5) Fractions: Multiply ~ Resizing, Comparing
5.NF.B.5 (A & B)
5.NF.B.5 (A & B)
I can think of multiplication as the scaling of a number (similar to a scale on a map.)
You'll often use this if you want to double a recipe. To double 1/4 cup water 2 x 1/4 = 2/4. Simplified, 2/4 = 1/2 You'll need 1/2 cup water Understand how numbers scale using multiplication and visual representations. (LearnZillion) Video: Multiplication as Scaling with Fractions Practice: Fraction Multiplication as Scaling I can mentally compare the size of a product to the size of one of the factors by thinking about the other factor in the problem
I can explain why multiplying a number by a fraction greater than 1 will result in a bigger number than the number I started with.
Example: Students want to paint a bench that measures 5/4 feet by 4 3/4 feet. They have enough paint to cover an area of 4 3/4 sq.ft. Will they have enough paint? To find the area, use the formula: Area = Length × Width [ A = L × W ] A = 5/4 × 4 3/4 But we don't need to multiply anything! Improper fractions like 5/4 are greater than 1. 5/4 > 1 so 5/4 × 4 3/4 > 4 3/4. They need more paint. Predict the product of multiplying a fraction greater than one by a whole number. (LearnZillion) I can explain why multiplying a number by a fraction less than 1 will result in a smaller number than the number I started with.
This is like the standard above, except you're multiplying proper fractions instead of improper fractions. Predict the product of multiplying a fraction less than one by a whole number. (LearnZillion) I can relate the notion of equivalent fractions to the effect of multiplying a fraction by 1.
Understand the effect of multiplying by a fraction equal to one. (LearnZillion) |
Here are the CA State Standards:
Big Idea: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5. Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a) / (n × b) to the effect of multiplying a/b by 1. Another way to explain the standards: a. You can sometimes figure out which product will be the largest without having to do the multiplication. How? If a group of equations all share one factor in common, then just look at the size of the other factor. b. Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); - explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and - relate the principle of fraction equivalence a / b = (n × a) / (n × b) to the effect of multiplying a / b by 1. (note: "/" means "divided by") - I can explain the relationship between two multiplication problems that share a common factor (1/4 x 8 and ¼ x 16). - I can compare the product of two factors without multiplying. Example: 2 x ? = <1 Answer must be less than ½. - I can explain why multiplying a number by a fraction greater than one will result in a product greater than the given number. - I can explain why multiplying a fraction by one (which can be written as various fractions, ex. 2/2, 3/3 , etc.) results in an equivalent fraction. - I can explain why multiplying a fraction by a fraction will result in a product smaller than the given number. |
Some Example Images from: https://www.learningfarm.com/web/practicePassThrough.cfm?TopicID=642