Bell Work Please get an index card from the back counter. On it answer the following questions: What is one thing you like about math (or feel you are good at) What is one thing you do not like about math (or struggle with) What is one thing you wish your teacher knew about you What is one thing you will do in this course to be successful?

R.01 Fractions Number Sense September 3, 2015 Review Unit Fractions Number Sense Number Sense - File Under Resources

10 3 What Format? (notes) The preferred format for our course is ‘Improper’ Fractions 10 3

Mixed to Improper (notes) “The Cartwheel” 3 1 4 Multiply then add Simplify (if necessary)

Addition (notes) 5 3 + 1 2 Ensure improper form Find COMMON DENOMINATOR ADD the NUMERATORS Simplify (if necessary)

Subtraction (notes) 5 3 − 1 2 Ensure improper form Find COMMON DENOMINATOR SUBTRACT the NUMERATORS Simplify (if necessary)

R.01 Fractions September 3, 2015 Try It! Change from mixed fractions to improper fractions Solve Solve 7 12 + 1 3 = 2 3 − 11 9 = 7 9 +2 2 7 = 1 1 5 − 4 3 = 7 12 + 1 3 = − 9 11 − 1 3 = 2 3 8 = 4 5 9 = −7 2 3 = Number Sense - File Under Resources

Try It! Solutions Change from mixed fractions to improper fractions Solve Solve 7 12 + 1 3 = 11 12 2 3 − 11 9 = − 5 9 7 9 +2 2 7 = 193 63 1 1 5 − 4 3 =− 2 15 2 5 + 4 5 = 6 5 − 9 11 − 1 3 = − 38 33 2 3 8 = 19 8 4 5 9 = 41 9 −7 2 3 = − 23 3

Addition (activity) Now that you know the rule to add fractions, I am interested in your deeper understanding. Please explain in detail why your solution makes sense and offer visual proof. 1 8 + 3 2 =

Subtraction (activity) Now that you know the rule to add fractions, I am interested in your deeper understanding. Please explain in detail why your solution makes sense and offer visual proof. 3 4 − 1 7 =

R.01 Fractions September 3, 2015 Bell Work You and 11 friends (12 people total) are going to order pizza for dinner. You are very hungry and the pizzas are small, so you order 13 of them. There are 2 suggestions for dividing the pizza: Each pizza is divided into 12 slices, and each person gets 13 slices Each person gets 1 2 of one pizza, 1 3 of another pizza, and 1 4 of another pizza. Which suggestion do you prefer? Why? The 2 suggestions are the same… but one gives you really thin pizza slices... This gets to the idea that any fraction can be written as the sum to unique unit fractions Number Sense - File Under Resources

Multiplication (notes) Ensure improper form What is the Final Sign? (same signs = positive; opposite signs = negative) Numerator TIMES Numerator Denominator TIMES Denominator Simplify (if necessary)

Division (notes) 5 3 ÷ 1 2 Ensure improper form What is the final Sign? Numerator (1) TIMES Denominator (2) Denominator (1) TIMES Numerator (2) Simplify (if necessary) Cross Multiply

Multiplication (activity) Now that you know the rule to add fractions, I am interested in your deeper understanding. Please explain in detail why your solution for each of the following makes sense and offer visual proof. 4× 2 3 = 1 8 × 2 3 =

Division (activity) Now that you know the rule to add fractions, I am interested in your deeper understanding. Please explain in detail why your solution for each of the following makes sense and offer visual proof. 1÷ 2 3 = 4 5 ÷ 2 3 =

Try It! Solve Solve 5 7 ÷ 3 5 = 4 5 ÷ 2 3 = 2 3 5 ÷−2 1 3 = 5 7 × 3 5 = 9 3 4 = 2 2 3 ∙ −1 1 4 =

Try It! Solutions Solve Solve 5 7 ÷ 3 5 = 25 21 4 5 ÷ 2 3 = 6 5 2 3 5 ÷−2 1 3 = − 39 35 5 7 × 3 5 = 3 7 9 3 4 = 27 4 2 2 3 ∙ −1 1 4 =− 4 12