5 th grade critical focus areas in the common core state standards 1: operations with fractions 2:...

5th Grade Critical Focus Areas in the Common Core State Standards

1: Operations with Fractions

2: Fluency with whole number and decimal operations

3: Understanding and solving problems with volume


1: Ratios, rates and proportions

2: Division of fractions

3: Negative numbers

4: Using expressions and equations

5: Statistical thinking


Critical Area 1: Fractions

• Add and subtract fractions with unlike denominators

• Multiply whole numbers and fractions by fractions

• Divide a unit fraction by a whole number and a whole number by a unit fraction.

Add and subtract fractions with unlike denominators

What do students need to know, coming into 5th grade, to master this?

Add and subtract fractions with unlike denominators

18+14

Multiply whole numbers and fractions by fractions – Case 1 (4th grade)

What do students need to know, coming into 5th grade, to do this?

This is multiplying a fraction by a whole number.

6×23

Multiply whole numbers and fractions by fractions – Case 1 (4th grade)

6 groups of - For example, each jar is 2/3 full of juice. How much juice is there altogether?

How would you do ?

Multiply whole numbers and fractions by fractions – Case 2


This is multiplying a whole number by a fraction, or rather, taking a fraction of a whole number.

34×6


I have 6 donuts. I want to give 3/4 of them to a friend. How many will the friend get?



23×34


Can you draw a picture that shows ⅔ of ¾?

What do these pictures show?

What’s the generalization?

23×34


25×23

What does the product of the denominators represent in this picture?What does the product of the numerators represent in this picture?

Divide a unit fraction by a whole number

This is division by partitioning. Take 4 sixths, and share it equally among 2 people. We have 4/6 of a pizza left. How much will we both get if we share it equally among the two of us?

1 2

3

4

and a whole number by a unit fraction

This is division by measurement. How many ½’s are in 6?If the serving size for Cheerios is ½ cup, how many servings are in a 6 cup box?

Division with whole numbers and unit fractions

Students need to learn that these types of problems are fraction division problems:• How much chocolate will each person get if 3

people share ½ lb of chocolate equally? • How many ⅓-cup servings are in 2 cups of

raisins?


Critical Area 2: Fluency with whole number and decimal operations

• Divide with 2-digit divisors• Finalize fluency with whole number arithmetic• Extend fluency with whole numbers to

operations with decimals

Acquisition – Fluency – Generalization

Practice – Drill – Application

Practice involves learning strategies.Drill involves repetitive use of the strategies until the pattern is habituated.Application generally takes the student to the next level in the learning progression.Knowing that multiplication is repeated addition allows students to multiply a fraction times a whole number (6 x ¾). Knowing how to divide a multi-digit number by a 1 digit-divisor allows students to generalize the procedure with 2-digit divisors.

Divide with 2-digit divisors

475 ÷ 25What do students need to know, coming into 5th grade, to master this?

Divide with 2-digit divisors

475 ÷ 25Since 475 = 400 + 70 + 5400 ÷ 25 = 16 and 75 ÷ 25 = 3so 475 ÷ 25 = 16 + 3 = 19

Finalize fluency with whole number arithmetic

• Practice in all kinds of real-world contexts, every day

• Two schools are getting together for a carnival. One of the schools has 378 students. The other school has 453 students. How many students would there be at the carnival if every student in both schools came?

• The key to this problem is for students to see it as an adding problem, since two groups are being brought together.

Extend fluency with whole numbers to operations with decimals

56.75 - 4.8 24.7 x 9.3 45.25 ÷ 2.50

What do students need to know from 4th grade to accomplish this in 5th grade?


Addition and subtraction are the same: add or subtract hundreds and hundreds, tens and tens, ones and ones, tenths and tenths, hundredths and hundredths.

Ah ha! This is the reason we line up

the decimal points!

56.75- 4.8 51.95


24.7 x 9.3 Students need a reason for the algorithm – why it works.1) Estimating gives ~ 240. Calculator says 229712) Area model


2) Area model

1.4 x 1.3= 1 + 0.4 + 0.3 + 0.12= 1.82tenths x tenths yields hundredths


45.25 ÷ 2.50How would you extend your understanding of division with 2-digit divisors to solve this problem?


Critical Area 3: Volume

• Understand the concept of volume• Relate the measurement of volume to

l x w x h or b x h• Solve problems using the formulas

V = l x w x h or V = b x h


1: Fluency with whole number and decimal operations (continuation from 5th grade)

2: Introduction to negative numbers

3: Division of fractions (con’t from 5th grade)

4: Ratios, rates and proportions

5: Using expressions and equations

6: Statistical thinking


Critical Area 1: Fluency with whole numbers and decimals

All students should be fluent with multiplication and division “facts” when they enter 5th grade.All students should be fluent with multi-digit operations with whole numbers and decimals when they leave 6th grade.


Critical Area 2: The meaning of negative numbers

–(3) = –3 –(–3) = 3

|–30| = 30 the distance from zero


Critical Area 3: Division of fractions by fractions

• Understand the meaning of division of a fraction by a fraction

• Make meaning for the procedure of dividing a fraction by a fraction

How many times is contained in 6?

How many times is contained in ?

How many times is contained in ?


Critical Area 4: Ratios and Rates

• Understand ratio and rate concepts• Use ratio reasoning to solve proportion

problems• If it took 7 hours to mow 4 lawns, then at that

rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Hours 7 14 21 28 35

Lawns 4 8 12 16 20

5 th grade critical focus areas in the common core state standards 1: operations with fractions 2:...

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