MAKING 10

(c) 2022 George Gadanidis

ABOUT

Topics: from patterns to algebra; relationships where one quantity varies while another stays constant; linear and non-linear relations

The Making 10 activity is designed to have a low floor and a high ceiling and may be used across a number grades.

  • We first did this activity in grades 4/5 classrooms.
  • Then in grades 6-8 classrooms.
  • And also in a grade 9 classrooms.
  • We also did part of this activity in grades 1-3 classrooms with concrete materials, as shown in the concept map below.

MENU

  1. Initial task
  2. In a story
  3. With a simulation
  4. What did you learn?
1. INITIAL TASK

1.a. Do the following

  • Roll a number cube to get a number 1-6
  • Place the number rolled in the first blank of __ + __ = 10
  • Calculate and record the missing number for the second blank
    • For example, if you rolled a 3, your number sentence would become 3 + 7 = 10
  • Repeat this until you exhaust all possibilities
    • 3 + 7 = 10
    • __ + __ = 10
    • __ + __ = 10
    • …
  • Record the pairs of numbers in a table, and also as ordered pairs
  • Plot the ordered pairs on a grid, as shown below for (3, 7): 3 across and 7 up

1.B. REFLECT

  1. What do you notice about the graph?
  2. Offer an explanation.

1.C. VIDEO OVERVIEW

View the video below, which summarizes and extends the activity above.

2. IN A STORY

2.A. READ THE STORY

Read The Pleasure of Making 10.

  • STOP ON PAGE 7
    • What surprise did Molly and Alexander experience?
    • What made it surprising?
  • STOP ON PAGE 17
    • What is the most interesting fact you learned about Rene Descartes?
    • Conduct an Internet search to find one more interesting fact about Rene Descartes.
  • STOP ON PAGE 21
    • What beauty have you experienced in mathematics?
  • STOP ON PAGE 26
    • What would you do next if you were Molly or Alexander?

2.B. MATH EXTENSIONS

  1. Complete the math extensions on pages 27-30 of the story.

2.C. A CODING EXTENSION

  1. Run the RANDOM and the CONSTRAINED code blocks at https://scratch.mit.edu/projects/408092534/editor
  2. What is the difference in the graphs produced by the 2 code blocks?
  3. What does the RANDOM code do?
  4. How does it do it?
  5. What does the CONSTRAINED code do?
  6. How does it do it?
  7. Change x + y = 100 in the CONSTRAINED code as shown below:
    • x – y = 100
    • x + y < 100
    • x + 2y > 100
  8. Make your own edits and run the code.
  9. What did you learn?
  10. What else do you want to know?
3. WITH A SIMULATION

1.A. SIMULATION

Try the simulation at https://researchideas.ca/mathncode/sims-randpairs.html

  1. Click on the number cube to run the code
  2. Edit the + and the 10 in x + y = 10 and notice how the graph changes.

2.B. GAME

Try the game at https://researchideas.ca/mathncode/games-randpairs.html

  1. Select a level.
  2. Edit the code to try to hit the points with water balloons.
4. WHAT DID YOU DO IN MATH TODAY?

Imagine someone in your family asks you: What did you do in math today?

Script a dialogue that would share what you learned in a way that would offer a mathematics surprise.