ALEX Resources

   View Standards     Standard(s): [MA2019] (5) 10 :

10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.

[MA2019] (5) 9 :

9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Example: Recognize an incorrect result ²/₅+ ¹/₂= ³/₇ by observing that ³/₇ < ¹/₂.

This hands-on, minds-on activity helps students use what they already know about customary measurement (CCRS 2010 #18 [5.MD.1]: Convert among different-sized standard measurement units within a given measurement system.) to help them add and subtract fractions with like and unlike denominators.

   View Standards     Standard(s): [MA2019] (5) 9 :

9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Example: Recognize an incorrect result ²/₅+ ¹/₂= ³/₇ by observing that ³/₇ < ¹/₂.

[MA2019] (5) 10 :

10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.

[MA2019] (5) 12 :

12. Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction.

a. Use a visual fraction model (area model, set model, or linear model) to show (^a/_b) x q and create a story context for this equation to interpret the product as a parts of a partition of q into b equal parts.

b. Use a visual fraction model (area model, set model, or linear model) to show (^a/_b) x (^c/_d) and create a story context for this equation to interpret the product.

c. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

d. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths to show that the area is the same as would be found by multiplying the side lengths.

[MA2019] (5) 14 :

14. Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.

Students will solve problems using addition, subtraction, and multiplication of fractions in this interactive from WNET. In the accompanying classroom activity, students work in groups of two and watch a series of Cyberchase videos; answer associated discussion questions; and complete an activity that uses fraction knowledge, proportion, addition, and multiplication.

   View Standards     Standard(s): [MA2019] (5) 9 :

9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Example: Recognize an incorrect result ²/₅+ ¹/₂= ³/₇ by observing that ³/₇ < ¹/₂.

[MA2019] (5) 10 :

10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.

In this short practice, students review how to simplify fractions, or reduce fractions to their lowest terms, and practice with an interactive game.

   View Standards     Standard(s): [MA2019] (5) 9 :

9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Example: Recognize an incorrect result ²/₅+ ¹/₂= ³/₇ by observing that ³/₇ < ¹/₂.

[MA2019] (5) 11 :

11. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

a. Model and interpret a fraction as division of the numerator by the denominator (^a/_b= a ÷ b)

b. Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers

[MA2019] (5) 14 :

14. Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.

[MA2019] (5) 15 :

15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.

[MA2019] (5) 17 :

17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.

[MA2019] (5) 19 :

19. Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

a. Use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.

b. Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

c. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the two parts, applying this technique to solve real-world problems.

[MA2019] (5) 20 :

20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

Module 6, Topic E provides an opportunity for students to encounter complex, multi-step problems requiring the application of the concepts and skills mastered throughout the Grade 5 curriculum. Students use all four operations with both whole and fractional numbers in varied contexts. The problems in Topic E are designed to be non-routine problems that require students to persevere to solve them.  

While wrestling with complexity is an important part of Topic E, the true strength of this topic is derived from the time allocated for students to construct arguments and critique the reasoning of their classmates. After students have been given adequate time to ponder and solve the problems, two lessons are devoted to the sharing of approaches and solutions. Students partner to justify their conclusions, communicate them to others, and respond to the arguments of their peers.

   View Standards     Standard(s): [MA2019] (5) 9 :

9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Example: Recognize an incorrect result ²/₅+ ¹/₂= ³/₇ by observing that ³/₇ < ¹/₂.

[MA2019] (5) 10 :

10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.

[MA2019] (6) 8 :

8. Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

a. Use factors and multiples to determine prime factorization.

In this interactive activity, students will be led through steps to add and subtract fractions with unlike denominators. There are teaching activities as well as practice activities available. A handout that reviews the strategies taught in the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.