Grades 7 Numeracy

Intentions

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

• Demonstrate an understanding of linear patterns in various representations.

• Solve problems using linear relations.

• Draw a visual to show the steps used to solve a linear equation.

• Solve a problem using a linear equation and show my work symbolically.

• Check my work by substituting the answer into the original linear equation and solving

Mental Mathematics

MM#1: Venn Diagram

Look at the Image MM#1. Create a Venn diagram to sort the following numbers based on the divisibility rules for 3 and 5:

6, 8, 10, 15, 18, 25, 26, 36, 40, 45, 120.

Extension: Which numbers are also divisible by 15?

MM#2: What’s My Number

Create a different number for each:

1. That is divisible by 8 and 5.

2. That is divisible by 2, 3, and 10

3. That is divisible by 9 but not 2.

4. That is divisible by 4, 9, and 10.

Review and Practice

RP#1: Working with Fractions

Look at the Image RP#1. Create fractions with unlike denominators to find the sum or differences.

RP#2: Number Lines

Solve the equation. Use a number line strategy to justify your answer.

123+ 256=

RP#3: What does it Mean?

Part 1: Look at each of the images in RP#3. Try to use as many of the words in the word bank as possible to explain your understanding about what you see in each image. Word Bank: evaluate or solve, unknown, balanced, equality, variable, equation, expression, linear relation

Part 2: Choose one of the images and create a real-life context for the relationship. Explain what is happening and the variables involved.

Problem Solving and Learning Explorations

PS/LE#1: Strategies to Solve Equations

Part 1: Kate, a grade 7 student, received the following equation to solve: 2n + 3 = 11. She knew that the answer 11 had to be 3 more than a multiple of 2. Is she correct? How do you know?

Explain the following equations:

3p + 4 = 10

18 = 5w + 3

Part #2: Look at the image PS/LE#1 to see how Kate solved the equation 2n + 3 = 11 pictorially and symbolically.

Use this example to help you solve each of the equations below pictorially and symbolically:

3p + 4 = 10

18 = 5w + 3

PS/LE#2: Tables and Chairs Problem

Mary’s Seafood restaurant has a variety of table and chair arrangements to accommodate any size gathering of customers.

Look at the image in PS#2. The tables are square and arranged end to end, with chairs around the perimeter. Use this pattern to answer the following questions.

1. Draw the fourth and fifth table arrangement. How many chairs are needed for each of these table arrangements?

2. Make a table of values to show the relationship between the number of tables (x) and the number of chairs (y) following the same pattern. Include the first 6 table arrangements in your table of values.

3. Describe the pattern rule for the number of chairs you would need for each table arrangement. Explain your thinking.

4. Use this rule to predict the number of chairs needed for 10 tables.

5. Mary used the linear equation y = 2x + 2 to represent this problem. Look at image PS/LE#2 to see how she used substitution to determine the total number of chairs needed for 12 tables.

6. Use substitution to determine the number of chairs needed for 20 tables. Substitute x = 20 in the equation. Show all your steps.

7. Look at image PS/LE#2 to see how Mary used substitution to determine the total number of tables needed for 18 chairs.

8. How many tables would Mary need to push together to accommodate one table arrangement with 32 chairs? Use substitution to determine the number of tables needed for 32 chairs. Substitute y = 32 into the equation y = 2x + 2 and solve for x. Show all your steps.

PS/LE#3: Making Drums

Pi’jkwej (Nighthawk) is in grade 7, and lives in the Glooscap Mi’kmaw Community of Hants County, N.S., He enjoys using deer hides to make drums, which are important for use in Mi’kmaw ceremonies, such as performing the honour song.

Pi’jkwej has found that he can make 3 drums from an average sized hide. This leads to the linear equation, d = 3h, where d represents the number of drums and h represents the number of hides needed.

a.) How many drums can he make using 3 hides? Use the relation and show your work.

b.) If Pi’jkwej needs to make 12 drums, then how many hides would he need? Use the relation and show work.

c) Pi’jkwej has 2 hides left before the fall hunt begins. If he makes 24 drums that season, how many additional hides did he need?

Project Learning

PL#1: Comic Strip

Create a comic strip using characters to explain one (or more) of the following:

• the difference between an expression and an equation

• one strategy for solving an unknown in an equation

• how a balance scale can show equality

Try creating a series (or book) of comics with your characters. Can you come up with other math ideas to explain?

Grade 8 Numeracy

Learning Intentions

I know I’m on track with my learning about how to critique ways in which data is presented when I can:

• differentiate between graphs that are accurate and graphs that are misleading.

• recognize false conclusions that misleading graphs try to represent.

Mental Mathematics

MM #1

Split 25 - Take the number 25 and split it up into as many pieces as you want and find the product of those pieces. For example 10 and 15 have a product of 150. 10 and 10 and 5 have a product of 500. What is the biggest product you can make if you multiply those pieces together? Will your strategy work for any number?

MM #2

Prime numbers have exactly two factors – 1 and itself. The number 9 has exactly three factors (1,3,9). Which other numbers have exactly 3 factors? How many two digit numbers can you find that have exactly 4 factors?

Review and Practice

RP #1

Which group would you rather be a member of? Use mathematics to justify your choice.

Group 1 - 9 friends are washing 4 cars

Group 2 - 7 friends are washing 3 cars

Explain your reasoning. What assumptions are you making?

RP #2

Think of 3 or 4 categories to sort the fruit and vegetables in this picture. Create a bar graph to display how many items are in each of these categories.

Create your own bar graph using items around your house. You might use books, food, tools, etc. Be creative!

RP #3

The Pythagorean Theorem describes a relationship between the sides of a right triangle. The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides. It is mathematically stated as a² + b² = c². Draw a right triangle and use a ruler or measuring tape to measure its three sides. Use the Pythagorean Theorem to verify that these measures form a right triangle. Find a rectangle around your house (e.g. the side of a box of cereal). Measure the sides and use the Pythagorean theorem to calculate the length of the diagonal of the rectangle. Measure the rectangle’s diagonal to check your work. If you don’t have a ruler at home, you can create your own by marking off regular intervals on a long piece of paper.

Problem Solving and Learning Explorations

PS/LE #1 Two common types of data are discrete data and continuous data. Discrete data is data that is counted whereas continuous data is data that is measured (i.e. it can take on any value). Examples of discrete data are the number of coins in a jar or the number of people in a gym. Examples of continuous data are the length of a leaf or the time it takes to run a race. Brainstorm 5 different examples of both discrete data and continuous data. How would you explain the difference between discrete and continuous data to a friend or family member?

PS/LE #2 What data might the circle graph below be representing? Brainstorm a few different ideas. Pick your favourite idea and write a short story, comic strip or draw a picture that includes the graph and the data it represents as part of the story.

PS/LE #3 A survey was conducted at a middle school to determine how students typically get to school. The results are are below:

• School bus: 45%

• Car: 7%

• Walk: 25%

• Bicycle: 10%

• Public transit: 9%

• Other: 4%

Use the hundredths circle to make a circle graph to display this data. Remember that a good graph accurately shows the facts; has a title and labels; and shows data without misrepresenting it.

PS/LE #4 What type of graph would you use to represent data from each of the scenarios below? Explain your choices.

− the cost of a movie ticket over the last 20 years

− prices of different brands of athletic shoes

− the average monthly temperatures for Nova Scotia for the past year

− the favorite ice-cream flavours of grade 8 students

Here are some tips when choosing which type of graph best fits each scenario:

- A circle graph compares parts of the data relative to the whole.

- A line graph shows change over time and is easy to draw by hand.

- A bar graph shows the number of items in specific categories.

PS/LE #5 What conclusions can you make based on this graph?

How do you think this data may have changed since 2014? How could you display the change since 2014 in a new graph?

Sources of Energy made by Nova Scotia Power in 2014

Project Learning

Bird Watching

Counting birds is an opportunity to explore and investigate our local nature-hood. You can count birds from wherever you live. Depending on where you live, you might see different types of birds. We’ll just be counting the number of birds you see but you might also try to identify the types of birds you see.

• Count birds from your backyard, balcony, porch or window for AT LEAST 15 minutes, but you may count as long as you wish.

• For each day you make an observation, record the following data: Date, number of individual birds you saw, and how long and what time of day you watched. It may be helpful to create a chart to record your data for several days. You could add additional categories if you wish (type of bird, colour of bird, size of bird, etc.)

• If you wish, you could count other objects you might see from your residence such as vehicles or pedestrians.

Once you have collected your data, decide what data you’re going to display and what type of graph you’re doing to display it with. Once you have created your graph, what do you notice from looking at it? What other questions do you have now?

Grade 9 Numeracy

Learning Intentions

I know I’m on track with my learning about how to critically analyze the collection of data when I can:

• describe the effect on the collection of data of bias, timing, privacy, and cultural sensitivity.

• describe how the wording of survey questions might affect the data collected.

Mental Mathematics

MM #1

Use the numbers 3, 5, 4 and 9 along with any mathematical operations as +, -,✕,or ÷ and grouping symbols such parenthesis ( ), to make an expression with a value as close to 30 as possible. For example, 3 x 4 + 5 + 9 = 26 which is 4 away from 30. How close can you get? Can you get exactly 30? Pick 4 different random digits and try again.

MM #2

You have 10 silver coins in your pocket (silver means that the coins could be any of nickels, dimes or quarters). How many different amounts of money could you have?

Review and Practice

RP #1

Use these numbers to make 4 fractions: 2, 3, 4, 5, 6, 8, 10, 12

a) Use the 4 fractions to write an expression with 3 operations (+,-,✕,÷). Evaluate the expression.

b) Use the same 4 fractions to create a different expression. How many different expression values can you get with your four fractions? How close to 0 can you get using your four fractions?

RP #2

Insert brackets in the expression below so the statement is correct. Is it possible to insert brackets and get a positive answer? Explain your thinking.

−3.8 + 9.1 ✕ −2.5 − 0.5 = −31.1

RP #3

Five subtract 3 times a number is equal to 3.5 times the same number, subtract 8. Write, then solve an equation to determine the number. Verify the solution.

RP #4

A rectangle has dimensions 5x and 3x + 8.

a) Sketch the rectangle and label it with its dimensions.

b) Write an expression for the area of the rectangle.

c) Write an expression for the perimeter of the rectangle.

d) Write an expression for the length of the diagonal of the rectangle.

Problem Solving and Learning Explorations

PS/LE #1

There are several factors that might lead to problems with data collection. These factors include:

• Bias - The way a question is worded may influence responses in favour of, or against the topic.

• Timing - When or where the data is collected could lead to inaccurate results.

• Privacy - If the topic of the data collection is personal, a person may not want to participate or may not give an honest answer.

• Cultural Sensitivity - Cultural sensitivity means that you are aware of other cultures. Some questions might be offensive or not apply to certain cultures.

Suppose you wanted to find out how much support there is for building a new bus terminal in your town. You go to an existing bus terminal on a warm summer day and survey the people there while they are waiting for a bus.

a) Describe how the timing of your question may influence the responses.

b) In what location might the responses be different than those you recorded in the scenario described above?

PS/LE #2

A survey question is biased if it is phrased or formatted in a way that skews people towards a certain answer. Survey question bias also occurs if your questions are hard to understand, making it difficult for respondents to answer.

For the following questions, identify the source of bias. Suggest some ways to avoid bias from the scenario.

– At a soccer game, a survey was given and the results showed that when asked to give their

favourite sport, 85% of the youth responded it was soccer.

– Do you think that small dogs make good pets even though they are yappy?

PS/LE #3

You may have discussed bias in English Language arts. In this context, bias is a judgment based on a personal point of view. This bias can also affect the accuracy of data collected in mathematics. Bias in data can result from:

• survey questions that are constructed with a particular slant

• choosing a known group with a particular background to respond to surveys

• reporting data in misleading categorical groupings

Create an example using one of the factors from the list above to help explain the term “bias” to a classmate. How does this example demonstrate bias?

Project Learning

Granola Bar Survey

A group of friends are planning to sell granola bars at the school shop as a fundraiser for a charity. They want to estimate how many granola bars they might sell in a week. They conduct a small survey among 30 people, asking the question: “How many granola bars do you eat in a typical week?”

Here are their results (number of bars per week):

1, 5, 2, 25, 13, 2, 9, 6, 10, 19, 11, 0, 1, 3, 25, 13, 8, 2, 0, 28, 4, 1, 0, 16, 14, 1, 10, 16, 30, 0

1. How could you use this data to inform your sales estimate? What additional survey question(s) might be helpful to have a better understanding of this market. Brainstorm at least three more questions that you could add to your survey. Consider the wording of these questions carefully to ensure they are unbiased.

2. How and when would you ask these survey questions in order to get the most accurate results?

3. What additional information would you want to know about this scenario to make a good estimate of granola bar sales (e.g. how many students go to the school? How much will granola bars cost you and what price should you charge? etc)

4. Write a letter to the school describing your business plan for selling granola bars at the school shop. How much profit do you predict and what cause do you intend to donate your profits to support?