Grades 7-9 - Numeracy

Suggested Times 7-9 Numeracy

Students are encouraged to do four different types of math activities each week. Suggested activities and recommended daily times are provided for each.

Mental Math (5-10 minutes daily)

Review and Practice (5-10 minutes daily)

Problem Solving and Learning Explorations (10-15 minutes daily)

Project Learning (20-30 minutes daily)

LEARNING INTENTIONS

I know I’m on track with my learning about fractions, when I can:

• Explain the meaning of proper, improper and mixed fractions

• Add and subtract improper and mixed fractions

• Use my knowledge of fractions to solve problems

Mental Mathematics

MM#1: Estimation

To play this game you will need a set of dice or a deck of cards and the following numbers:

11 26 79 121 345 878

Roll the dice, (or draw a card from the deck). Estimate the product if you were to multiply the number you rolled (or pulled from the deck) with one of the numbers above. Repeat with the other numbers above. Roll the dice (or draw a different card) and play again.

MM#2: Riddles

Riddle #1: The total cost for a new pair of headphones and a new pair of sunglasses is $140. The headphones cost $100 more than the sunglasses. How much do the headphones cost?

Riddle #2: When Miguel was 6 years old, his little sister, Leila, was half his age. If Miguel is 40 years old today, how old is Leila?

Riddle #3: Alvin spent half as much as Lorie did on holiday presents this year and Chris spent 3 times more than Alvin did. The total spent between the three of them was $720. How much money did each person spend?

Problem Solving and Learning Explorations

PS/LE#1: Understanding Mixed Numbers and Improper Fractions

Look at the image in PS/LE#1. What do you notice about mixed numbers and improper fractions? Look for examples around your home or yard of things that you can use to create mixed numbers or improper fractions. Draw or take pictures of these.

PS/LE#2: Task Practice

Task 1: Record a mixed number and an improper fraction for each of the pictures in PS/LE#2:

Task 2: Write as many improper fractions as you can with the numbers 3, 6, 7, and 8.

Rewrite each of your improper fractions as an equivalent mixed number.

Draw a picture to represent each of your fractions.

PS/LE#3: Understanding Addition and Subtraction of Mixed Numbers and Improper Fractions

Look at the images in PS/LE#3. Explain each strategy to someone in your home. Can you think of any other strategies?. Solve each equation below using a strategy of your choice.

2 1/3+ 1 1/4 = ___ 7/2- 2 1/5 = ___ 3 2/5 + 15/4 = ___

PS/LE#4: Fraction Chain

Create a chain of fractions using Image PS/LE#4. Make sure the answer from the previous equation is carried forward to start the next equation. Try using addition and subtraction, and always remember to show your answer in as many different forms as possible (proper fraction, improper fraction, mixed number) also remember to reduce your fraction to its lowest form. For a challenge, cut up strips of paper to make a paper fraction chain. Each of the boxes in the image would be a separate paper loop. Each day add another equation. How long can you make your chain?

PS/LE#5: Solving Problems

Problem #1: The three seventh grade classes at Sunview Middle School collected the most boxtops for a school fundraiser, and so they won a $600 prize to share among them. Mr. Aceves’ class collected 3760 box tops, Mrs. Baca’s class collected 2301, and Mr. Canyon’s class collected 1855. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of the box tops that they collected?

Problem #2: Andrew plays guitar in a rock band. For a song that is 36 measures long he plays for 412 measures, rests for 8 38 measures, plays for another 16 measures, rests for 214 measures, and plays for the last section. How many measures are in the last section?

Problem #3: A container is half full. When half a cup of juice is added to it, the container is three-quarters full. How much liquid can the container hold? Model or draw your answer.

Problem #4: This week, Mark practiced piano for 31/2hours, played soccer 61/4 hours, and talked on the phone for 4 1/3 hours.

1. How many hours did Mark spend practicing piano and playing soccer?

2. How many more hours did Mark spend playing soccer than talking on the phone?

Problem #5: When solving a problem today, a friend suggested that 5/6+ 5/8= 10/14. How can you convince your friend that this is not a reasonable solution?

Project Learning

PL#1: Planting Gardens For Your School or Backyard

Design a garden for your school or home where you can grow healthy vegetables. Design a garden with 3 raised boxes similar to image PL#1.

Choose a minimum of 5 different vegetables to plant. Each of the 3 garden boxes must contain a different amount of each vegetable. For example: you might plant peas in ¼ of box 1, ⅓ of box 2, and ⅙ of box 3.

• Decide on the dimensions for your gardens. Draw the outside dimensions of each garden using the grid paper in PL#1.

• Draw the portion of each garden planted with each vegetable.

• Make your plans proportionally accurate to the size of the box, and to the other vegetables in your garden. Example: if carrots take up ⅓ of the garden box and peas are ⅙ of the garden box, the peas will need half the space of the carrots because ⅙ is half the size of ⅓.

• Color code and label each fraction of your garden boxes to show what you have planted.

• Remember, all of your fractional pieces in each garden box must add up to one whole.

More math:

• Record the fractions of each vegetable you planted.

• Write 2 or 3 equivalent fractions for each vegetable.

• Add the fractions of each vegetable you planted.

(Example: peas box 1 + peas box 2 + peas box 3 = ?).

• Represent each vegetable as a fraction, decimal and percent of each of your garden boxes.

• Represent each vegetable as a fraction, decimal and percent of all three boxes combined.

• You decide to ‘equal up’ the amount of each vegetable you are growing. What fractions of each vegetable are needed to make the total amount of each vegetable planted equal? To make this work how many additional gardens will you need to plant? Will you completely fill a fourth box? Will you need a fifth box? Or will one of your extra boxes be partially empty?

Science Challenge: Actually plant and grow your garden. Use a different type of soil, or different amounts of compost or fertilizer in each garden. Grow your vegetables and record your observations about the quality of vegetables in each garden. What growing conditions resulted in the best veggies?

Grade 8 Numeracy

Learning Intentions

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

• use calculations to simplify expressions

• use my proportional reasoning and algebraic reasoning skills to solve problems

Mental Mathematics

MM#1: Integer Addition

You will need a deck of cards or you could make your own set of number cards (2 copies of digits 0-9 in black, 2 copies of digits 0-9 in red). In this game, red cards are negative integers while black cards are positive. Each person turns over 3 cards and finds their sum. Person with the greatest sum keeps cards in a pile. When cards are out, most cards in a pile wins.

MM#2: Integer Multiplication

Play the game as above, but instead of adding your cards to find the sum, multiply your cards to find the product.

Review and Practice

RP#1: Fraction Practice

For this activity, you will need a deck of cards with the face cards removed. You could also make your own set of number cards (4 copies of numbers 1-10)

1. Turn over 4 cards. Create 2 fractions using these cards. Add the two fractions and record your answers. Subtract the fractions and record your answer. Multiply the fractions and record your answer. Repeat this at least 4 times

2. Turn over 6 cards. Create 2 mixed numbers using these cards. Add the mixed numbers then subtract the mixed number. Record your answers and repeat this activity at least 4 times.

RP#2: Target 24

Using a deck of cards or your own set of number cards, lay out 4 cards. Can you make the number 24 by adding, subtracting, multiplying and/or dividing? For example, using the cards 1, 9, 6, 2 you could make the following equations: 9x2= 18, 18+6 = 24

RP#3: Percent

The number of students at school A is 240% of the number of students at school B, but only 60% of the number of students at school C. What could the number of students at each school be?

RP#4: Order of Operations

To win a free trip, the following skill-testing question must be answered correctly:

−3 x (−4) + (−18) ÷ 6 – (−5). The contest organizers say that the answer is +4.

Write a note to the organizers explaining why there is a problem with their solution.

RP#5: Ratio and Proportion

During a heavy rain storm, 40 mm of rain fell in 30 minutes. How much rain would you expect to fall in one hour? In three hours? What assumptions are you making?

Problem Solving and Learning Explorations

PS/LE#1: Solving Equations

Examine the graph below about pizza prices. Answer the questions and complete the table of values.

PS/LE#2: Solve Me Mobiles

Imagine a mobile made up of strings, sticks and shapes. The strings and sticks are weightless but the shapes have weight. The total weight of the mobile is shown on top. Your goal is to figure out the weight the shapes must be to keep the mobile in balance.

Project Learning

Pulse Rates

Key Questions: How steady is your pulse rate? When you alter your activity how much does your pulse rate change?

A pulse rate is the relationship of heart beats to time. It is typically recorded in beats per minute. The pulse rate is a function of the rate of respirations (breathing) taking place in the body. The rate is low when the body is at rest and is elevated (higher) when a person is active.

For this activity, you are going to need a watch, a clock or some sort of timer that displays seconds, a piece of paper and something to write with. You are also going to need to find your pulse. To find your pulse, put your middle and pointer finger across your neck from under your ear to your throat just below your jaw.

Procedure: While you are seated, record your pulse every 10 seconds for one minute. What patterns do you notice? Transfer your data for your sitting pulse rate into the table and then graph it. What pattern do you see in the graph and how does it relate to your data in the table?

Next, you are going to record your pulse rate again, but this time you need to be moving (You can walk, dance, move your arms, etc…) Transfer your data for your moving pulse rate into the table and then graph it. What pattern do you see in the graph and how does it relate to your data in the table?

How do the differences between sitting and moving data show up in the table and the graph?Describe a few methods you could use to find your pulse rate per minute.

Extension: How many times do you think your heart beats in a day, a month, a lifetime?

Grade 9 Numeracy

Learning Intentions

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

• use calculations to simplify expressions

• use my proportional reasoning and algebraic reasoning skills to solve problems

Mental Mathematics

MM#1: Open Middle

Using the numbers 1-20, using each number once, fill in the boxes to create equivalent expressions.

MM#2: Simplifying Expressions

Simplify the following expressions. Calculate mentally where possible. Then order the answers from least to greatest.

Project Learning

Nova Scotia Flooring - Continued from week 2 flyer

Last week you examined the floor plan for a new school. You created simplified algebraic expressions for the total area of the floor to be tiled and the perimeter of the school. This week, you will use your work from last week to complete the next two parts of the project.

The owners of the building have decided to use a measurement of x = 10.5 meters. Use this to complete all remaining questions.

PART B:

1. Calculate the total area that would be tiled given this measurement.

2. Calculate the perimeter of the building given this measurement.

PART C:

1. Nova Scotia Flooring charges $12 per square meter for installation. What will be the total cost for the installation?

2. Each tile measures 30 cm x 30 cm and costs $3.00. What is the minimum number of tiles you would need to buy to cover the floor?

3. Determine the total price for the tiles, installation and tax that Nova Scotia Flooring would charge to do the work.

Did the total cost of the flooring surprise you? Why or why not?