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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 – compare shapes of graphs of linear and non-linear relations, describe their rates of change, make connections to growing and shrinking patterns, and make predictions
- C4.1 – compare characteristics of graphs, tables of values, and equations of linear and non-linear relations
- 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.
- 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.
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