Grade 8 Math: Algebra and Coding unit
Students describe, compare and extend patterns, paying close attention to linear patterns and what their constant rate and initial value mean in real situations. They show patterns with tiles, tables, graphs and equations, use pattern rules to make far predictions, and see how patterns explain number facts like 10⁰ = 1. They combine like terms, add binomials, evaluate expressions and formulas, and solve multi-step equations and inequalities, checking every solution. Two coding lessons use loops, conditions, lists and sub-programs to analyse data, and students read, debug and improve existing code. A modelling lesson and the performance task, Fundraiser Water Bottles, bring it all together.
What's included
- Unit overviewBig ideas, expectations by code, learning goals and success criteria
- Day-by-day calendar18 days planned, including catch-up and review days
- 12 three-part lessonsMinds On, Action and Consolidation, with timings, questions to ask and common mistakes
- Student worksheets with answer keys108 questions in all, every numeric answer checked by software
- Diagnostic and quick checksA Day 1 diagnostic and 3 quick checks to adjust your teaching
- Performance task and rubric“Fundraiser Water Bottles”, with a rubric across all four achievement chart categories
- Unit test and answer key31 marks, sorted by achievement chart category
- AccommodationsSupports for students with IEPs, English language learners, and extensions
Look inside
These are real pages from the unit.
Day-by-day calendar
| Day | Lesson or assessment | Expectations |
|---|---|---|
| 1 | Diagnostic and unit launch | |
| 2 | Lesson 1: Repeating, growing and shrinking patterns | C1.1 |
| 3 | Lesson 2: Showing linear patterns in many ways | C1.2 |
| 4 | Lesson 3: Pattern rules and predictions (Quick check 1) | C1.3 |
| 5 | Lesson 4: Patterns that explain numbers | C1.4, C1.2 |
| 6 | Lesson 5: Adding and subtracting like terms | C2.1 |
| 7 | Lesson 6: Adding binomials | C2.1 |
| 8 | Lesson 7: Evaluating expressions and formulas (Quick check 2) | C2.2 |
| 9 | Lesson 8: Solving multi-step equations | C2.3 |
| 10 | Lesson 9: Solving and graphing inequalities (Quick check 3) | C2.4 |
| 11 | Lesson 10: Writing code with loops, conditions and lists | C3.1 |
| 12 | Lesson 11: Reading, debugging and improving code | C3.2 |
| 13 | Lesson 12: The modelling cycle: choosing a rink | C4, C1.1, C2.3 |
| 14 | Catch-up and conferencing day (reteach from quick checks) | All |
| 15 | Performance task: Fundraiser Water Bottles (part 1) | C4, C1.2, C2.3 |
| 16 | Performance task: Fundraiser Water Bottles (part 2) | C4, C2.4, C3.1 |
| 17 | Review: stations and practice test | All |
| 18 | Unit test | All |
Lesson 1: Repeating, growing and shrinking patterns
Learning goal: We are learning to sort patterns and to compare linear patterns by their constant rate and initial value.
Success criteria:
- I can tell whether a pattern repeats, grows or shrinks.
- I can find the constant rate and initial value of a linear pattern and explain what they mean.
Minds On (10 min)
- Show three patterns: traffic lights (red, green, yellow, red, …), a gym that costs $25 to join plus $12 a month (37, 49, 61, …), and a phone battery that drops 8% an hour (100, 92, 84, …).
- Pairs sort them and name what makes each kind different. Collect words: repeats, core, grows, shrinks, same amount each time.
Action (35 min)
- Define repeating (a core repeats), growing and shrinking patterns. A linear pattern changes by the same amount each term.
- Introduce constant rate (change per term) and initial value (the value at term 0). Work backwards one term to find the initial value: 37 − 12 = 25.
- Compare Gym A ($25 + $12 a month) with Gym B ($15 a month, no fee) in a table and on one graph. Which line is steeper? Which starts higher?
- Students complete the worksheet in pairs.
Consolidation (15 min)
- Discuss question 3: when does the steeper line catch up, and why?
- Exit: "Describe a pattern from your life. Is it repeating, growing or shrinking? If it is linear, what are its constant rate and initial value?"
Kinds of patterns
Show the change from term to term.
- Is each pattern repeating, growing or shrinking? a) 4, 9, 14, 19, … b) ▲ ● ● ▲ ● ● … c) 80, 72, 64, 56, … d) 2, 4, 8, 16, …
- A gym charges $25 to join plus $12 per month. What is the initial value and the constant rate? What is the total cost after 8 months?
- Gym A costs $25 to join plus $12 per month. Gym B costs $15 per month with no fee. Which has the greater constant rate? Which has the greater initial value? From which month does Gym B cost more in total?
- A phone battery is at 100% and drops 8% every hour. Is this pattern growing or shrinking? What is the constant rate? After how many hours is it at 20%?
- Pattern P is 3, 7, 11, 15, … and pattern Q is 10, 12, 14, 16, … (term 1, 2, 3, 4). Which has the greater constant rate? Which has the greater initial value (term 0)?
- How is the graph of a linear growing pattern different from the graph of a linear shrinking pattern?
Answer keys with worked steps are in the Teacher Guide.
Performance task: Fundraiser Water Bottles
Your Grade 8 class wants to raise at least $500 by selling custom water bottles for $12 each. Three suppliers make the bottles. Supplier A charges a $60 set-up fee plus $4.50 per bottle. Supplier B charges $7.00 per bottle with no set-up fee. Supplier C charges a $150 set-up fee plus $3.25 per bottle. Your job is to recommend a supplier and the number of bottles to order. Assume every bottle you order is sold.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Few equations, table values and solutions are correct. | Some equations and solutions are correct; several errors. | Most equations, table values and solutions are correct; minor errors. | All equations, table values, solutions and inequalities are correct. |
| Thinking | Follows the modelling cycle with limited success; assumptions not stated. | Follows some steps of the modelling cycle; some assumptions stated. | Follows the modelling cycle, states assumptions, and revises the model when shipping is added. | Follows the full cycle, tests the model against the situation, and explains how each change affects the decision. |
| Communication | Tables, graph and code are hard to follow; labels often missing. | Tables, graph and code are somewhat clear; some labels missing. | Tables, graph and code are clear and labelled; recommendation is clear. | All work is clear and organized; the recommendation is convincing and uses the math as evidence. |
| Application | Connects the model to the fundraiser with limited effectiveness. | Connects the model to the fundraiser with some effectiveness. | Uses equations, an inequality and code to make a sensible decision. | Uses equations, an inequality and code to make and justify a thoughtful decision (e.g. rounding up, checking the cheapest supplier at the final order size). |
Lessons in this unit
- Repeating, growing and shrinking patternsLearning to sort patterns and to compare linear patterns by their constant rate and initial value.C1.1
- Showing linear patterns in many waysLearning to show the same linear pattern with tiles, a table, a graph and an equation.C1.2
- Pattern rules and predictionsLearning to use pattern rules to make predictions and to find missing values.C1.3
- Patterns that explain numbersLearning to use patterns to explain how rational numbers behave.C1.4, C1.2
- Adding and subtracting like termsLearning to add and subtract monomials by combining like terms.C2.1
- Adding binomialsLearning to add binomials by grouping like terms.C2.1
- Evaluating expressions and formulasLearning to substitute rational numbers into expressions and formulas.C2.2
- Solving multi-step equationsLearning to solve equations with several terms, integers and decimals, and to check the solutions.C2.3
- Solving and graphing inequalitiesLearning to solve inequalities with integers, check the solutions and graph them.C2.4
- Writing code with loops, conditions and listsLearning to write efficient code that uses loops, conditions, lists and sub-programs to solve problems with data.C3.1
- Reading, debugging and improving codeLearning to read code, predict what it does, fix it, and change it to make it more useful or efficient.C3.2
- The modelling cycle: choosing a rinkLearning to build a model of a real situation, test it, and change it when our assumptions change.C1.1, C2.3
Ontario curriculum expectations covered
- C1.1
- Recognize and compare repeating, growing and shrinking patterns from real life, and compare linear patterns by their constant rate and their starting (initial) value.
- C1.2
- Make patterns with fractions, decimals and integers and show them in several ways; for linear patterns that grow or shrink, this includes writing an expression and an equation.
- C1.3
- Work out the rule behind a pattern, then use it to continue the pattern, make near and far predictions, fill gaps, and solve for an unknown term in linear patterns.
- C1.4
- Use patterns to show and explain how rational numbers behave, such as powers of ten and integer signs.
- C2.1
- Add and subtract first-degree monomials, and add first-degree binomials with integers, using tools such as algebra tiles.
- C2.2
- Substitute rational numbers into algebraic expressions and formulas and evaluate them.
- C2.3
- Solve equations with several terms, integers and decimals in real situations, and check the solutions.
- C2.4
- Solve inequalities with integers, check the solutions and graph them on a number line.
- C3.1
- Write and run code with loops, conditions, lists and sub-programs to represent math situations and analyse data to make decisions.
- C3.2
- Read, predict, debug and change existing code, and explain how the changes affect the results and the efficiency of the code.
- C4
- Mathematical modelling (an overall expectation with no specific expectations): understand a real problem, build a model, test it against the situation and revise it. Taught in Lesson 12 and assessed in the performance task.
- A1
- Every lesson builds in the strand A skills: problem solving, reasoning, communicating, representing, and coping with challenges.
Questions about this unit
How long is this unit?
18 school days: 12 lessons plus a diagnostic, a catch-up day, a two-day performance task, a review day and the unit test.
Which expectations does it cover?
C1.1, C1.2, C1.3, C1.4, C2.1, C2.2, C2.3, C2.4, C3.1, C3.2 from Mathematics (2020), Strand C: Algebra.
What format are the files?
Each unit comes as a Teacher Guide and Student Pages, both as editable Word files and print-ready PDFs. The Word files open in Google Docs, so you can change anything.
Can I share it with my colleagues?
A single licence is for one teacher's classes. For a grade team, the team licence covers up to 5 teachers at one school for $49.99.
What if it isn't right for my class?
Email help@unitplans.ca within 7 days of buying for a full refund.