Numbersense and Numeration Unit 2: Ratios, Rates, Decimals, Fractions and Percents
Progression
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Lesson Progression
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Percents
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Rates, Ratios and Decimals
Nana's Eggs
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Sequel to Nana's Eggs
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Videos
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Percent Video link
Unit Conversion
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Practice Tests
| numeration_test_term_2_unit_3_practice_test_1__ratios_and_scale_.docx |
| additional_questions_for_test_3.docx |
| number_sense_and_numeration_term_2_unit_4_test_1_practice_test.docx |
Fractions
Fraction work
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Fraction Practice Tests
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Multiplying using an area model and dividing using a numberline
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Why we invert when dividing fractions
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How to Understand Dividing by Fractions
Let's think about why dividing by a whole number produces a smaller
result. Dividing 24 by 4 means I want to find out how many 4's it
takes to make 24.
If I have 24 sticks |||||||||||||||||||||||| 24
I can divide 24 by 4 by counting out 6 groups of 4 sticks: |||| |||| |||| |||| |||| |||| 1 2 3 4 5 6
Since each group contains more than one stick, there are fewer groups than sticks.
Now let's divide 6 by 1/4.
That means I want to find out how many 1/4's it takes to make 6.
If I have 6 sticks |||||| 6
and I break each of them into 4 pieces: |||| |||| |||| |||| |||| |||| 1 2 3 4 5 6
I find that there are 24 quarter-sticks.
Since each stick has been turned into 4 pieces, there are more pieces than sticks - the result of the division is greater than the original number of sticks. (By the way, this also helps to explain why dividing by a fraction is the same as multiplying by the reciprocal.)
The quotient is now larger than the dividend. In fact, you're multiplying by the reciprocal, which is a number greater than one, and you therefore increase the number.
Similarly, multiplying by a number greater than one increases a number, and multiplying by a number less than one decreases it: 24 / 4 = 6 smaller 6 * 4 = 24 bigger 6 / 1/4 = 24 bigger 24 * 1/4 = 6 smaller
If I have 24 sticks |||||||||||||||||||||||| 24
I can divide 24 by 4 by counting out 6 groups of 4 sticks: |||| |||| |||| |||| |||| |||| 1 2 3 4 5 6
Since each group contains more than one stick, there are fewer groups than sticks.
Now let's divide 6 by 1/4.
That means I want to find out how many 1/4's it takes to make 6.
If I have 6 sticks |||||| 6
and I break each of them into 4 pieces: |||| |||| |||| |||| |||| |||| 1 2 3 4 5 6
I find that there are 24 quarter-sticks.
Since each stick has been turned into 4 pieces, there are more pieces than sticks - the result of the division is greater than the original number of sticks. (By the way, this also helps to explain why dividing by a fraction is the same as multiplying by the reciprocal.)
The quotient is now larger than the dividend. In fact, you're multiplying by the reciprocal, which is a number greater than one, and you therefore increase the number.
Similarly, multiplying by a number greater than one increases a number, and multiplying by a number less than one decreases it: 24 / 4 = 6 smaller 6 * 4 = 24 bigger 6 / 1/4 = 24 bigger 24 * 1/4 = 6 smaller
Fractions and Algebra
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Fraction Word Problems
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Working together problems
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Extension Work
Factoring Trinomials Step-by-Step
| factoring_trinomials.pdf |
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