Fractions/Percent/ Unit Rate/Ratio

Number Sense & Numeration - Grade 6

Overall Expectations:

  • proper and improper fractions, and mixed numbers;

  • demonstrate an understanding of relationships involving percent, ratio and unit rate.

Specific Expectations: Fractions


  • represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, number lines, calculators) and using standard fractional notation (Sample problem: Use fraction strips to show that 1 1/2 is greater than 5/4 .);
  • estimate quantities using benchmarks of 10%, 25%, 50%, 75%, and 100% (e.g., the container is about 75% full; approximately 50% of our students walk to school);

Proportional Relationships:


By the end of Grade 6, students will:

  • represent ratios found in real-life contexts, using concrete materials, drawings, and standard fractional notation (Sample problem: In a classroom of 28 students, 12 are female.What is the ratio of male students to female students?);

  • determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions (i.e., with denominators of 2, 4, 5, 10, 20, 25, 50, and 100), decimal numbers, and percents (e.g., use a 10 x 10

    grid to show that 14 = 0.25 or 25%);

  • represent relationships using unit rates (Sample problem: If 5 batteries cost $4.75, what is the cost of 1 battery?).

Let's Investigate Fractions!

Where are fractions found in real-life?

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Could this be true? (We'll get back to this)

Why are these funny?

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Virtual Manipulatives

Mathies.ca

What is this funny chart?

How can you use it?

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Fractions

Math Antics - Fractions Are Parts

Compare & Equivalent Fractions (Up to 2:22 only of video)

Hands On - Represent

How Big Is 1/3?

What is another fraction that is equivalent to 1/3?

How many ways can you represent it?

Hands On - Represent

Represent 1/4

How many ways can you represent it?

Exit Ticket

Represent 2/3 - How many ways can you represent it?

_______________

Math Antics - Working With Parts

Activation

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What strategies can you use to compare the burgers?

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Hands On

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Exit Ticket

Which is larger 5/6 or 2/3? Convince me!

Write as many equivalent fractions as you can.

Represent these fractions.

Then answer the question, which fraction has the smallest value?

Activate

How would you represent this fraction 5/4?

Hands On

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Exit Ticket

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Activation

How can you compare 17/20 and 22/25?

Why do we need to compare fractions? What is it we are doing?

Hands On

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Exit Ticket

Which fractions are equal? Please prove with 2 strategies :)

1/2, 12/20, 15/25, 60/100

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Exit Ticket

Find a fraction between 5/4 and 1 4/6

A fraction between 5/4 and 1 and 4/6 is _________________________.
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Percentages

Learning Goal:

We are learning to estimate (educated guess) quantities using benchmarks of 10%, 25%, 50%, 75%, and 100%.

What is a percentage?

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Can these fractions be written as percentages?

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What are percentages? (Watch until 4:15 of video)

Math Antics - What Are Percentages?
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This class has approximately 20 students. 25% of students say strawberry is their favourite flavour of ice cream. How many students does that represent?

What strategies can you use to figure out the answer?

Hands On

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Exit Ticket

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Learning Goal

We are learning to use denominators of 2, 4, 5, 10, 20, 25, 50, and 100), decimal numbers, and percents (e.g., use a 10 x 10 grid to show that 14 = 0.25 or 25%);

How do we make fractions into percents?

What is 1/2 as a percent?

1/4

1/5

1/10

1/20

1/25

1/50

1/100

What strategy can we use to turn these fractions into percents?

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Hands On

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Exit Ticket

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Ratio

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Can you put ratio into your own words?

Ratio - (Watch Video Up Until 5:09)

Math Antics - Ratios And Rates

Activation

How do put fractions in their lowest form?

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Hands On

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Exit Ticket

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Unit Rate

https://www.smore.com/myrzy

What is unit rate?

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Rate (Start video at 5:09)

Math Antics - Ratios And Rates
6th Grade Math Rate and Unit Rate
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Hands On

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Exit Ticket

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Order Of Operations

Order Of Operations:

  • explain the need for a standard order for performing operations, by investigating the impact that changing the order has when performing a series of operations (Sample problem: Calculate and compare the answers to 3 + 2 x 5 using a basic four- function calculator and using a scientific calculator.).

Does it matter how we answer a math questions with different operations?

Performing Math Operations must be preformed in a certain way.

Example: 3 + 2 x 5

Multiplication or division are done before addition or subtraction, it depends on the in order in which they appear.

Therefore:


3 + 2 x 5

= 3 + 10

= 13

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Prime Numbers and Factors

  • identify composite numbers and prime numbers, and explain the relationship between them (i.e., any composite num- ber can be factored into prime factors) (e.g., 42 = 2 x 3 x 7).

Composite Numbers - A whole number that can be divided evenly by numbers other than 1 or itself.

Example: 9 can be divided evenly by 3 (as well as 1 and 9), so 9 is a composite number.

Prime Numbers - A whole number that can ONLY be divided evenly by 1 and itself.

7 cannot be divided evenly (except by 1 and 7), so is NOT a composite number (it is a prime number).

Whole numbers above 1 are either composite or prime.

Hands On

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Exit Ticket

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