Grade 7 Numeracy

Learning Intentions

I know I’m on track with my learning about expressions and equations, when I can:

● Demonstrate how to preserve equality

● Demonstrate an understanding of linear patterns in various representations

● Solve problems using linear relations

● Evaluate an expression

Mental Mathematics

MM#1: Make it True

Look at the image in MM#1. Use mental math to figure out what values of and make these equations true. Try to solve this in more than one way.

Reminder: Both sides of the equation must balance (ex. 8 + 4 is the same as 5 + 7, therefore 8 + 4 = 5 + 7)

MM#2: Divisibility Rules

Complete the number by filling in each blank with a digit. Explain how you know your answer is correct:

26_ is divisible by 10

154_ is divisible by 2

_6_ is divisible by 6

26_ is divisible by 3

1_2 is divisible by 9

15_ is divisible by 4

MM#3: Crack the Code: Divisibility Riddles

Each of Eli’s four friends has a code number. Keile’s number is divisible by 3, 5, and 8. Max’s number is divisible by 2 and 3. Jennifer’s number is divisible by 4 and 5, but not 3. Ben’s number is divisible by 2 and 8, but not 5. Eli receives a message with the code number 5384 from one of his four friends. Determine who sent the message.

Make your own Divisibility Crack the Code for someone in your family to solve.

Review and Practice

RP#1: Word Sort

Sort the list of words below. How many different ways can you organize these words?

plus, minus, times, divide, add, increased by, quotient, subtract, multiply, sum, product, reduced by, less than, total, difference, decreased by, more than, less than, subtracted from, added to, shared equally, equivalent to, factor of, groups of

RP#2: Complete the Chart

Look at the image in RP#2. Use the example in the first row, and your prior knowledge, to show your understanding of each of the algebraic expressions in the chart.

Problem Solving and Learning Explorations

PS/LE#1: Growing Shapes Pattern

Look at the image in PS/LE#1. There are 3 copies of the same pattern. How do you see the shapes growing? Use color-coding to show 3 different ways that you see the shapes growing. How would you describe the growth to someone in your home? What would the 10th or 20th image look like?

PS/LE#2: Lifeguards Needed for Swimmers

Look at the image in PS/LE#2. How would you answer the following questions?

● How many swimmers would be allowed for 10 lifeguards?

● How many lifeguards would be needed for 50 swimmers?

● Describe the pattern in words to someone in your home.

● Write an equation for the number of (l) lifeguards needed for (s) swimmers.

PS/LE#3: Describe the Pattern

Look at the image in PS/LE#3. Complete the chart by drawing in the next 2 stages/terms. Describe the pattern in words.

Go outside and find natural objects and create your own linear pattern.

PS/LE#4: Bike Ride

Each day you and your family go for a bike ride. On Monday, you biked 3 km. Each day, you bike 2 more km than the day before. Create a table of values for this data (starting on Monday and ending on Sunday). Describe the pattern, and create a graph using the image in PS/LE#4. Can you determine how many km you would be biking on day 21 if the pattern continued? Show your strategy.

PS/LE#5: Task Practice

Task A: Determine the value of the variable to make a true statement.

18 + n = 31 81 = 9 x t 8 x w = 56 x ÷ 6 = 7

Task B: Determine which expression has the greatest value if p = 8.

p + 7

2p

10 – p

8 ÷ p

3p – 12

2 + 2p

PS/LE#6: Balanced Scales.

Look at the image in PS/LE#6. Which of the scales balance? How do you know? Create balanced expressions using the empty balance.

Project Learning

PL#1: Pizza Pricing

When buying a pizza, the pricing is often linear- a base price with each topping adding additional cost. Look at the sample pricing below and complete each of the tasks.

Bradford’s Pizzaria: Large Cheese Pizza $12 + $1 per topping

Tina’s Tasty Pizza Pies: Large Cheese Pizza $10 + $2 per topping

Raeanne’s Pizza Palace: Large Cheese Pizza $8 + $3 per topping

Task 1 - Make a table of values, graph the relationship between toppings (t) and cost (c), and write an equation for each pizza place.

Task 2 - Explain which place you would prefer to buy form. Consider things like how many toppings you like on your pizza and best pizza for its value.

Task 3 - Is there ever a time when each pizza place would cost the same amount for the same number of toppings on the pizza? Explain your thinking.

Your Turn

Use the recipe in PL#1 to make your own personal pizzas. Calculate the cost of your pizza if you were to buy the same pizza in each of the three restaurants above. Where would the best place be to buy your pizza? (if using the pricing above).

Create your own pizza place. Decide on a name and create a logo. Decide how much a large cheese pizza will cost and the cost per additional topping. Be sure to keep it competitive with the other pizza places listed. Create a mathematical menu that shows the pizzas available, and the costs for each as an equation.

Grade 8 Numeracy

Learning Intentions

I am reinforcing, and applying my math skills. I know I got it when I

● solve problems using my operations and algebraic reasoning skills

● communicate my mathematical reasoning using both words and symbols

Mental Mathematics

MM#1 Integer Patterns

Find the next two terms in the following patterns:

1, 5, 9, 13, ____, ____

22, 19, 16, 13, ____, ____

7, 11, 8, 12, 9, ____, ____

Make up three of your own patterns.

MM#2 Percent

Represent 25% in many different ways. Consider using words, pictures, graphs, numbers, symbols, equations, examples, etc.

MM#3 Percent Estimation

You will need a deck of cards or you could make your own set of number cards (digits 0-9). You may still have cards from last week’s work.

Part A - Turn over 3 cards. The first card is a percent and the second two cards are a number to estimate. Estimate ___ % of ___ ___. Example: if you turned over the cards 872, you would estimate 8% of 72… about 6. Repeat several times.

Part B - Turn over 4 cards. The first two cards are a percent and the second two cards are a number to estimate. Estimate ___ ____ % of ___ ___. Example: if you turned over the cards 1265, you would estimate 12% of 65… about 8. Repeat several times.

Review and Practice

RP#1 Mosaic

A mosaic is a picture or pattern made by putting together small colored pieces of hard material, such as stone, tile, or glass. Pictured here is a picture of a Mi’kmaq Eight Pointed Star mosaic from LeMarchant-St. Thomas Elementary school in Halifax. Imagine that you’re on the telephone with a friend. Describe the complete pattern as precisely as you can, so someone else can draw it without seeing it. Try to describe the shapes, colours, symmetry and angles.

Extension: Read your description to someone and see if they can draw the picture of the mosaic. Compare their drawing to the picture shown here.

RP#2 Baking Fractions

A set of measuring cups includes 1/4, 1/3, 1/2 and 1 cup. How could you measure ¾ of a cup of flour usings these measuring cups? Can you find more than one way to measure this amount? How could you measure 1 ⅚ cups of flour? Create your own amount and see if you can find a strategy to measure that much. Are there any amounts you can’t make with this set of measuring cups? If you could add one more measuring cup to your set, what amount would be the most useful?

RP#3 Ratio and Rates

The Guinness World Record for claps in one minute is 1,103 claps. Estimate how many times you can clap your hands in one minute. Use a timer to count how many times you can clap your hands in 10 seconds. At this pace, how many hand claps should you have in a minute? Use a time to count your hand claps for 30 seconds. Is it the same pace as before or different? Ask another member of your household to see how many times they can clap their hands in one minute. How close is your rate to the record rate?

Extension: What other things could you measure doing in one minute? What do you think the world record might be for these measurements?

Problem Solving and Learning Explorations

PS/LE #1 Graphing

How many different ways can you describe the relation shown in this graph? Can you create a real-world context for this relationship? Can you create a table of values or an equation for this graph?

PS/LE #2 Area and Perimeter Expressions

PS/LE #3 Add ‘Em Up

Solve the following four equations. If the solutions to the four equations (g + h + m + n) sum to 8, you know you’ve solved them all correctly! Create another set of four equations whose solutions also add up to 8.

PS/LE #4 Find the Integer

Therese chose an integer. She subtracted 7, then multiplied the difference by –4.

The product was 36.Which integer did Therese choose?

a) Write an equation you can use to solve the problem.

b) Solve the equation.

c) Verify the solution.

Project Learning

Printing T-Shirts

Ultimate Screen Printing charges $55 to set up the artwork for processing the graphics and creating a screen for printing t-shirts. They charge $9 for each shirt printed. You want to create t-shirts for your school’s club.

a) Write an equation where c represents the total cost and n represents the number of t-shirts ordered.

b) Draw a picture of what your club t-shirt looks like.

c) Use the equation to create a table of values and a graph.

d) Use the equation to find the cost of ordering 35 t-shirts. Check the answer.

e) Use the equation to find out how many t-shirts you can order if you have $250.

Grade 9 Numeracy

Learning Intentions

I am reinforcing, and applying my math skills. I know I got it when I…

● solve problems using rational numbers and my proportional reasoning skills

● use my algebraic reasoning skills to solve real world problems

Mental Mathematics

MM#1 Rational Number Patterns

Find the next two terms in the following patterns:

0.125, 0.250, 0.375, ____, ____

1/2, 3/4, 1, 5/4, ____, ____

7/8, 3/4, 5/8, 1/2, ____, ____

Make up three of your own patterns using fractions or decimals.

MM#2 Pizza Estimation

A group of co-workers wants to purchase pizza for lunch. There are seven co-workers and the pizza costs $84. If each co-worker pays an equal amount of the cost, how much should each person pay? Estimate how many pizzas they ordered and how many slices of pizza each co-worker got? Do you think they ordered the correct amount?

MM#3 More or Less

Use estimation strategies to determine if each expression below will be more or less than 8:

a) 4.1 + 4.7

b) 2.7 + 5.1

c) 8.9 - 1.9

d) 12.3 - 5.5

e) 2.3 ✕ 4.1

f) 40.8 ÷ 8.7

Review and Practice

RP #1 Grade 8 Review

Try some of the activities from the grade 8 section. This is a great review for learning grade 9 concepts.

RP#2 Linear Relations

Suppose that there are some spiders in a tank and each spider has 8 legs.

x = the number of spiders and y = the total number of legs on all the spiders.

Circle each equation below that you think is correct to describe the relationship between number of spiders and number of spider legs. Explain why you did or did not circle each equation.

RP #3 Area

The area of a field is 120 m². The dimensions of a barn in the field are 10 m x 8 m. What is the area of the field not taken up by the barn? Draw a picture to show the field and barn using appropriate measurements. There are lots of ways to do this. Can you draw a field that is not rectangular?

Problem Solving and Learning Explorations

PS/LE #1 Creating Fractions

Part I. Write a fraction for each of the criteria listed below:

A. Is less than 1

B. Has a denominator greater than 10

C. Is fully simplified

D. Can be rewritten as a terminating decimal

E. Has a numerator greater than its denominator

F. Is greater than 2/3

G. Has a numerator greater than 20

H. Is equivalent to 1/2

Part II. Can you write a fraction that satisfies two or more of the listed criteria from Part I? Example: 3/6 satisfies A, D, and H.

Part III. What is the fewest number of fractions you can write to satisfy every criteria from Part I at least once. Could you do it with only four fractions? What about 3 fractions or just 2 fractions?

PS/LE #2 Add ‘Em Up

Solve the following four equations. If the solutions to the four equations (g + h + m + n) sum to 2.8, you know you’ve solved them all correctly! Create another set of four equations whose solutions add up to 2.8.

PS/LE #3 Find the Error

Examine this student’s work. Identify the mistakes and fix them to make a correct and complete solution.

PS/LE #4 Model and Solve

Bicycles can be rented from two different shops downtown.

Shop R charges $15 plus $3 per hour

Shop S charges $10 plus $5 per hour

Determine the time in hours for which the rental charges in both shops are equal.

a) Model this problem with an equation.

b) Solve the problem.

c) Verify the solution. Show your work.