Illuminations: Links Away

Links Away

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:
  • review the models for subtraction
  • justify use of specific strategies for solving a subtraction problem
  • recall subtraction facts

Materials
 
Teacher-Generated Subtraction Problem(s)
Links or Connecting Cubes (in two or more colors)
Paper
Crayons
Pan Balances
Number Lines

Instructional Plan
With students in their seats, ask them to name the models used during this unit. Prompt them if they forget any of them. Then have them illustrate with links a fact family of their choice. Have a few students share their fact family.

Give students a story problem in which the number left is provided and they have to find the number taken away. For example, on large chart paper, write:

Kim had 8 stickers. She gave some to her friend Sara. Now Kim has 5 stickers. How many stickers did Kim give to Sara?

Provide students access to paper, crayons, links, pan balances, and number lines. Allow them to choose their solution strategies and materials. After students have solved the problem, have them share their strategies and discuss which strategies worked the best.

Next have the children choose five or six facts that they need to learn from their set of flash cards. Put the children into pairs to practice those facts using the cards they selected.

Questions for Students
 
How can you subtract 1 from a number?
[Count backward.]

How many weights would you need to take away from the right side to balance a scale with 6 links on the right side and 4 on the left side?

[Take away 2 links.]

What will you land on if you start at 10 and take 5 hops backward on the number line?

[You will land on 5.]

What happens if you subtract 0 from a number?

[The number stays the same.]

What are the addition facts and the subtraction facts in one family where the difference is 6?

[One possible answer: 8 – 2 = 6, 8 – 6 = 2, 6 + 2 = 8, 2 + 6 = 8]

What activity did you like most? Which was hardest for you? Why?

[Answers will vary.]

Assessment Options
 
  1. Give students a subtraction sentence. Have students draw how they would solve this problem. Then have students write the rest of the fact family for this subtraction problem.

Extensions
 
  1. Put the children in pairs, and give each pair a die and a supply of paper links. Then tell each child to make a chain of 20 links so they can play "Race From 20." (Instead of using paper links, this game can also be played using the Race From 20 activity sheet. However, paper links are preferable, because they allow students to visualize each subtraction.) To play, the children take turns rolling the die and removing the indicated number of links from their chain. The child whose chain disappears first will be the winner for that round. Make sure students understand they can not take away more links than they have. For example, if they have 3 links and they roll a 5, they cannot take 5 away, so play passes to the next person. Ask the children to play several rounds with the links and then challenge them to play without the links, keeping score on a piece of paper.

Teacher Reflection
 
  • Can students demonstrate understanding of the terms difference, take away, and equals?
  • What models were the majority of the students most comfortable with?
  • Can students explain how to find differences?
  • Do the students recognize the facts they know and those they have yet to learn?
  • What were the greatest challenges for the students?
  • What other situations would extend their experiences with subtraction?
  • How might I connect the essential ideas of this unit with lessons about similar mathematics content?

NCTM Standards and Expectations
 
Algebra Pre-K-2
  1. Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
  2. Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

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