Unit 0 - Grade 7 Review Package

In this review package, students will be reviewing their understanding of the grade 7 math curriculum. Students will be engaging in integer operations, solving equations, solving circle properties, experimental probability, financial literacy, and how to graph. Students will be required to be competent in this review package in order to be successful in the grade 8 math curriculum.

Lesson # Lesson Notes1 Integer Operations2 Solving Equations3 Solving Circles4 How to solve volume5 Circle Graphs and Percents6 Experimental Probability7 Financial Literacy8 How to Graph

Curricular Competencies

Reasoning and Analyzingo Students to be using logic and patterns to solve puzzles. Students will also reason

to explore, analyze, and apply mathematical ideas. They will estimate reasonably, apply mental math strategies, and use tools to create patterns and relationships.

Understanding and Solvingo Apply multiple strategies to solve problems. Develop, demonstrate, and apply

mathematical understanding through play, inquiry, and problem solving. Visualize to explore mathematical concepts.

Communicating and Representingo Use mathematical vocabulary and language to contribute to mathematical

discussions. Explain and justify mathematical ideas and decisions. Communicate mathematical thinking and represent mathematical ideas in concrete, pictorial, and symbolic forms.

Connecting and Reflectingo Reflect on mathematical thinking. Connect mathematical concepts to each other

and to other areas and personal interest

Lesson #1 - Orders of Operations with Integers

Big Idea - We must follow the orders of operations with integers in order to solve problems correctly and effectively.

What is BEDMAS?

What are the rules of addition with integers?

Example 1. Solve the following

2 + 9 = (-3) + (-5) =

(10) + (-5) = (-13) + (4) =

(5.3) + (3.1) = (6.5) + (-2.5) =

Where can we see addition of integers used in real world situations?

What are the rules of subtraction with integers?

Example 2. Solve the following

12 - 4 = 3.2 - 9.5 =

(-10) - (-2) = (-4.1) - (-9.5) =

15 - (-3) = 4 - (-7.5) =

(-13) - 2 = (-5.9) - 9.8 =

What are the rules for multiplication and division with integers?

Example 3. Solve the following

9.2 x 1.5 = (-6.5) x (-1.4) =

9.9 x (-1.6) = 15 ÷ 3

(-20) ÷ (-4) 36 ÷ (-9)

Example 4. If you are currently in the coldest place in the world in Oymyakon, Russia which averages -50°C and move to the hottest place in the world in El Azizia, Libya which is 58°C, what is the temperature difference you just experienced?

Example 5. Solve the following

(-5.3) x (-1.3) + (3.4) ÷ (-1.7)

Lesson #2 - Solving Equations

Big Idea - Solving equations involves using the understanding of orders of operations and using the inverse operations to solve them.

What does the word balance mean? in math?

Can you show an example of a balanced equation?

How do you solve equations?

What are the inverse operations?

Example 1. Solve the following for X

X + 9 = 12 X - 3 = -6

5X = 15 X/5 = 2

How do you solve two-step problems?

Example 2. Solve the following for Y

2Y + 6 = 12 -3Y - 2 = 13

Y/2 + 2 = 14 Y/5 - 7 = -1

Example 3. Mr. Chio collects stamps as a fun hobby. His friend gave him 20 stamps to add to his collection. He now has 25 stamps in total. How many did he have before?

Example 4. Ted sold 12 games for $132. If each game was sold as the same price, how much did each game cost?

Example 5. Joan makes $5 commission for each TV she sells. She also makes a daily wage of $60. If Joan made $150 for the day, how many TV's did she sell?

Lesson #3 - Solving Circles

Big Idea - Circles have very unique and identifiable properties that can be solved with various formulas

What are the various terms of a circle?

How are the radius, diameter, and circumference related?

How is the radius related to the circumference?

Example 1. What is the radius of this circle? What is the circumference?

Example 2. If a circle has a circumference of 628cm, what is the diameter of the circle? what is the radius?

How do you find the area of a circle?

Example 3. What is the area of the following circle?

Example 4. You are building a circular canvas to paint on. You need to calculate how much paint you will need to cover the whole canvas. You measure the diameter of the canvas to be 2.5m across. How much paint do you need?

Lesson #4 - How to solve for volume?

Big Idea - The volume of various 3D objects is concrete and has specific formulas related to each object.

How does the volume of 3D objects relate to the area of a 2D object?

Example 1. What is the area of the following 2D objects?

Example 2. What is the volume of the following triangular prism?

Example 3. What is the volume of the following rectangular prism?

Example 4. What is the volume of the following cylinder?

Example 5. What is the volume of this classroom?

Lesson #5 - Circle Graphs and Percents

Big Idea - Circle graphs show information relating to a whole between various values.

What information does a circle graph provide?

Example 1. Refer to the follow circle graph about students favourite sport. 500 students participated in this survey.

What is the favourite sport in the school?

Which sport is the least favourite?

How many votes did each sport receive?

How does a circle graph relate to the percentage?

Example 2. You survey Netflix to find out what their customers like to watch the most. Below is the responses.

Genre PercentComedy 33Romance 25Sci-Fi 17Drama 8Horror 12Documentary 5

a. Construct a circle graph to show this data.

b. How many people like comedies if Netflix has 1,000,000 suscribers?

How are percents, fractions, and decimals related?

Example 3. Complete the table below

Decimal Fraction

1.5

6/15

6.33...

25/9

What are repeating and terminating decimals?

Example 4. Order the following from least to greatest

1.5, 5/6, 1.33..., 6/5, 3/2, 1

Example 5. Complete the table below

Percent Fraction Decimal

15%

20%

55%

83%

Example 6. Complete the table below

Fraction Percent Decimal

6/10

25/30

36/48

99/121

Lesson #6 - Experimental Probability

Big Idea - Experimental probability can be determined if we know the occurrence of the event over the total number of event

What is the range of an event occurring?

What is the formula for experimental probability with independent events?

Example 1. You roll a 6 sided dice. What are the chances you roll a 3? What are the chances you roll an even number? What are the chances you do not roll an even number?

Example 2. Using a real dice, roll 60 times and record your results below. Do the probabilities match up with the calculated response above? Why or why not? How can you make it match the response above?

Example 3. You have a Dungeon and Dragons dice which is 20 sided and you also have a coin. Show on a tree diagram the possible outcomes. What are the chances you roll a number divisible by 5 and flip a heads?

Lesson #7 - Financial Literacy

Big Idea - Financial literacy is the understanding of finance and how to utilize it in the real world for employment, merchandising, and services.

What is sales tax?

How does a sales tax work?

Is there a quicker way to calculate sales tax?

Example 1. What is the total cost of a cheeseburger costing $12.99 in BC with a sales tax of 5%?

Example 2. What is the total cost of the same cheeseburger sold in Ontario with a sales tax of 13%?

Example 3. What is the difference in cost between BC and Ontario for the cheeseburger?

How are discounts applied for products?

Example 4. What is the cost of a basketball that is 25% off if the original price is $34.99?

How does tipping work for restaurants?

Example 5. You go eat a fancy restaurant and you receive the bill. It cost $150 for the meal + tax. How much should you tip if you want to tip 20%?

Lesson #8 - How to Graph

Big Idea - Graphing is an important skill to possess which allows us to represent data in an efficient visual format

What are relations?

Example 1. Write the relation of the following

Five less than a number

A number increased by 10

Triple a number

5 more than 2 times a number

Example 2. Complete the following table with the output

Input n Output 3n + 2

0

1

2

3

4

5

6

7

Example 3. Determine the relation from the table below

Input n Output0 31 62 93 124 155 186 21

Example 4. From the graph below, create a table of values for the number of pizza's consumed daily in Vancouver per hour.

Example 5. Mr. Chio is paid $40 per day to sell newspapers and an additional $2 for every newspaper sold.

a. Create a relation for this scenario

b. Create a table of values for this scenario

c. Graph the scenario

d. How much money will Mr. Chio make if he sells 30 newspapers?

e. How many newspapers does Mr. Chio need to sell to make $74?

What is the Cartesian coordinate system?

Example 6. Plot the following points on the graph below A (-4, 3), B (3, 6), C(0, -3) and join to form triangle ABC.

A. On the plot above, translate the triangle 2 units to the right

B. Translate the triangle 1 unit up

C. Reflect the triangle about the Y-axis.