Chapter 33: Coding Simulations and Geometric Transformations
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Coding Simulations and Geometric Transformations with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- Simulation (a model used to imitate a situation or experiment)
- Dilation (an enlargement or reduction using a scale factor)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
33.1 Coding a translation
A translation slides every point of a figure the same distance in the same direction. This topic focuses on Coding a translation .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Translate (2,3) by vector (3,-2).
- Add 3 to x.
- Subtract 2 from y.
Very beginner explanation: A translation slides every point of a figure the same distance in the same direction. This topic focuses on Coding a translation .
Answer: (5,1)
Worked Example 2
Problem: Translate (-1,4) by vector (3,-2).
- Add 3 to x.
- Subtract 2 from y.
Very beginner explanation: A translation slides every point of a figure the same distance in the same direction. This topic focuses on Coding a translation .
Answer: (2,2)
Worked Example 3
Problem: Translate (5,-2) by vector (3,-2).
- Add 3 to x.
- Subtract 2 from y.
Very beginner explanation: A translation slides every point of a figure the same distance in the same direction. This topic focuses on Coding a translation .
Answer: (8,-4)
Worked Example 4
Problem: Translate (0,6) by vector (3,-2).
- Add 3 to x.
- Subtract 2 from y.
Very beginner explanation: A translation slides every point of a figure the same distance in the same direction. This topic focuses on Coding a translation .
Answer: (3,4)
Worked Example 5
Problem: Translate (-3,-5) by vector (3,-2).
- Add 3 to x.
- Subtract 2 from y.
Very beginner explanation: A translation slides every point of a figure the same distance in the same direction. This topic focuses on Coding a translation .
Answer: (0,-7)
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Coding a translation. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.2 Coding a reflection
A reflection flips a figure across a line of reflection. This topic focuses on Coding a reflection .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Reflect (2,3) across the x-axis.
- Keep x the same.
- Change the sign of y.
Very beginner explanation: A reflection flips a figure across a line of reflection. This topic focuses on Coding a reflection .
Answer: (2,-3)
Worked Example 2
Problem: Reflect (-1,4) across the x-axis.
- Keep x the same.
- Change the sign of y.
Very beginner explanation: A reflection flips a figure across a line of reflection. This topic focuses on Coding a reflection .
Answer: (-1,-4)
Worked Example 3
Problem: Reflect (5,-2) across the x-axis.
- Keep x the same.
- Change the sign of y.
Very beginner explanation: A reflection flips a figure across a line of reflection. This topic focuses on Coding a reflection .
Answer: (5,2)
Worked Example 4
Problem: Reflect (0,6) across the x-axis.
- Keep x the same.
- Change the sign of y.
Very beginner explanation: A reflection flips a figure across a line of reflection. This topic focuses on Coding a reflection .
Answer: (0,-6)
Worked Example 5
Problem: Reflect (-3,-5) across the x-axis.
- Keep x the same.
- Change the sign of y.
Very beginner explanation: A reflection flips a figure across a line of reflection. This topic focuses on Coding a reflection .
Answer: (-3,5)
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Coding a reflection. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.3 Coding a rotation
A rotation turns a figure around a fixed centre. This topic focuses on Coding a rotation .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Rotate (2,3) 90° counterclockwise about the origin.
- Use rule (x,y)→(-y,x).
Very beginner explanation: A rotation turns a figure around a fixed centre. This topic focuses on Coding a rotation .
Answer: (-3,2)
Worked Example 2
Problem: Rotate (-1,4) 90° counterclockwise about the origin.
- Use rule (x,y)→(-y,x).
Very beginner explanation: A rotation turns a figure around a fixed centre. This topic focuses on Coding a rotation .
Answer: (-4,-1)
Worked Example 3
Problem: Rotate (5,-2) 90° counterclockwise about the origin.
- Use rule (x,y)→(-y,x).
Very beginner explanation: A rotation turns a figure around a fixed centre. This topic focuses on Coding a rotation .
Answer: (2,5)
Worked Example 4
Problem: Rotate (0,6) 90° counterclockwise about the origin.
- Use rule (x,y)→(-y,x).
Very beginner explanation: A rotation turns a figure around a fixed centre. This topic focuses on Coding a rotation .
Answer: (-6,0)
Worked Example 5
Problem: Rotate (-3,-5) 90° counterclockwise about the origin.
- Use rule (x,y)→(-y,x).
Very beginner explanation: A rotation turns a figure around a fixed centre. This topic focuses on Coding a rotation .
Answer: (5,-3)
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Coding a rotation. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.4 Coding a dilation
A dilation enlarges or reduces a figure using a scale factor while preserving shape. This topic focuses on Coding a dilation .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Dilate (2,3) from the origin by scale factor 2.
- Multiply both coordinates by 2.
Very beginner explanation: A dilation enlarges or reduces a figure using a scale factor while preserving shape. This topic focuses on Coding a dilation .
Answer: (4,6)
Worked Example 2
Problem: Dilate (-1,4) from the origin by scale factor 2.
- Multiply both coordinates by 2.
Very beginner explanation: A dilation enlarges or reduces a figure using a scale factor while preserving shape. This topic focuses on Coding a dilation .
Answer: (-2,8)
Worked Example 3
Problem: Dilate (5,-2) from the origin by scale factor 2.
- Multiply both coordinates by 2.
Very beginner explanation: A dilation enlarges or reduces a figure using a scale factor while preserving shape. This topic focuses on Coding a dilation .
Answer: (10,-4)
Worked Example 4
Problem: Dilate (0,6) from the origin by scale factor 2.
- Multiply both coordinates by 2.
Very beginner explanation: A dilation enlarges or reduces a figure using a scale factor while preserving shape. This topic focuses on Coding a dilation .
Answer: (0,12)
Worked Example 5
Problem: Dilate (-3,-5) from the origin by scale factor 2.
- Multiply both coordinates by 2.
Very beginner explanation: A dilation enlarges or reduces a figure using a scale factor while preserving shape. This topic focuses on Coding a dilation .
Answer: (-6,-10)
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Coding a dilation. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.5 Doubling a shape with code
Doubling a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Add two numbers
- INPUT a,b → total=a+b → OUTPUT total
- Trace each step and record changing variable values.
Very beginner explanation: Doubling a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: a=4,b=7 → 11
Worked Example 2
Problem: Repeat a movement
- REPEAT 4 TIMES: x=x+2
- Trace each step and record changing variable values.
Very beginner explanation: Doubling a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: x starts 1 → x ends 9
Worked Example 3
Problem: Check an even number
- IF n MOD 2 = 0 THEN even ELSE odd
- Trace each step and record changing variable values.
Very beginner explanation: Doubling a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: n=8 → even
Worked Example 4
Problem: Simulate a die
- Generate a random integer from 1 to 6
- Trace each step and record changing variable values.
Very beginner explanation: Doubling a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Possible outputs: 1,2,3,4,5,6
Worked Example 5
Problem: Debug a loop
- Change count=count to count=count+1
- Trace each step and record changing variable values.
Very beginner explanation: Doubling a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: The loop can now finish
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Doubling a shape with code. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.6 Shrinking a shape with code
Shrinking a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Add two numbers
- INPUT a,b → total=a+b → OUTPUT total
- Trace each step and record changing variable values.
Very beginner explanation: Shrinking a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: a=4,b=7 → 11
Worked Example 2
Problem: Repeat a movement
- REPEAT 4 TIMES: x=x+2
- Trace each step and record changing variable values.
Very beginner explanation: Shrinking a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: x starts 1 → x ends 9
Worked Example 3
Problem: Check an even number
- IF n MOD 2 = 0 THEN even ELSE odd
- Trace each step and record changing variable values.
Very beginner explanation: Shrinking a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: n=8 → even
Worked Example 4
Problem: Simulate a die
- Generate a random integer from 1 to 6
- Trace each step and record changing variable values.
Very beginner explanation: Shrinking a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Possible outputs: 1,2,3,4,5,6
Worked Example 5
Problem: Debug a loop
- Change count=count to count=count+1
- Trace each step and record changing variable values.
Very beginner explanation: Shrinking a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: The loop can now finish
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Shrinking a shape with code. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.7 Coordinate rules in code
Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate rules in code .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Locate (2,3).
- Move 2 units right.
- Move 3 units up.
Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate rules in code .
Answer: Quadrant I
Worked Example 2
Problem: Locate (-4,5).
- Move 4 units left.
- Move 5 units up.
Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate rules in code .
Answer: Quadrant II
Worked Example 3
Problem: Locate (-3,-2).
- Move 3 units left.
- Move 2 units down.
Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate rules in code .
Answer: Quadrant III
Worked Example 4
Problem: Locate (6,-1).
- Move 6 units right.
- Move 1 units down.
Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate rules in code .
Answer: Quadrant IV
Worked Example 5
Problem: Locate (0,4).
- Move 0 units right.
- Move 4 units up.
Very beginner explanation: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate rules in code .
Answer: on an axis
Worked Example 6
Problem: Locate (2,3) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.
Answer: Quadrant I
Worked Example 7
Problem: Locate (-4,5) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.
Answer: Quadrant II
Worked Example 8
Problem: Locate (-3,-2) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.
Answer: Quadrant III
Worked Example 9
Problem: Locate (6,-1) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.
Answer: Quadrant IV
Worked Example 10
Problem: Locate (0,4) on the coordinate plane.
- Move horizontally using x.
- Move vertically using y.
- Identify the quadrant or axis.
Very beginner explanation: Ordered pairs are written (x, y): horizontal movement first, vertical movement second.
Answer: on an axis
Practice Exercise
Create one new question about Coordinate rules in code. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.8 Loops for repeated transformations
A loop repeats a set of instructions in code. This topic focuses on Loops for repeated transformations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Add two numbers
- INPUT a,b → total=a+b → OUTPUT total
- Trace each step and record changing variable values.
Very beginner explanation: A loop repeats a set of instructions in code. This topic focuses on Loops for repeated transformations .
Answer: a=4,b=7 → 11
Worked Example 2
Problem: Repeat a movement
- REPEAT 4 TIMES: x=x+2
- Trace each step and record changing variable values.
Very beginner explanation: A loop repeats a set of instructions in code. This topic focuses on Loops for repeated transformations .
Answer: x starts 1 → x ends 9
Worked Example 3
Problem: Check an even number
- IF n MOD 2 = 0 THEN even ELSE odd
- Trace each step and record changing variable values.
Very beginner explanation: A loop repeats a set of instructions in code. This topic focuses on Loops for repeated transformations .
Answer: n=8 → even
Worked Example 4
Problem: Simulate a die
- Generate a random integer from 1 to 6
- Trace each step and record changing variable values.
Very beginner explanation: A loop repeats a set of instructions in code. This topic focuses on Loops for repeated transformations .
Answer: Possible outputs: 1,2,3,4,5,6
Worked Example 5
Problem: Debug a loop
- Change count=count to count=count+1
- Trace each step and record changing variable values.
Very beginner explanation: A loop repeats a set of instructions in code. This topic focuses on Loops for repeated transformations .
Answer: The loop can now finish
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Loops for repeated transformations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.9 Conditions in simulations
A condition is a test in code that decides which instructions run. This topic focuses on Conditions in simulations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Add two numbers
- INPUT a,b → total=a+b → OUTPUT total
- Trace each step and record changing variable values.
Very beginner explanation: A condition is a test in code that decides which instructions run. This topic focuses on Conditions in simulations .
Answer: a=4,b=7 → 11
Worked Example 2
Problem: Repeat a movement
- REPEAT 4 TIMES: x=x+2
- Trace each step and record changing variable values.
Very beginner explanation: A condition is a test in code that decides which instructions run. This topic focuses on Conditions in simulations .
Answer: x starts 1 → x ends 9
Worked Example 3
Problem: Check an even number
- IF n MOD 2 = 0 THEN even ELSE odd
- Trace each step and record changing variable values.
Very beginner explanation: A condition is a test in code that decides which instructions run. This topic focuses on Conditions in simulations .
Answer: n=8 → even
Worked Example 4
Problem: Simulate a die
- Generate a random integer from 1 to 6
- Trace each step and record changing variable values.
Very beginner explanation: A condition is a test in code that decides which instructions run. This topic focuses on Conditions in simulations .
Answer: Possible outputs: 1,2,3,4,5,6
Worked Example 5
Problem: Debug a loop
- Change count=count to count=count+1
- Trace each step and record changing variable values.
Very beginner explanation: A condition is a test in code that decides which instructions run. This topic focuses on Conditions in simulations .
Answer: The loop can now finish
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Conditions in simulations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.10 Random-number simulations
A simulation uses a model, often code or repeated trials, to imitate a mathematical or real-world situation. This topic focuses on Random-number simulations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Add two numbers
- INPUT a,b → total=a+b → OUTPUT total
- Trace each step and record changing variable values.
Very beginner explanation: A simulation uses a model, often code or repeated trials, to imitate a mathematical or real-world situation. This topic focuses on Random-number simulations .
Answer: a=4,b=7 → 11
Worked Example 2
Problem: Repeat a movement
- REPEAT 4 TIMES: x=x+2
- Trace each step and record changing variable values.
Very beginner explanation: A simulation uses a model, often code or repeated trials, to imitate a mathematical or real-world situation. This topic focuses on Random-number simulations .
Answer: x starts 1 → x ends 9
Worked Example 3
Problem: Check an even number
- IF n MOD 2 = 0 THEN even ELSE odd
- Trace each step and record changing variable values.
Very beginner explanation: A simulation uses a model, often code or repeated trials, to imitate a mathematical or real-world situation. This topic focuses on Random-number simulations .
Answer: n=8 → even
Worked Example 4
Problem: Simulate a die
- Generate a random integer from 1 to 6
- Trace each step and record changing variable values.
Very beginner explanation: A simulation uses a model, often code or repeated trials, to imitate a mathematical or real-world situation. This topic focuses on Random-number simulations .
Answer: Possible outputs: 1,2,3,4,5,6
Worked Example 5
Problem: Debug a loop
- Change count=count to count=count+1
- Trace each step and record changing variable values.
Very beginner explanation: A simulation uses a model, often code or repeated trials, to imitate a mathematical or real-world situation. This topic focuses on Random-number simulations .
Answer: The loop can now finish
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Random-number simulations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.11 Testing and debugging simulations
Debugging means finding and fixing errors in code or logic. This topic focuses on Testing and debugging simulations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Add two numbers
- INPUT a,b → total=a+b → OUTPUT total
- Trace each step and record changing variable values.
Very beginner explanation: Debugging means finding and fixing errors in code or logic. This topic focuses on Testing and debugging simulations .
Answer: a=4,b=7 → 11
Worked Example 2
Problem: Repeat a movement
- REPEAT 4 TIMES: x=x+2
- Trace each step and record changing variable values.
Very beginner explanation: Debugging means finding and fixing errors in code or logic. This topic focuses on Testing and debugging simulations .
Answer: x starts 1 → x ends 9
Worked Example 3
Problem: Check an even number
- IF n MOD 2 = 0 THEN even ELSE odd
- Trace each step and record changing variable values.
Very beginner explanation: Debugging means finding and fixing errors in code or logic. This topic focuses on Testing and debugging simulations .
Answer: n=8 → even
Worked Example 4
Problem: Simulate a die
- Generate a random integer from 1 to 6
- Trace each step and record changing variable values.
Very beginner explanation: Debugging means finding and fixing errors in code or logic. This topic focuses on Testing and debugging simulations .
Answer: Possible outputs: 1,2,3,4,5,6
Worked Example 5
Problem: Debug a loop
- Change count=count to count=count+1
- Trace each step and record changing variable values.
Very beginner explanation: Debugging means finding and fixing errors in code or logic. This topic focuses on Testing and debugging simulations .
Answer: The loop can now finish
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Testing and debugging simulations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.12 Comparing predicted and simulated results
Comparing predicted and simulated results is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Comparing predicted and simulated results: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Comparing predicted and simulated results is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Comparing predicted and simulated results: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Comparing predicted and simulated results is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Comparing predicted and simulated results: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Comparing predicted and simulated results is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Comparing predicted and simulated results: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Comparing predicted and simulated results is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Comparing predicted and simulated results: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Comparing predicted and simulated results is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Comparing predicted and simulated results in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing predicted and simulated results becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Comparing predicted and simulated results and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing predicted and simulated results becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Comparing predicted and simulated results using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing predicted and simulated results becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Comparing predicted and simulated results problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing predicted and simulated results becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Comparing predicted and simulated results could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Comparing predicted and simulated results becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Comparing predicted and simulated results. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
33.13 Documenting code logic
Documenting code logic is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Add two numbers
- INPUT a,b → total=a+b → OUTPUT total
- Trace each step and record changing variable values.
Very beginner explanation: Documenting code logic is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: a=4,b=7 → 11
Worked Example 2
Problem: Repeat a movement
- REPEAT 4 TIMES: x=x+2
- Trace each step and record changing variable values.
Very beginner explanation: Documenting code logic is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: x starts 1 → x ends 9
Worked Example 3
Problem: Check an even number
- IF n MOD 2 = 0 THEN even ELSE odd
- Trace each step and record changing variable values.
Very beginner explanation: Documenting code logic is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: n=8 → even
Worked Example 4
Problem: Simulate a die
- Generate a random integer from 1 to 6
- Trace each step and record changing variable values.
Very beginner explanation: Documenting code logic is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Possible outputs: 1,2,3,4,5,6
Worked Example 5
Problem: Debug a loop
- Change count=count to count=count+1
- Trace each step and record changing variable values.
Very beginner explanation: Documenting code logic is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: The loop can now finish
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Documenting code logic. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Coding a translation . Show your reasoning and check your answer.
- Create and solve a new question about Coding a reflection . Show your reasoning and check your answer.
- Create and solve a new question about Coding a rotation . Show your reasoning and check your answer.
- Create and solve a new question about Coding a dilation . Show your reasoning and check your answer.
- Create and solve a new question about Doubling a shape with code . Show your reasoning and check your answer.
- Create and solve a new question about Shrinking a shape with code . Show your reasoning and check your answer.
- Create and solve a new question about Coordinate rules in code . Show your reasoning and check your answer.
- Create and solve a new question about Loops for repeated transformations . Show your reasoning and check your answer.
- Create and solve a new question about Conditions in simulations . Show your reasoning and check your answer.
- Create and solve a new question about Random-number simulations . Show your reasoning and check your answer.
- Create and solve a new question about Testing and debugging simulations . Show your reasoning and check your answer.
- Create and solve a new question about Comparing predicted and simulated results . Show your reasoning and check your answer.
Common Mistakes
- Combining unlike terms.
- Changing only one side of an equation.
- Forgetting to distribute to every term.
- Using a pattern rule that works only for the first few terms.
- Writing code without tracing variable values.
- Using a mathematical model without stating assumptions.
30 Review Questions and Answers
Q1. What is important to remember about Coding a translation?
Answer: A translation slides every point of a figure the same distance in the same direction. This topic focuses on Coding a translation.
Q2. What is important to remember about Coding a reflection?
Answer: A reflection flips a figure across a line of reflection. This topic focuses on Coding a reflection.
Q3. What is important to remember about Coding a rotation?
Answer: A rotation turns a figure around a fixed centre. This topic focuses on Coding a rotation.
Q4. What is important to remember about Coding a dilation?
Answer: A dilation enlarges or reduces a figure using a scale factor while preserving shape. This topic focuses on Coding a dilation.
Q5. What is important to remember about Doubling a shape with code?
Answer: Doubling a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Shrinking a shape with code?
Answer: Shrinking a shape with code is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Coordinate rules in code?
Answer: Coordinates locate a point as (x, y): horizontal movement first, vertical movement second. This topic focuses on Coordinate rules in code.
Q8. What is important to remember about Loops for repeated transformations?
Answer: A loop repeats a set of instructions in code. This topic focuses on Loops for repeated transformations.
Q9. What is important to remember about Conditions in simulations?
Answer: A condition is a test in code that decides which instructions run. This topic focuses on Conditions in simulations.
Q10. What is important to remember about Random-number simulations?
Answer: A simulation uses a model, often code or repeated trials, to imitate a mathematical or real-world situation. This topic focuses on Random-number simulations.
Q11. What is important to remember about Testing and debugging simulations?
Answer: Debugging means finding and fixing errors in code or logic. This topic focuses on Testing and debugging simulations.
Q12. What is important to remember about Comparing predicted and simulated results?
Answer: Comparing predicted and simulated results is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Documenting code logic?
Answer: Documenting code logic is an important Grade 7 idea in Coding Simulations and Geometric Transformations. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.