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C. Algebra · Patterns, Expressions, Equations, Inequalities, Coding and Modelling

Patterns, Expressions, Equations, Inequalities, Coding and Modelling: Unit Review

A1 C1.1 C1.2 C1.3 C1.4 C2.1 C2.2 C2.3 C2.4 C3.1 C3.2 C4About 40 minutes
Learning goals
  • I can show what I learned about patterns, expressions, equations, inequalities, coding and modelling.
  • I can find the parts of the unit I need to practise more.

Words to know

linear growing pattern
A growing pattern that adds the same amount each time; its graph points make a straight line.
monomial
An expression with one term, like 4x or 7.
boundary point
The value that makes both sides of an inequality equal.
efficient code
Code that does the job with fewer lines or steps and still works.

Let's review!

In this unit you spotted linear patterns; showed patterns with tables, graphs, expressions and equations; used pattern rules to predict and to solve for unknowns; made patterns with decimals; added monomials; evaluated expressions with tenths; solved equations with multiple terms and inequalities with two operations; wrote and changed efficient code; and used a math model to plan a hot chocolate stand.

This review has a few questions from every lesson. Try each one, then press Show answer to check. If a part feels tricky, go back to that lesson for more practice.

Algebra in Grade 6Patternslinear or not?tables, graphs, t = 3n + 1decimal patternsExpressionsadd monomialsevaluate with tenthsEquations andinequalitiessimplify, undo, verifyboundary point, graphCoding andmodellingefficient loops, ELSE IFassume, model, revise
The four big ideas of the unit. Each review section below matches one of the lessons in these branches.
Pattern4, 7, 10, 13, ...Jump+3 each timeEquationt = 3n + 1Solve for t = 313n + 1 = 31 →n = 10Verify3 × 10 + 1 = 31 ✓One pattern, followed from start to finish.
A whole-unit workout in one strip: find the jump, write the equation, solve backward, then verify.

Repeating, Growing and Shrinking Patterns: Which Are Linear?

1

Is 6, 13, 20, 27, ... linear? What is the next term?

2

Is 2, 6, 18, 54, ... linear? Explain.

3

Describe 72, 64, 56, 48, ...

Representing Patterns: Tables, Graphs, Expressions and Equations

1

Write an equation for 7, 12, 17, 22, ...

2

Make a table for t = 3n − 1, for n = 1 to 4.

3

A graph shows (1, 9), (2, 13), (3, 17). Write the expression.

4

Translate ⭐⭐🌙⭐⭐🌙 into letters.

Pattern Rules: Predictions, Missing Elements and Unknown Values

1

Use t = 6n + 4 to find term 20.

2

For t = 6n + 4, which term has the value 88?

3

Find the missing terms: 3, ☐, 17, 24, ☐

4

The core is 🍁❄️⛄. What is the 25th element?

Patterns with Whole Numbers and Decimals

1

Continue: 900, 90, 9, ☐, ☐, ☐

2

Count by 0.125 from 0. Which term is 1?

3

Find the missing terms: 3.6, 3.2, ☐, 2.4, ☐

Variables and Adding Monomials

1

Add 7x + 5x.

2

Add 4m + 2 + m + 6.

3

A rectangle is 5k long and 2k wide. Write its perimeter as a monomial.

4

Can 6a + 3b be written as one term?

Evaluating Expressions with Whole Numbers and Tenths

1

Evaluate 4x + 0.6 when x = 1.5.

2

Evaluate 2(y + 1.3) when y = 2.7.

3

Evaluate 3a + b when a = 2.2 and b = 0.4.

Solving Equations with Multiple Terms

1

Solve 5x + 3x = 64.

2

Solve 2n + n + 9 = 45.

3

A triangle has two sides of length x and one side of 15 cm. The perimeter is 41 cm. Find x.

Inequalities with Two Operations: Solve, Verify and Graph

1

Solve 4n + 7 < 43.

2

Solve 3n − 5 ≥ 25, using whole numbers up to 100.

3

Is 6 a solution of 5n + 2 ≤ 32?

Writing Efficient Code

1

Run: SET t = 3. REPEAT 5 times: SAY t, ADD 6 to t.

2

Make this more efficient: SAY "🎿" written 5 times, then SAY "done".

3

IF temp < −10 THEN SAY "stay in" ELSE IF temp < 0 THEN SAY "toque" ELSE SAY "jacket". What does it say for temp = −4?

Reading and Altering Code: Outcomes and Efficiency

1

SET n = 4. REPEAT 3 times: ADD 4 to n, SAY n. What does it say? How would you change it to say 4, 8, 12?

2

Will this stop? SET n = 2. REPEAT UNTIL n = 11: ADD 2 to n.

3

Code A checks every number from 1 to 40 and says the multiples of 4. Code B starts at 4 and adds 4, ten times. Which is more efficient?

Math Modelling: Planning a Winter Carnival Hot Chocolate Stand

1

Option A costs 30 + 0.5c and Option B costs 1.5c. Which is cheaper for 100 cups?

2

Give one assumption the class made in their model.

3

With Option A and a $2 price, profit is 1.5c − 30. What is the profit for 140 cups?

Just for fun

Riddle: I'm a linear pattern. I start at 5 and add 5 each time. What is my 100th term?

500! My equation is t = 5n, so t = 5 × 100. (No need to write out all 100 terms!)

How to use this review

  • Do the review in two or three short sittings. Each section matches one lesson.
  • Use tools: grid paper for graphs, algebra tiles (or sticks and buttons) for monomials, a number line for inequalities, coins and a measuring tape for decimals, and objects to act out code.
  • For equations and inequalities, always verify by substituting your answer.
  • For code, keep a tracking table for every variable.
  • Put a star next to any question you got wrong, then go back to that lesson's practice.
Check your understanding

Quiz

1.

Which growing pattern is linear?

2.

Which equation matches 3, 7, 11, 15, ...?

3.

For t = 5n + 3, which term has the value 63?

4.

What comes next: 0.008, 0.08, 0.8, ...?

5.

Add: 3y + 4 + 5y

6.

Evaluate 6n − 1.2 when n = 0.5.

7.

Solve 4x + 2x + 5 = 47.

8.

What are the solutions of 2n + 9 > 31?

9.

SET n = 2. REPEAT 4 times: SAY n, then ADD 3 to n. What is the outcome?

10.

In a math model, what is an assumption?

For parents and teachers

Use mistakes to choose what to revisit. Each review section matches one lesson.

  • Calls every growing pattern linear, or checks only the first jump: revisit Repeating, Growing and Shrinking Patterns: Which Are Linear?.
  • Puts the first term in front of n (t = 4n + 3 for 4, 7, 10), or joins the dots on a graph: revisit Representing Patterns: Tables, Graphs, Expressions and Equations.
  • Divides before subtracting when finding a term number, or miscounts cores in a repeating pattern: revisit Pattern Rules: Predictions, Missing Elements and Unknown Values.
  • Moves digits the wrong way when multiplying or dividing by 10, or thinks 0.25 > 0.3: revisit Patterns with Whole Numbers and Decimals with coins and a measuring tape.
  • Combines unlike terms (5m + 4 = 9m) or forgets that x means 1x: revisit Variables and Adding Monomials with tiles.
  • Reads 2a as "2 and a" or ignores the order of operations: revisit Evaluating Expressions with Whole Numbers and Tenths.
  • Forgets to add like terms first, or does an operation to only one side: revisit Solving Equations with Multiple Terms.
  • Includes the boundary with < or >, or follows the sign without testing: revisit Inequalities with Two Operations: Solve, Verify and Graph.
  • Writes long code with repeated lines, or mixes up what is inside a loop: revisit Writing Efficient Code.
  • Misses order bugs (SAY after ADD), boundary bugs (> vs ≥) or infinite loops: revisit Reading and Altering Code: Outcomes and Efficiency.
  • Gives an answer with no assumptions or units, or doesn't revise when facts change: revisit Math Modelling: Planning a Winter Carnival Hot Chocolate Stand.

A few mistakes are normal. Praise the strategy your child explains and the habit of checking, not only the right answer.