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# 2. MAKING 10

“I know numbers are beautiful. If they aren’t beautiful, nothing is.”

― Paul Erdős

MAKING 10 MENU | MATH + CODING MENU |

2. Making 10 — Linear relations + coding — In the classroom 2A. Making 10 hands-on 2B. Plotting random pairs 2C. Video overview 2D. Graphing puzzle 2E. Coding simulation 2F. Coding puzzle – plotting with Scratch | Home page 1. Squares and spirals — introducing variables [gr. 3-9] 2. Making 10 — random coordinates line up [gr. 1-10] 3. Inequalities — in 1D, 2D & 3D [gr. 1-10] 4. Infinity — it’s big but fits in your hand [gr. 3-12]5. Binary choice — probability, Pascal’s triangle & algebra [gr. 1-12] |

#### Linear Relations + Coding

#### IN THE CLASSROOM

###### Ontario Curriculum

**Gr. 1/2**- B2.2 – addition facts up to 10/20

**Gr. 3/4**- B2.1 – use properties of operations to solve problems
- C2.1 – use variables in various contexts
- C.3.2 – read and alter existing code; sequential, concurrent, and repeating & nested events

**Gr.5-8**- C2.2 – evaluate algebraic expressions
- C2.3 – solve equations
- C3.2 – conditional coding structures

**Gr. 6**- C1.1 – growing, shrinking & linear patterns
- C1.2 – various representations of linear growing patterns, algebraic expressions and equations

**Gr. 7/8**- C1.1 – constant rates & initial values)
- C1.2 – various representations of linear growing patterns, algebraic expressions and equations

**Gr. 9**- C1.1 – research an algebraic concept to tell a story
- C3.1
- C4.1
- C2 – apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands
- C4 – demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate

###### Implementation

**Gr. 1-2**- Students use concrete materials to represent possible solutions to
**__ + __ = 10**. - They notice that bars fit together to form a
**staircase pattern**. As the number of yellow increases, the number of green decreases.

- Students use concrete materials to represent possible solutions to
**Gr. 3-9**- Students use a number cube to get the first number in
**__ + __ = 10**. The calculate the second number. - When they plot the pairs of numbers (ordered pairs) on a grid, they are
**surprised that they line up**! - Students start with a
**Scratch code**that plots __ + __ = 100. - They edit the code to
**solve puzzles**of matching different graphs. - The complexity of the puzzles can vary depending on the grade level.
- This develops the conceptual basis for
**understanding linear and non-linear relationships**.

- Students use a number cube to get the first number in

#### 2.A MAKING 10 – HANDS-ON

**Q1.** What does this image represent in grades 1/2 classrooms?

#### 2B. PLOTTING RANDOM PAIRS

**Q2.** 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
- 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

#### 2C. VIDEO OVERVIEW

**Q3.** View the video below, which summarizes and extends the activity above. What did you learn?

#### 2D. Graphing Puzzle

**Q4.** Create number sentences that have graphs approximately like the ones shown on the right. Try these as a start:

- __ – __ = 2
- __ x __ = 12
- __
^{2}+ __^{2}= 25

#### 2E. CODING SIMULATION

**Q5.** Try the simulation at https://imaginethis.ca/mathncode/sims-randpairs.html

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

#### 2F. CODING PUZZLE – PLOTTING WITH SCRATCH

**Q6.** Run the code below at this link: https://scratch.mit.edu/projects/1055468823/editor

- What does the code do?
- How does it do it?

**Q7. **Edit the code to get the following graphs.

MAKING 10 MENU | MATH + CODING MENU |

2. Making 10 — Linear relations + coding — In the classroom 2A. Making 10 hands-on 2B. Plotting random pairs 2C. Video overview 2D. Graphing puzzle 2E. Coding simulation 2F. Coding puzzle – plotting with Scratch | Home page 1. Squares and spirals — introducing variables [gr. 3-9] 2. Making 10 — random coordinates line up [gr. 1-10] 3. Inequalities — in 1D, 2D & 3D [gr. 1-10] 4. Infinity — it’s big but fits in your hand [gr. 3-12]5. Binary choice — probability, Pascal’s triangle & algebra [gr. 1-12] |

by George Gadanidis, PhD