Grade 7 Math: Algebra and Coding unit
Students study repeating, growing and shrinking patterns, write rules for linear patterns in several forms, and use integer patterns to explain sign rules. They simplify and evaluate expressions, solve multi-step equations and inequalities, read and write short Python programs with loops and sub-programs, and finish by using the modelling cycle on a real-life problem. The performance task asks students to model and compare two bike-rental offers for a class trip.
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
- Lesson slidesA ready-to-project deck for every lesson: goals, worked examples, discussion questions and exit tickets, with your lesson steps in the speaker notes
- Student worksheets with answer keys122 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“Bike Rental for the Trip”, with a rubric across all four achievement chart categories
- Unit test and answer key39 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 | C1.3 |
| 5 | Lesson 4: Patterns that explain integers (Quick check 1) | C1.4 |
| 6 | Lesson 5: Adding and subtracting like terms | C2.1 |
| 7 | Lesson 6: Evaluating expressions and formulas | C2.2 |
| 8 | Lesson 7: Solving two-step equations | C2.3 |
| 9 | Lesson 8: Solving equations with several terms | C2.3, C2.1 |
| 10 | Lesson 9: Solving and graphing inequalities (Quick check 2) | C2.4 |
| 11 | Lesson 10: Writing code with loops | C3.1, C3.2 |
| 12 | Lesson 11: Sub-programs, conditions and improving code (Quick check 3) | C3.1, C3.2 |
| 13 | Lesson 12: The modelling cycle: planning a school dance | C4, C2.3, C3.1 |
| 14 | Catch-up and conferencing day (reteach from quick checks) | All |
| 15 | Performance task: Bike Rental for the Trip (part 1) | C4, C1.2, C2.3 |
| 16 | Performance task: Bike Rental for the Trip (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 tell repeating, growing and shrinking patterns apart, and to compare growing patterns by how fast they grow and where they start.
Success criteria:
- I can name the core of a repeating pattern and use it to find a far-away term.
- I can tell a growing or shrinking pattern from a repeating one.
- I can find the constant rate and the initial value of a linear pattern.
- I can compare two linear patterns using their rates and initial values.
Minds On (10 min)
- Show 2, 5, 5, 2, 5, 5 and a tile pattern that gets bigger. Ask: "What is the same and what is different about these two patterns?"
- Collect words on the board: repeat, grow, shrink, rule.
Action (35 min)
- Teach the three kinds: repeating (a core repeats), growing (values go up), shrinking (values go down). Build a tile pattern with counters.
- Define constant rate (the amount that changes each step) and initial value (what the pattern would be at figure 0). Use the tile pattern to find both.
- Compare two gym-plan patterns: which starts higher, which grows faster, and when are they equal? Students then complete Worksheet 1.
Consolidation (15 min)
- Discuss question 5: how do the starting value and the rate each change the story?
- Exit: "Pattern A starts at 3 and adds 2 each step. Pattern B starts at 1 and adds 4. Which is bigger after 10 steps?"
Worksheet 1: Kinds of patterns
Show your work. Use the tile pictures to help.
- A repeating pattern has the core 2, 5, 5. What is the 25th term?
- The tile pattern is growing. How many tiles are in Figure 6?
- Tell whether each pattern is repeating, growing or shrinking. For the growing or shrinking ones, say if the rate is constant. A: 4, 8, 12, 16 B: 50, 45, 40, 35 C: red, blue, red, blue, red, blue D: 2, 4, 8, 16
- A tank holds 120 L of water. It drains 8 L every minute. How many litres are left after 7 minutes?
- Plan A costs $15 to join plus $4 per class. Plan B costs $5 to join plus $6 per class (made-up prices). Which plan has the greater initial value? Which grows faster? After how many classes do the plans cost the same, and what is that cost?
- Is the pattern 3, 6, 12, 24 a linear growing pattern? Explain.
- A snail is 40 cm up a wall and climbs 6 cm each hour. A beetle is 10 cm up the wall and climbs 9 cm each hour (made-up). After how many hours are they at the same height?
Answer keys with worked steps are in the Teacher Guide.
Performance task: Bike Rental for the Trip
A class of 32 riders is planning a bike trip (made-up prices). Riverside Bikes charges a $25 booking fee plus $11.50 per bike. TrailRoll charges $16 per bike with no fee. The class has $400 to spend.
| Category | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| Knowledge and Understanding | Writes equations or tables with major errors and little understanding of rate and starting cost. | Writes equations and tables with some errors; shows partial understanding of rate and starting cost. | Writes correct equations and tables and solves the equations with minor errors. | Writes correct equations and tables, and shows deep understanding by connecting them to the graph and the story. |
| Thinking | Makes little progress comparing the companies or testing the model. | Compares the companies with limited reasoning; tests the model in few cases. | Compares the companies, finds the equal-cost point, tests the model and adjusts it with sound reasoning. | Compares the companies, tests the model in several ways, adjusts it thoughtfully and justifies each choice. |
| Communication | Explanations are unclear or missing; graph is missing key parts. | Explanations are partly clear; graph or code has some missing parts. | Explains the work clearly with a labelled graph, correct notation and readable code. | Explains the work precisely and with insight; graph, notation and code are clear and well organized. |
| Application | Does not link the maths to the trip decision. | Links the maths to the decision with some gaps and few assumptions. | Makes a sensible recommendation supported by the model and names assumptions. | Makes a well-supported recommendation, names assumptions and limits, and suggests how to improve the model. |
Lessons in this unit
- Repeating, growing and shrinking patternsLearning to tell repeating, growing and shrinking patterns apart, and to compare growing patterns by how fast they grow and where they start.C1.1
- Showing linear patterns in many waysLearning to show the same pattern as a table, a graph, words, an expression and an equation.C1.2
- Pattern rules and predictionsLearning to find a pattern rule, use it to predict far-away terms and missing terms, and solve for an unknown with an equation.C1.3
- Patterns that explain integersLearning to build patterns that show why adding and subtracting integers works the way it does, and a pattern of powers.C1.4
- Adding and subtracting like termsLearning to add and subtract terms that have the same variable, using tiles and then rules.C2.1
- Evaluating expressions and formulasLearning to put numbers in place of variables and calculate the value of an expression or formula, including with decimals.C2.2
- Solving two-step equationsLearning to solve equations that need two steps, including ones with decimals, and to check that the answer is right.C2.3
- Solving equations with several termsLearning to combine like terms in an equation before solving it, and to write equations for situations with several parts.C2.3, C2.1
- Solving and graphing inequalitiesLearning to solve inequalities with more than one step, check solutions, and graph them on a number line.C2.4
- Writing code with loopsLearning to read and write short programs that repeat steps a set number of times or until a condition is met.C3.1, C3.2
- Sub-programs, conditions and improving codeLearning to build sub-programs, use if statements, and change code to see how the output and the efficiency change.C3.1, C3.2
- The modelling cycle: planning a school danceWe are learning the steps of mathematical modelling: understand a situation, build a model, test it against the real world, and improve it.C2.3, C3.1
Ontario curriculum expectations covered
- C1.1
- Tell repeating, growing and shrinking patterns apart, and compare linear patterns by how fast they change and where they start.
- C1.2
- Build patterns and show them as tables, graphs, expressions and equations, using whole and decimal numbers.
- C1.3
- Find pattern rules, extend patterns, justify predictions and fill in gaps; use an equation to find an unknown term.
- C1.4
- Invent and describe patterns that reveal how integers relate to each other.
- C2.1
- Combine monomials of degree 1 by adding and subtracting, using physical or picture tools.
- C2.2
- Find the value of expressions when variables are replaced by whole or decimal numbers.
- C2.3
- Solve equations that have several terms and decimal numbers in real contexts, and check the answers.
- C2.4
- Solve inequalities with several terms, check the solutions, and draw them on a number line.
- C3.1
- Write and run efficient programs that use counted loops, sub-programs and other control structures to solve problems.
- C3.2
- Read and change existing programs, and explain how the changes affect the results and the efficiency.
- C4
- Use the modelling cycle to represent a real situation, test the model, make predictions and improve the model.
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, plus a PowerPoint deck of lesson slides. The Word files open in Google Docs and the slides open in Google Slides, 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.