Fifth grade students work with strategies when investigating division.  One strategy that assists students is multiplying up.

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Roadmap

Grade	5

Key Concepts: Multiplication & Division Working with Fractions

This student has used the partial quotient
strategy to divide this problem.
634 ÷ 26 =

A strategy a fifth grader might use for division is proportional reasoning.
768 ÷ 16
768 ÷ 16 =	÷ 2  ÷ 2
384 ÷ 8
÷ 2 ÷  2
192 ÷ 4
÷ 2 ÷  2
96 ÷ 2
÷ 2 ÷  2
48  ÷ 1 = 48	
	
Students in grade 5 will use equivalent fractions in order to
add and subtract.	  +  
 +  	=  	
	
Fifth graders solve fraction word problems. This example involves multiplication of a whole number and a fraction.

There are 4 sheets of colored paper, and I
need to use   	of each sheet to   finish my art project. How  much paper will I use?

 four times means that   of the paper is used which is 3 whole sheets of paper and
 of the last sheet.	
	
Fifth graders explore division of fractions.
		is the result of 3 ÷ 4 and they should note that  multiplied by 4 is 3.
If 3 pizzas were shared equally by
4 people each person has a share of size   .	

Division of a fraction by a fraction is not a requirement in grade 5.

Strategies for division,

Working with decimals and fractions

2013-2014

Math

Having worked with addition, subtraction, multiplication and division in both third and fourth grade, fifth grade students are expected to continue apply this understanding when working with decimals.

A strategy used in earlier grades is working with place value.  This is a written example of what students are able to do in grade 5.

1.8 + 2.86 =

Fifth graders also do this with subtraction.

Students may solve a decimal subtraction problem by using an open number line. This strategy is still based on place value understanding.

23.6 – 0.79 = 22.81

The strategy doubling and halving is applied to decimal multiplication.

8 x 2.5 =

Fifth grade students are expected to be able to fluently multiply
multi-digit whole numbers using the standard algorithm.

A fifth grader should apply knowledge of multiplication working with decimals.
2	•  3

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Student will use a grid to show a model of a problem. The use of models continues as does working with the distributive property.

1.2 x 2.3 = 2.76

(1.0 x 2.0) + (1.0 x 0.3) + (0.2 x 2.0) + (0.2 x 0.3)

2.0 + 0.3 +  0.4  + 0.06 = 2.76

A student’s model of 1.2 x 2.3 (which means 1 and 2-tenths of 2 and 3-tenths). Each section is labeled to show the product.