#### Alison Kimbley

pdf

Subject Area:

Mathematics

Strand:

Patterns and Relations

Four

Content (topic)

Exploring one-step equations with variables

WNCP:

 Outcome P4.2: Demonstrate an understanding of equations involving symbols to represent an unknown value by: Writing an equation to represent a problem solving one-step equations. Solving one-step equation. Indicators: Identify the unknown in a story problem, represent the problem with an equation, and solve the problem concretely, pictorially, or symbolically. Solve a one step equation using manipulative. Explain what is meant by “one step equations with one unknown.” Represent and solve an addition or subtraction problem involving a “part-part-whole” or comparison context using a symbol to represent the unknown. Mathematical Processes: Connections Communication Problem Solving Reasoning

Lesson Preparation

Equipment/materials:

• A variety of small diamond shape cutouts in various colors. See Dcimal Fractions and Star Quilts.
• An equation template from Appendix 1 for each group of four students.
• One plus sign and one minus sign for each group of four students.

Presentation

Set

• Tell the students that the star is meaningful to Lakota people as star are seen in the Lakota culture as a traditional symbol and central to may celebrations and ceremonies.  The Star quilt is known and respected as a powerful symbol, binding the community together and strengthening ties between generations.

Development

• Split the students up in groups of four, each group will receive a variety of small diamond shaped cutouts, a copy of the equation template from Appendix 1 as well as a plus sign and a minus sign.

• In each group of four students have two students work together to create an equation using the diamonds, the template, a plus or minus sign and an empty square to signify the unknown.  For example a group of two may create the following equation.
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• The other team of two students must write the equation down in their notebooks, using a symbol such as a triangle or circle and solve the equation. In this case if a triangle is used for the variable the equation is 6 - Δ = 4.

• Have the teams reverse roles and create another equation.

• Design questions which use the diamonds where students can set up equations using variables in order to describe situations that require equations. Some sample questions are in Appendix 2.

• Have each group of four students work together to represent the problem with an equation, and solve it using the diamonds and symbolically.

Appendix 1:

Equation template

Appendix 2:

Sample Questions

Mary needs 15 light blue diamonds for her design. She has cut out 8 light blue diamonds. How many more does she need to cut out? Write an equation to represent this problem. (8 + Δ = 15.)

Bob cut out 12 green diamonds and gave some to Jack. Bob counted the green diamonds he has left and got 5. How many did he give to Jack? ? Write an equation to represent this problem. (12 - Δ = 5.)

Alison needs 10 yellow diamonds to finish her design on the quilt she has 2 yellow diamonds.  How many more diamonds will she need to cut out?  Write an equation to represent this problem.

Jake cut out 20 black diamonds, however during recess 7 diamonds fell off his desk, how many diamonds does Jack have left?

Amy needs 45 diamonds in total; she has 12 red diamonds, 13 blue diamonds, 3 black diamonds and 4 yellow diamonds.  How many diamonds is Paige needing to reach 45?

Katherine forgot to keep count when she was cutting out her diamonds; she only needed 23 diamonds in total.  However she cut 4 purple diamonds, 12 black diamonds, and 12 yellow diamonds.  How many extra diamonds did Katherine cut out?  Show this in an equation.

Lidia needed 16 purple diamonds to finish her design; she had cut 10 purple diamonds. How many more does she need to cut out?  Write an equation to represent this problem.