EQAO preparation

EQAO will begin on Monday June 2nd. It will last for three days. Here are some ways you can prepare for the test.

1. Get lots of rest on the weekend and for the days you are writing the test.
2. Bring water to drink during the test - an hydrated mind is a lot clearer.
3. Make sure you make good choices for your snacks and lunch. Sugar only gives you energy for a little bit, protein will last you a lot longer.
4. Bring quiet activities that you can do independently ( sudoku, crossword puzzles, books, magazines, colouring books, etc) You will have to sit quietly in your desk while the others finish the test.
5. You will not be allowed to go t the bathroom while you are working on the test. When you are finished writing the test then you can leave to go to the bathroom.
6. The schedule for next week will be a bit different than usual.

If you do want to practice but it is not necessary you can visit:

www.eqao.com for practice tests.

Unit Rates

Unit Rates - A comparison of two quantities where the second one is described as 1 unit. 

We find rates in the world around us; km/per hour - to describe the distance we drive in a certain number of kilometres. $/per litre - how much gas is per litre. $/per hour - how much money you would make per hour. 12/ $4.99 - how much 12 items would be for $4.99

As smart consumers it is a good idea to determine what the cost of one item is, so you can determine what the better deal is. We can do this by dividing the number of items by the amount it costs. 

2 kiwis for 95 cents = 47.5 cents each
4 kiwis for $1.80 = 45 cents each
3 kiwis for $1.50 = 50 cents each

Therefore the best deal is the 4 kiwis for $1.80

Try This:

5 cookies for $3.75
7 cookies for $6.30
$4.00 for 8 cookies
$6.00 for 6 cookies

What is the best deal?

Ratios and Equivalent Ratios

Ratios - a comparison of two numbers or quantities measured in the same units. 

For instance I could describe the number of boys to girls in the class for every 1 boy there are 2 girls

1:2 so if there are 12 boys how many girls are there? The top row represents boys and the bottom row represents girls, how many girls are there if there are 12 boys?

We can find the number of girls by finding the equivalent ratios.

Equivalent fractions

Equivalent Fractions

Equivalent fractions means that the area or fractional part that we are talking about are the same but one might have more parts. 

For example: 

1/2     and      2/4 are equivalent meaning the area that is shaded is the same size but in the fraction on the bottom it has been divided into more parts.

To find equivalent fractions:

We can multiply the numerator and denominator by the same number to find an equivalent fraction.

We can divide our the numerator and denominator by the same number to find an equivalent fraction.

For example:

1 x 2 = 2 

2 x 2 = 4

In this case I multiplied numerator by 2 and denominator by 2 gives me an equivalent fraction of 2/4

12 / 12 = 1

36 / 12 = 3

In this case I divided the numerator by 12 and the denominator by 12 which gives me an equivalent fraction of 1/3

Study Guide - Fractions Math Test

Fractions, Ratios and Rates Math Test

Look at notes on blog for review

1. Comparing fractions  - can you compare unlike denominators
2. Representing fractions - can you represent fractions using the area model, set model, measure model
3. Ordering fractions - can you order fractions on a number line
4. Equivalent fractions - how can you find equivalent fractions
5. Converting fractions into decimals and percents - converting fractions to decimals and percents
6. ratios - what are ratios
7. equivalent ratios - can you find equivalent fractions
8. unit rates - finding out what one item will cost

Comparing Fractions

Comparing Fractions

We compare fractions to determine which one is greater or which one is less. We may have two fractions and we want to determine which one is bigger. We may have several fractions and want to put the fractions on a number line. We may want to determine if a fraction is greater than 1.


We can compare fractions in two ways with like denominators (denominators are the same)
or with unlike denominators (denominators are different). The second one is more challenging.

Comparing Fractions with like denominators

                                                   3/5        compared to            4/5

The denominators are the same meaning the size of the parts are the same. To compare these we simply look at the numerators and determine which one is greater. In this case the 4 is greater than the 3 so 4/5 is greater.

It also means that 4/5 is closer to 1 than th 3/5 is.


Comparing Fractions with unlike denominators

 2/3         compared to                4/5

1. In this case it is difficult to determine which fraction is greater so we need to draw a model to decide which one is bigger.

By looking at the fractions as a picture we can see that 4/5 is greater than 2/3.


2. We can also compare fractions by finding common denominators.

To find common denominators we need find a number they can both be multiplied by.

      2/3                    compared to      4/5



        2 x 5    =  10                                       4 x 3        = 12
        3 x 5        15                                        5 x 3          15


I multiplied the numerator and the denominator by the same number and got a new fraction or what we refer to as an equivalent fraction.
Now I can compare the two fractions and say that 12/15 is greater than 10/15.


Try This!

1. Choose 6 fractions less than 1 and place them on a number line. How did you decide where they belonged on the number line?

2. Choose 6 fractions that are greater than 1 place them on a number line. How did you decide where they belonged on the number line?

3. Was it easier or harder to put the fractions that were less than one on the number line or the numbers that were greater than 1. Explain why?

Improper and Mixed Fractions

Improper Fractions

Improper fractions are fractions that are greater than 1. We know they are improper when the numerator is greater than the denominator.

Ex.      5          
           4

We know this fraction is an improper fraction because the numerator is 5 and the                     denominator is 4.

Just like proper fractions the denominator tells us how many parts are needed to make up the whole
The numerator tells us how many parts there are. In this case there is one whole and 1 part left over.

Mixed Fractions

Mixed fractions are fractions that are a combination of a whole number and a fraction.
We can convert a improper fraction to a mixed fraction, because it makes it easier to know how many wholes there are.

Ex:         5       =      1 1/4
              4

I can convert an improper fraction into a mixed fraction 3 ways:

1. Division.
    I can divide the denominator by the numerator. The denominator only goes into the numerator 1 time and I have 1 left over.

The one time represents the 1 whole. The left over is the number I put over the the denominator 4 so that it shows I have a whole plus 1/4 quarter.


2. Draw a model
    Another way of converting improper fractions to mixed fractions is by drawing a model.

1. To draw my model I begin by making an area model that has four parts. I know there are four parts because that is what my denominator tells me.
2. Then I shade in the number of parts that we are talking about. In this case there are 5 parts that we are talking about. So I coloured in 5 parts.
3. Finally I can determine how many wholes I have and what I have left over.
4. I have 1 whole and 1/4 left over

3. Use manipulatives.
    I can use manipulatives to show 5/4 and convert it to a mixed number.
    pattern blocks - if you are at school
    fraction circles - available online if you google fraction circles or strips images
    fraction strips
    counters

 

In this picture there are 5 parts and there are 4 parts that make up the whole. I have more than one whole in this case.



Show the fraction and determine the mixed number. How many wholes do you have.

Try This!


What is the mixed fraction for these improper fractions. Be sure to show how you know.


a)  10/3
b)   17/4
c)   8/2
d)   7/5
e)  15/6


Show this mixed number as a model


a)   1 1/2
b)   2 2/3
c)   4  7/8
d)   3  1/2