice about those you do not find easy? Why do you think they are harder for you to remember?

[Answers will vary.]

4. How can addition facts help you learn subtraction facts you don’t know?

[If I want to learn a subtraction fact, I can remember an addition fact in the same fact family.]

Teacher Reflection 

  • Which students have most of the facts memorized?
  • Did most students remember the effects of adding 0?
  • Which students still have many facts to memorize? What additional instructional experiences do they need?
  • What would you do differently the next time that you teach this lesson?

Counting Back and Counting On

This lesson, which focuses on the counting model for subtraction, begins with reading a counting book. The students model the numbers as the book is read. Then they make a chain of links and write in vertical and horizontal format the differences suggested by adding and subtracting one link at a time from their chains. Finally, they draw a chain showing one link being taken away and write in two formats the difference it represents.

Taking Away Sets

This lesson encourages students to explore another model for subtraction, the familiar set model. Reading one of the many books that feature subtraction set the stage for this lesson in which the students write story problems, find differences using sets, and present results in a table. In the discussion of the table, they focus on the effects of subtracting all and subtracting 0.

Hopping Backward on the Number Line

In this lesson, students generate differences using a number line model. Because this model highlights the measurement aspect of subtraction, it is a distinctly different representation from the models presented in the previous lessons of this unit. The order property for subtraction is investigated. At the end of the lesson, children are encouraged to predict differences and solve puzzles involving subtraction.

Finding the Balance

Pre-K-2, 6-8
This lesson encourages students to explore another model of subtraction, the balance. Students will use real and virtual balances. Students also explore recording the modeled subtraction facts in equation form.

Finding Fact Families

In this lesson, students explore the relation of addition to subtraction with books and links. Then the children search for related addition and subtraction facts for a given number. They also investigate fact families, including those where one addend is 0 and where the addends are alike.

Looking Back and Moving Forward

This final lesson reviews the work of the previous lessons and suggests a framework for summative assessment. Students will self-select a solution strategy for subtraction from the models introduced in this unit. An extension activity is suggested in which students use the mathematical knowledge and skills developed in the previous lessons to demonstrate understanding and ability to apply that knowledge to playing a new game.

Learning Objectives

Students will be able to:

  • Recognize addition and subtraction facts in the same family.
  • Practice subtraction facts.

NCTM Standards and Expectations

  • Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.

Common Core State Standards – Mathematics

-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.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.MP6
    Attend to precision.