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Chapter 2 Fractions Part 3 Day….. 1) Recipe Magic 2) Models 3) Multistep Story Problems 4) End of Unit Assessment Day 1 Vocabulary Dividend- The number being divided in a division equation. (inside or 1st number) Divisor- The number doing the dividing in a division equation. (outside or 2nd number) Equivalent- equal or the same Fraction- a number that represents part of a whole or part of a set Greatest Common Factor- the greatest of the common factors of two or more numbers Improper Fraction- a fraction with a numerator that is greater than or equal to the denominator Mixed Number- a number that has a whole number part and a fraction part Product- the answer to a multiplication equation Quotient- the answer to a division equation Reciprocal – two numbers with a product of 1 (flipped upside down) Scaling- to increase or decrease a ratio Simplest Form- a fraction in which the GCF of the numerator and denominator is 1 Test Critiques Please take out a blue ink pen and your grade assessment. Today's Standard Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Recipe Magic Wrap it Up • Review • Questions • Station Work Day 2 Bell Work Create a story problem for 6÷¼= Illustrate the solution Vocabulary Dividend- The number being divided in a division equation. (inside or 1st number) Divisor- The number doing the dividing in a division equation. (outside or 2nd number) Equivalent- equal or the same Fraction- a number that represents part of a whole or part of a set Greatest Common Factor- the greatest of the common factors of two or more numbers Improper Fraction- a fraction with a numerator that is greater than or equal to the denominator Mixed Number- a number that has a whole number part and a fraction part Product- the answer to a multiplication equation Quotient- the answer to a division equation Reciprocal – two numbers with a product of 1 (flipped upside down) Scaling- to increase or decrease a ratio Simplest Form- a fraction in which the GCF of the numerator and denominator is 1 Today's Standard Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Fraction Models Essential Understandings: Fractions are numbers used to represent part of a whole or part of a set. •You can show/solve fraction equations using models. Example: ¼ divided by ½ But first, you must know how to model different types of fractions. •You can model a part of a whole by using a single figure. Example: •You can model part of a set using multiple figures. Example: Modeling Fraction Equations Essential Understandings: Fractions equation models can be used to solve/prove… •Addition Equations Example: •Subtraction Equations Example: •Multiplication Equations Example: •Division Equations Example: Division Models Essential Understanding: •Double bar graphs/ fraction strips are an easy way to illustrate fraction equations involving division. To do this: • Begin by drawing two bars of equal length, one above the other. •The top bar will represent the dividend and the bottom bar will represent the divisor. •Remember to draw the missing portions of wholes, if the dividend is a proper fraction. Example: •Now, divide both bars into equal sized parts to represent any wholes in your dividend. If you dividend is a fraction the entire bar will represent 1 whole. Example: •Next, Divide the wholes in the top bar, to represent the denominator of the dividend. •Then, shade the specified fraction. Example: •Now, divide the wholes of the bottom bar to represent the denominator of the divisor. Example: •Finally, use the numerator of the divisor to determine how many parts per group need to be circled. •The number of groups you can create is the answer to the equations. •Don’t forget to account for any unfinished groups. Example: Types of Division Models • Double Bar / Fraction Strips Example: • Double Number Line Example: • Picture Models Example: Watch This • http://learnzillion.com/lessons/212-multiplyfractions-by-whole-numbers-using-bar-models • http://learnzillion.com/lessons/199-dividewhole-numbers-by-unit-fractions-using-visualmodels • http://learnzillion.com/lessons/1383-solveword-problems-involving-division-of-mixednumbers-and-fractions-using-picture-models Wrap it Up • Review • Questions • Station Work Day 3 Bell Work Create fraction models to illustrate the following equations. ① ½ of 8 = ② 8÷½= ③ ½÷8= Explain the differences and similarities. Vocabulary Dividend- The number being divided in a division equation. (inside or 1st number) Divisor- The number doing the dividing in a division equation. (outside or 2nd number) Equivalent- equal or the same Fraction- a number that represents part of a whole or part of a set Greatest Common Factor- the greatest of the common factors of two or more numbers Improper Fraction- a fraction with a numerator that is greater than or equal to the denominator Mixed Number- a number that has a whole number part and a fraction part Product- the answer to a multiplication equation Quotient- the answer to a division equation Reciprocal – two numbers with a product of 1 (flipped upside down) Scaling- to increase or decrease a ratio Simplest Form- a fraction in which the GCF of the numerator and denominator is 1 Today's Standard Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Story Problems Essential Understanding: To solve multistep word problems, easily, follow this procedure. 1. Read and visualize the problem. 2. Illustrate what you have visualized . 3. Find key vocabulary that helps you decide what operations to use. (Hint: In multistep problems, you will notice more than one) 4. Write down what you know and questions you need to answer. 5. Determine the order of events (what has to happen first? What should be the final outcome?). 6. Write equations using the determined operations. 7. Determine if your equations makes sense. 8. Solve equations in order, carrying information over as necessary. 9. Determine if your answer makes sense. 10. Check or Revise, as needed. Wrap it Up • Review • Questions • Station Work Day 4 Bell Work Taylor has cow pasture that has an area of 300yd2. The length of his pasture is 12 ½ yd2. What is the width? He wants to build a barn that covers 1/5 of the pasture. How much pasture will be left for the cows to graze? Vocabulary Dividend- The number being divided in a division equation. (inside or 1st number) Divisor- The number doing the dividing in a division equation. (outside or 2nd number) Equivalent- equal or the same Fraction- a number that represents part of a whole or part of a set Greatest Common Factor- the greatest of the common factors of two or more numbers Improper Fraction- a fraction with a numerator that is greater than or equal to the denominator Mixed Number- a number that has a whole number part and a fraction part Product- the answer to a multiplication equation Quotient- the answer to a division equation Reciprocal – two numbers with a product of 1 (flipped upside down) Scaling- to increase or decrease a ratio Simplest Form- a fraction in which the GCF of the numerator and denominator is 1 Today's Standard Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Equivalent Equations Essential Understanding: You can create equivalent equations for the division of fractions using the following methods. 1. Mixed Numbers and Improper Fractions 2. Scaling 3. Keep Change Flip 4. Commutative Property 5. Common Denominators 6. One Step Equations 7. Using Variables Exit Ticket Create a KWL chart for Chapter 1 - Decimals Know Want to Know What I Learned Wrap it Up • Review • Questions • Station Work