Grade by Grade
C. Algebra · Patterns, Integers, Equations, Inequalities, Coding and Modelling

Patterns, Integers, 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 describe, compare, create and extend patterns, including linear patterns and integer patterns.
  • I can add and subtract monomials and evaluate expressions with decimals.
  • I can solve equations and inequalities with multiple terms, and verify and graph the solutions.
  • I can write, read and alter code with counters and sub-programs, and use math to model a real situation.

Words to know

constant rate
The amount a linear pattern changes each term.
initial value
The value of a pattern at term 0.
like terms
Terms with the same variable, like 3x and 5x.
boundary point
The number where the two sides of an inequality would be equal.
sub-program
A named group of instructions you define once and call many times.
assumption
Something you treat as true so you can build a model.

Let's review!

In this unit you described and compared repeating, growing and shrinking patterns; compared linear patterns using their constant rate and initial value; created and translated patterns; found missing terms and solved for unknown values; explored integer patterns; added and subtracted monomials; evaluated expressions; solved equations and inequalities with multiple terms; wrote and altered code with counters and sub-programs; and built a mathematical model for a ski club.

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. (All prices in this review are made up.)

x < 6x > 6x ≤ 6x ≥ 6024681012open circle: 6 is not includedclosed circle: 6 is included
The four kinds of inequality graphs with boundary point 6. An open circle leaves 6 out; a closed circle includes it. Shade in the direction of the solutions.
02468101214012345term number n1 stepup 2starts at 3: initial valuet = 2n + 3constant rate 2(how steep)initial value 3(where it starts)
In a linear pattern, the initial value is where the points start (at n = 0) and the constant rate is how far they rise for each step to the right.

Repeating, Growing and Shrinking Patterns in Real Life

1

Describe 3, 9, 27, 81, ... Is it linear?

2

Describe 15, 12.5, 10, 7.5, ... and give the next term.

3

Pattern P: 6, 10, 14, 18. Pattern Q: 1, 2, 4, 8. Which is bigger at term 6?

Comparing Linear Patterns: Constant Rate and Initial Value

1

Find the equation of 13, 18, 23, 28, ... (starts at term 1).

2

Plan X: $30 plus $5 a month. Plan Y: $11 a month. After how many months do they cost the same?

3

Which has the steeper graph: t = 3n + 40 or t = 8n + 1?

Creating and Translating Patterns

1

Make a table for t = 1.5n + 2 for n = 0 to 3.

2

Write the equation for the graph with points (0, 20), (1, 17.5), (2, 15).

3

Translate hop, hop, clap, hop, hop, clap into letters.

Pattern Rules: Predictions, Missing Elements and Unknown Values

1

Find the missing terms: 4.5, ?, ?, 6.3.

2

For t = 6n + 5, which term is 77?

3

Is 60 a term of t = 7n + 3?

4

What is the 40th item in A B C D E A B C D E ...?

Patterns with Integers

1

Next three terms: 7, 4, 1, ...

2

Continue: 3 + 0 = 3, 3 + (−1) = 2, 3 + (−2) = ?, 3 + (−3) = ?

3

Continue: 1 − 0 = 1, 1 − (−1) = ?, 1 − (−2) = ?

Adding and Subtracting Monomials

1

Simplify 9x + 4 − 3x + 2.

2

Simplify 5a + 2b − a + b.

3

Is 3m + 3 = 6m? Explain.

Evaluating Expressions with Whole Numbers and Decimals

1

Evaluate 3.5x + 2 when x = 4.

2

Evaluate 2a + 5b when a = 1.25 and b = 0.3.

3

Evaluate 6(k − 0.5) when k = 2.

Solving Equations with Multiple Terms and Decimals

1

Solve 3x + 2x + 1.5 = 26.5.

2

Solve 0.25n + 3 = 5.

3

A bowling party costs $20 plus $7.50 per person. The total is $110. How many people?

Inequalities with Multiple Terms: Solve, Verify and Graph

1

Solve 4x + x + 3 < 38.

2

Describe the graph of y ≥ 9.

3

Solve 60 − 3x − 2x ≥ 20.

Coding with Counts and Sub-programs

1

SET c = 0, REPEAT 15 times: ADD 1 to c, IF c is a multiple of 5 THEN SAY c. What does it say?

2

Using PATTERN(start, jump, terms), what does PATTERN(0.5, 1.5, 4) say?

3

Why use a sub-program instead of copying the same lines?

Reading and Altering Code: Counts, Sub-programs and Efficiency

1

Find the bug: SET x = 0, REPEAT UNTIL x = 20: ADD 3 to x.

2

SET n = 1, REPEAT 4 times: SAY n, ADD 2 to n. What does it say? What if the two lines inside the loop are swapped?

3

Code A loops 80 times to find 4 answers. Code B loops 4 times and gets the same 4 answers. Which is more efficient?

Math Modelling: Choosing a Plan for the Winter Ski Club

1

In the ski club model, what is Plan B's cost for 7 visits? Plan A's?

2

Why is 7.5 visits not a possible answer in real life?

3

Name the five steps of the modelling process.

Just for fun

Why did the algebra textbook look so tired?

It had too many problems to solve!

How to use this review

  • Do the review over two or three short sittings. Each section matches one lesson.
  • Write every step on paper, especially for equations, inequalities and code tracing.
  • Check your answers: substitute solutions back in, test a number for inequalities, and use a tracking table for code.
  • Put a star next to any question you got wrong, and go back to that lesson's practice.
Check your understanding

Quiz

1.

Which pattern is linear?

2.

What is the equation of 6, 10, 14, 18, ... (starting at term 1)?

3.

Find the missing term: 1.4, 2.1, ?, 3.5

4.

Continue the pattern: 6 − 1 = 5, 6 − 0 = 6, 6 − (−1) = ?

5.

Simplify 8x + 5 − 2x − 1.

6.

Evaluate 4y − 1.5 when y = 2.5.

7.

Solve 2x + 4x + 3 = 33.

8.

Solve 3n + 2n − 5 > 20.

9.

SET k = 0, REPEAT 9 times: ADD 1 to k, IF k is a multiple of 3 THEN SAY "Hi". How many times does it say "Hi"?

10.

Plan A costs $20 + $4 a visit. Plan B costs $9 a visit. For 3 visits, which is cheaper?

For parents and teachers

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

  • Checks only the first jump, or calls a doubling pattern linear: revisit Repeating, Growing and Shrinking Patterns in Real Life.
  • Uses term 1 as the initial value, or thinks the higher-starting line is steeper: revisit Comparing Linear Patterns: Constant Rate and Initial Value.
  • Mixes up the constant rate and initial value in an equation, or can't move between table, graph and equation: revisit Creating and Translating Patterns.
  • Counts terms instead of jumps, or divides before subtracting when solving for a term number: revisit Pattern Rules: Predictions, Missing Elements and Unknown Values.
  • Thinks −8 > −2, or that 4 − (−1) = 3: revisit Patterns with Integers. Build the pattern again.
  • Combines unlike terms (5x + 3 = 8x) or forgets that x means 1x: revisit Adding and Subtracting Monomials. Use paper tiles.
  • Reads 3n as "3 and n" or adds before multiplying: revisit Evaluating Expressions with Whole Numbers and Decimals.
  • Forgets to combine like terms first, or verifies in the simplified equation: revisit Solving Equations with Multiple Terms and Decimals.
  • Mixes up open and closed circles, or shades without testing: revisit Inequalities with Multiple Terms: Solve, Verify and Graph.
  • Thinks DEFINE runs the code, or loses track of a counter: revisit Coding with Counts and Sub-programs. Use a tracking table.
  • Misses infinite loops or the effect of swapping lines: revisit Reading and Altering Code: Counts, Sub-programs and Efficiency.
  • Gives an answer with no assumptions, or doesn't interpret decimals like 7.5 visits: revisit Math Modelling: Choosing a Plan for the Winter Ski Club.

A few mistakes are normal. Praise clear steps, checking and explaining, not only the right answer.