CyberArts Grade 8
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 Numbersense and Numeration Unit 2: Ratios, Rates, Decimals, Fractions and Percents

Progression

Explain what fractions, decimals and percentages are in multiple ways

Translate between equivalent forms of a number (percent, fraction and decimals)

​Compare and order fractions, decimals and percentages in multiple ways.

Represent the addition, subtraction, multiplication and division of fractions in multiple ways.

Solve problems involving addition, subtraction, multiplication and division using BEDMAS.

Solve proportion (ratio), fraction and percentage word problems.


Lesson Progression

Fraction posters - explain what you know of fractions and operations - highlight 3 things you think are notable and explain in detail.

Represent fractions in 3 different ways (concrete, representational and abstract)

Order varying representations of fractions

Find fraction in-between two different fractions.

​Create equivalent fractions and ratios.

Fraction cards - Match similar fractions represented in different forms

Fraction wheel activity and math talk

Represent operations with fractions (array, numberline, etc.)

Solve equations with fractions (BEDMAS)

Solve simple algebraic equations with fractions

Translate between equivalent decimals, fractions and percents

Represent ratios in various ways

Ratio cards - Match similar ratios

Fraction, percent and ratio word problems


Percents

percent_intro.pptx
File Size: 77 kb
File Type: pptx
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percent_interestdiscountsales_.pptx
File Size: 94 kb
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percent_word_prob.pdf
File Size: 113 kb
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statement-1.pdf
File Size: 38 kb
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Double Sunglass Task

act1.mov
File Size: 5358 kb
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act3.mov
File Size: 3005 kb
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fivepercent.mov
File Size: 2524 kb
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fraction-method.pdf
File Size: 43 kb
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increase.pdf
File Size: 33 kb
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calculating_percents.pdf
File Size: 6714 kb
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markup_discount_and_tax__hard_.pdf
File Size: 25 kb
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unknown-from-ratio-simple-1.pdf
File Size: 38 kb
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word_percent_probs.pdf
File Size: 25 kb
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proportion_word_problems.pdf
File Size: 30 kb
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percentage_word_problems2.pdf
File Size: 121 kb
File Type: pdf
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Rates, Ratios and Decimals

ratio_and_proportion.pptx
File Size: 82 kb
File Type: pptx
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convert-ratio-medium.pdf
File Size: 38 kb
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ratio-to-fraction.pdf
File Size: 40 kb
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solving_proportions.pdf
File Size: 31 kb
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convert-ratio-hard.pdf
File Size: 38 kb
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Nana's Eggs

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act1.mov
File Size: 9044 kb
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doublenumberline-chocolate.pdf
File Size: 7 kb
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act3.mov
File Size: 3337 kb
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Sequel to Nana's Eggs
act1.mov
File Size: 8448 kb
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doublenumberline-eggs.pdf
File Size: 7 kb
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act3.mov
File Size: 3481 kb
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Picture

create-proportion.pdf
File Size: 32 kb
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convert-ratio-simple.pdf
File Size: 37 kb
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solve-proportion.pdf
File Size: 31 kb
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fractions, decimals.pdf
File Size: 2781 kb
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ratio_and_rates.pdf
File Size: 5555 kb
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Videos

Percent Video link


Unit Conversion

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conversion worksheet.png
File Size: 74 kb
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md_conversion_wordproblems_metric.pdf
File Size: 139 kb
File Type: pdf
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Practice Tests

numeration_test_term_2_unit_3_practice_test_1__ratios_and_scale_.docx
File Size: 201 kb
File Type: docx
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additional_questions_for_test_3.docx
File Size: 67 kb
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number_sense_and_numeration_term_2_unit_4_test_1_practice_test.docx
File Size: 59 kb
File Type: docx
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Fractions

Fraction work

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Fraction Talks

fraction_talk_ppt.pdf
File Size: 2523 kb
File Type: pdf
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fractions_comparing.pdf
File Size: 25 kb
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equivalent_fractions.pdf
File Size: 30 kb
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fractions_improper.pdf
File Size: 32 kb
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fractions_ordering.pdf
File Size: 65 kb
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fractions_adding_simple_visual.pdf
File Size: 579 kb
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fractions_adding.pdf
File Size: 24 kb
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fractions_adding_three.pdf
File Size: 29 kb
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adding_mixed_numbers.pdf
File Size: 27 kb
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fractions_subtracting_simple_visual.pdf
File Size: 416 kb
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fractions_subtracting.pdf
File Size: 24 kb
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fraction-percentage-matching-cards.pdf
File Size: 102 kb
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Beginning fraction unit_.pdf
File Size: 873 kb
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fraction_lesson.pdf
File Size: 118 kb
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fractions_multiply.pdf
File Size: 24 kb
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finding_fractions_whole_numbers.pdf
File Size: 26 kb
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fractions_multiply_whole.pdf
File Size: 24 kb
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fractions_divide.pdf
File Size: 24 kb
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fractions_divide_whole.pdf
File Size: 23 kb
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multiplying-and-dividing-fractions-word-problems.pdf
File Size: 196 kb
File Type: pdf
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fractions_decimals_negative.pdf
File Size: 15 kb
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fractions_pemdas_twosteps_negative.pdf
File Size: 28 kb
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fractions_pemdas_threesteps_negative.pdf
File Size: 68 kb
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fractions_pemdas_fivesteps_negative.pdf
File Size: 28 kb
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fractions_pemdas_sixsteps_negative_all.pdf
File Size: 61 kb
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exponents_fraction.pdf
File Size: 31 kb
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Fraction Practice Tests

fraction_test_1_practice.pdf
File Size: 1962 kb
File Type: pdf
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fraction_test_2_practice.pdf
File Size: 2897 kb
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fraction_test_3_practice.pdf
File Size: 3586 kb
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Multiplying using an area model and dividing using a numberline

using_models_to_multiply_fractions.pdf
File Size: 1663 kb
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using_models_to_divide_fractions.pdf
File Size: 3074 kb
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Why we invert when dividing fractions


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

Fractions and Algebra

fractions_and_algebra_equations_easy.pdf
File Size: 280 kb
File Type: pdf
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algebra_and_fractions_1.pdf
File Size: 204 kb
File Type: pdf
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solving_algebra_equations_with_fractions.doc
File Size: 61 kb
File Type: doc
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algebra_and_fractions_2.pdf
File Size: 61 kb
File Type: pdf
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one-step_equations_with_fractions.pdf
File Size: 32 kb
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multi-step-fractions-algebra.pdf
File Size: 43 kb
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challenging_fraction_problem.pdf
File Size: 277 kb
File Type: pdf
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algebra_and_fractions_3.pdf
File Size: 32 kb
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multistep_fractions_algebra.pdf
File Size: 87 kb
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hard_fraction_problem.pdf
File Size: 786 kb
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Fraction Word Problems

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fraction_multistep_word_problems.pdf
File Size: 40 kb
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fractions_word problems.pdf
File Size: 55 kb
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more_fractions_word_problems.docx
File Size: 92 kb
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fraction_word_problems_by_difficulty.docx
File Size: 74 kb
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waterloo math easy.pdf
File Size: 181 kb
File Type: pdf
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legsinbarn.pdf
File Size: 166 kb
File Type: pdf
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fract_word_prob.docx
File Size: 199 kb
File Type: docx
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pineapple_island.docx
File Size: 67 kb
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waterloo math hard.pdf
File Size: 179 kb
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apples_and_bananas.pdf
File Size: 258 kb
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Working together problems

work_word_problems.png
File Size: 125 kb
File Type: png
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http://www.algebralab.org/Word/Word.aspx?file=Algebra_WorkingTogether.xml

Extension Work

Factoring Trinomials Step-by-Step

Definition of Polynomials
factoring_trinomials.pdf
File Size: 31 kb
File Type: pdf
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