GRADE 7 NUMERACY: LEARN ABOUT FRACTIONS

Learning Intentions:

I know I’m on track with my learning about fractions, whenI can: Explain when fractions are equivalent; Add and subtract fractions with like denominators; Add and subtract fractions with unlike denominators; Use my knowledge of fractions to solve problems.

MENTAL MATHEMATICS

MM#1: FIND EQUIVALENT FRACTIONS

Find equivalent fractions for the following:

3/8 3/4 2/5 1/4 5/4

Each day, create a different set of fractions and come up with 2 or 3 equivalent fractions for each. How do you know when your fractions are equivalent?

MM#2: MONEY, MONEY, MONEY

Think about 3 of our Canadian coins (nickels, dimes, quarters). What fraction of a loonie ($1) does each represent? What fraction of a toonie ($2) does each represent?

MM#3: RIDDLES

Riddle #1: I am a three-digit number. My tens digit is six more than my ones digit. My hundreds digit is eight less than my tens digit. What number am I?

Riddle #2: An online company can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, they sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons were shipped?

REVIEW AND PRACTICE

RP#1: HEADS OR TAILS

Put 8 of each coin (nickels, dimes, quarters) in a cup. Shake the cup and empty it on the table. Write as many fractions as you can. For example, 3/8 of the dimes are heads and 5/8 of the dimes are tails. Look for equivalent fractions in your coins. For example, 2/8 of the quarters are heads which is the same as 1/4 of the quarters are heads.

RP#2: ESTIMATING FRACTIONS

Use the number line in the image RP#2. Estimate the fraction represented by each dot on the number line.

RP#3: NAMING FRACTIONS

Use the number line in the image RP#3. Write the missing fractions.

RP#4: PAPER FOLDING

Work with a family member. Start with a square sheet of paper. Fold the square paper to make a new square with exactly 1/4 the area of the original square. Convince yourself and then your partner that it is a square and has 1/4 of the area. Repeat the activity with these different shapes. Fold to make a triangle with exactly the area of the original square. Convince yourself and then your partner that it has 1/4 of the area. Fold to make another triangle, also with 1/4 of the area, that is not congruent to the first one you constructed. Convince yourself and then your partner that it has 1/4 of the area.

RP#5: TASK PRACTICE

Task 1: 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.

Task 2: List all of the factors of 24 and the first six multiples of 6.

Task 3: List the first six multiples of the numbers 4, 6, and 9. What is the least common multiple of these three numbers?

PS/LE#1: Using your Fraction Kit

This activity uses a fraction kit similar to the one you created from construction paper in the last edition, or like the image PS/LE#1.

Task A: Choose a fraction from the fraction strips and find equivalent fractions.

Repeat the activity for other fractions. For example, 3/4 is equivalent to 6/8 and 9/12 .

Task B: Use the fraction strips to help you solve this question.

Sam wrote this equation: 3/4 hours + 4/6 hours = 1/2 hours, saying that he had worked on the computer for 45 minutes and watched television for 30 minutes.

Explain his mistake in determining the total time he spent on these activities. What is the correct answer (expressed as a fraction)?

Task C: Create three addition and three subtraction equations that each would have an answer of 6/12.

PS/LE#2: Adding and Subtracting Fractions with Like Denominators

Look at the image PS/LE#2. What do you notice when adding fractions with like denominators? Create your own examples of addition and subtraction of fractions with like denominators using models or pictures.

PS/LE#3: Heads or Tails (round 2)

Play the Heads or Tails game again (see PR#1), but this time use the coins to write addition or subtraction sentences. For example: 2/8 of the dimes are heads + 5/8 of the quarters are heads = 7/8 of the dimes and quarters are heads.

PS/LE#4: Adding and Subtracting Fractions with Unlike Denominators

Look at the image PS/LE#4. What do you notice when adding fractions with unlike denominators? Create your own examples of addition and subtraction of fractions with unlike denominators using models or pictures.

PS/LE#5: Heads or Tails (round 3)

Play the Heads or Tails game again (see RP#1 and PS/LE#3), but this time put different numbers of coins in the cup to start. How does this change the way you add or subtract the fractions?

PS/LE#6: Fraction Maze

Find your way through the maze in image PS/LE#6. Start with the question in the green block and try to make your way to the end of the maze. Which fraction is at the end? Solve and follow the path of correct answers. When you are done create your own maze using subtraction questions.

PS/LE#7: Creating Problems

Make up a real-life problem you could solve by adding 2/3 to 1/5. Solve your problem and show the solution with numbers, words, and pictures.

PROJECT LEARNING

PL#1: Make A Game

Show your understanding of fractions by creating a game that requires those playing to add and subtract fractions. Start by thinking about games you already know. For example: card games, a board game, maze or brain teaser puzzle. Next, think of what you know about how to add and subtract fractions. Decide on a game format for teaching these concepts to someone else.

To complete this project you need to: Design a game; Create all the materials needed to play the game (e.g. playing cards, board game design and/or maze design); Write clear instructions about how to play the game; Create an answer key if such a key would assist others to play the game. Play the game.

GRADE 8 NUMERACY

LEARNING INTENTIONS

I am revisiting, reinforcing, and applying the skills I learned in previous grade 8 math units. I know I got it when I ... remember key math terms and describe them in my own words; use my number sense to create and solve expressions integers; applying my proportional reasoning skills to solve problems

MENTAL MATHEMATICS

MM#1 Volume of Cubes

What could be the volume of a cube with a side length between 1 cm and 20 cm? On other days try a few side lengths that are whole numbers; try some side lengths using decimal numbers.

MM#2 Integer Products

See image MM#2 for this activity. Write a different integer in each of the five squares in the image so that the product of each pair of integers is shown on the line that connects them. On another day, try to find a second solution to the puzzle.

REVIEW AND PRACTICE

RP#1 Last week you were asked to remember as much as you can about important math terms you learned so far in grade 9. This week, you are going to dig deeper into what you know about fractions. In your own words, explain the following math terms. Use pictures and examples to help explain your thinking. Fraction, improper fraction, mixed number, order of operations, simplest form, numerator, denominator.

RP#2 Complete PS/LE#6: Fraction Maze - Grade 7. This is great practice for adding and subtracting fractions.

PROBLEM SOLVING AND LEARNING EXPLORATIONS

PS/LE#1 See image PS/LE#1 for this activity. Shade in one of the regions in this square. What fraction of the big square did you shade? Shade in a different region and name the fractional piece. How many different fractions can you create?

PS/LE #2 Find a simple mathematical expression for as many whole numbers from 0 to 100 as possible, using only common mathematical symbols and exactly four of the digit four (no other digit is allowed). For example, the number 1 could be made with the expression (4+4)/(4+4). Keep track of all the different expressions you create.

PS/LE#3 See image PS/LE#3 for this activity. If one of the triangles shown here has an area of 18 cm2, what must be the side length of the square? Choose different areas and solve for the side lengths.

PS/LE #4 Would You Rather? (www.wouldyourathermath.com) Choose the option you would rather and justify your reasoning with mathematics.

(see image)

PROJECT LEARNING

Reading Rates

Complete this activity when you are doing your daily reading.

How can you determine how long it will take to read a book? Brainstorm your ideas. Time yourself as you read a section of your book (between 5-10 minutes)

Pages read: _______ Minutes read: _______

Estimate how long it will take to read your book.

Pages in book: _______ Time to read book: _______

How did you estimate the time to read the book?

Read for one minute then count and record the number of words you read to find out how many words per minute you read.

Randomly select five lines on a page and count and record the number of words in each line. Make a table to organize the data. Find the average number of words per line. Randomly select five pages in your book and count and record the number of lines on each page. Make a table to organize the data. Find the average number of lines per page.

Using your data, answer the following questions: How many words do you estimate are on each page? How many words do you estimate are in the whole book? How many minutes do you estimate it will take you to read the book?

GRADE 9 NUMERACY

LEARNING INTENTIONS

I am revisiting, reinforcing, and applying the skills I learned in previous grade 9 math units. I know I got it when I ... remember key math terms and describe them in my own words; use my number sense to create and solve expressions fractions and percent; applying my proportional reasoning and algebraic reasoning skills to solve problems

MENTAL MATHEMATICS

MM#1 Fill in the blanks to make these statements true. On other days find different ways to complete each statement:

72 is ___% of ____.

___ is ___% of 50.

___ is 40% of ____.

MM#2 Given this list of fractions, which two have the sum that is closest to 1/2 ?

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

On other days, create your own list of four different fractions and find which two have a difference closest to 1/2 .

REVIEW AND PRACTICE

RP#1 See image RP#1 for this activity. Last week you were asked to remember as much as you can about important math terms you learned so far in grade 9. This week, you are going to dig deeper into what you know about exponent laws. Refer to the list of exponent laws on this page. Explain the exponent laws in your own words. Create 2-3 examples to show each exponent law.

RP#2 Complete PS/LE#6: Fraction Maze - Grade 7. This is great practice for adding and subtracting fractions.

PROBLEM SOLVING AND LEARNING EXPLORATIONS

PS/LE #1 Suppose you saved -- % on an item, which led to a savings of a little more than $5. What do you think the item might have cost? (use 5 different amounts for the %)

PS/LE#2 See image PS/LE#2 for this activity. The table contains data about the weekly sales of two shirt companies.

a. Calculate the increase in sales for each company from Week 1 to Week 2 and from Week 2 to Week 3.

b. Calculate the percentage increase in sales for each company from Week 1 to Week 2 and from Week 2 to Week 3.

c. From the information gathered in parts a) and b), which company is experiencing better growth in sales?

PS/LE#3 A rectangular garden is partitioned into 5 congruent squares. If 42m of fencing encloses the garden, what is its area? Suggestion: Draw a picture to help you visualize this problem.

PS/LE #4 Think of something you have been wanting to buy that costs more than $50. Imagine you have $30 saved. What discount does the store need to offer before you can afford it?

PS/LE #5 Which One Doesn’t Belong? See image PS/LE#5 for this activity Come up with a reason why each of the equations could possibly not belong to the set. Keep track of your thinking. Try creating your own “Which one doesn’t belong?” using equations.

PS/LE #6 Open Middle See image PS/LE#6 for this activity. Hints: How can you use the fact that anything to the zero power equals one? In what ways are 3 and 9 connected, as are 2, 4 and 8? How can we use this knowledge to build on creating equivalent expressions?

PROJECT LEARNING

Nova Scotia Flooring

See image PL#1 above for this activity. Nova Scotia Flooring has won the bid to tile the floors of a new school. They will be placing tile throughout the school in all areas except for the shaded regions. Decisions for the exact measurements for the school are still up in the air, but the proportions are set and are described using the polynomials in the diagram on this page. 1. Find the total area to be tiled (as a simplified algebraic expression). 2. Find the total combined area for the fountains (as a simplified algebraic expression). 3. Find the total distance required to walk around the outside of the school (as a simplified algebraic expression).

This project will be continued in the next flyer. Save this diagram and all of your work.