[FREE] End of Year Math Assessments (Grade 4 and Grade 5)

The assessments cover a range of topics to assess your students' math progress and help prepare them for state assessments.

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Here you will learn about subtracting decimals, including how to subtract decimals and solve problems that involve the subtraction of decimal numbers.

Students will first learn about subtracting decimals in 5th grade math using concrete models and expand that knowledge into 6th grade using the algorithm for subtraction.

**Subtracting decimals **is when you subtract numbers involving decimals.

Subtracting decimal numbers is very similar to subtracting multi-digit whole numbers.

Let’s look at strategies for subtracting decimals.

How does this relate to 5th grade math and 6th grade math?

**Grade 5 – Number and Operations – Base Ten (5.NBT.B.7)**Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

**Grade 6 – Number System (6.NS.B.3)**

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

In order to subtract decimal numbers using models:

**Show each number using decimal models.****Group matching parts.****Count up the leftover squares and write the answer in standard form.**

In order to subtract decimals:

**Stack the numbers with the larger one on top, lining up the decimal points and place values.****Add**\bf{0}**’s as placeholders where necessary.****Subtract each column from right to left regrouping when necessary.****Write your final answer with the decimal point and check to make sure your answer is reasonable.**

Use this quiz to check your grade 4 to 6 students’ understanding of decimals. 10+ questions with answers covering a range of 4th, 5th and 6th grade topics to identify areas of strength and support!

DOWNLOAD FREEUse this quiz to check your grade 4 to 6 students’ understanding of decimals. 10+ questions with answers covering a range of 4th, 5th and 6th grade topics to identify areas of strength and support!

DOWNLOAD FREESubtract 2.03 - 1.2

**Show each number using decimal models.**

2**Group matching parts.**

3**Remove the grouped parts and write what is left.**

There are 8 tenths and 3 hundredths left over. The answer in standard form is 0.83.

Subtract the numbers 7.3 - 2.8

**Stack the numbers with the larger one on top, lining up the decimal points and place values.**

**Add ** \bf{0} **’s as placeholders where necessary.**

All place values lined up.

**Subtract each column from right to left regrouping when necessary.**

**Write your final answer with the decimal point and check to make sure your answer is reasonable.**

Answer: 4.5

**Is the answer reasonable?**

7.3 rounds to 7 and 2.8 rounds to 3.

The answer should be close to 7 - 3 = 4.

It is, so 4.5 is reasonable.

Subtract the numbers 12.43 - 7.81

**Stack the numbers with the larger one on top, lining up the decimal points and place values.**

**Add ** \bf{0} **’s as placeholders where necessary.**

Not necessary because the decimals have the same number of decimal places.

**Subtract each column from right to left regrouping when necessary.**

**Write your final answer with the decimal point and check to make sure your answer is reasonable.**

Answer: 4.62

**Is the answer reasonable?**

12.43 rounds to 12 and 7.81 rounds to 8.

The answer should be close to 12 - 8 = 4.

It is, so 4.62 is reasonable.

Subtract the numbers 0.8 - 0.17

**Stack the numbers with the larger one on top, lining up the decimal points and place values.**

**Add ** \bf{0} **’s as placeholders where necessary.**

**Subtract each column from right to left regrouping when necessary.**

Subtract the numbers 9.1 - 3.276

**Stack the numbers with the larger one on top, lining up the decimal points and place values.**

**Add ** \bf{0} **’s as placeholders where necessary.**

**Subtract each column from right to left regrouping when necessary.**

**Write your final answer with the decimal point and check to make sure your answer is reasonable.**

Answer: 5.824

**Is the answer reasonable?**

9.1 rounds to 9 and 3.276 rounds to 3.

The answer should be close to 9 - 3 = 6.

It is, so 5.824 is reasonable.

Subtract the numbers 5 - 2.081

**Stack the numbers with the larger one on top, lining up the decimal points and place values.**

**Add ** \bf{0} **’s as placeholders where necessary.**

**Subtract each column from right to left regrouping when necessary.**

**Write your final answer with the decimal point and check to make sure your answer is reasonable.**

Answer: 2.919

**Is the answer reasonable?**

2.081 rounds to 2.

The answer should be close to 5 - 2 = 3.

It is, so 2.919 is reasonable.

- Use visual models to develop students’ understanding of place value along with subtraction.

- Although practice worksheets help students master skills, infusing resources that promote conceptual understanding will provide students with deep understanding of the numerical concepts. Strong number sense leads to strong algebraic understanding.

- Reinforce estimation strategies so that the decimal numbers make sense to students.

**Not lining up the decimal points and place values.**

A common error when subtracting decimals occurs when the decimal points are not lined up but instead the last digits are lined up.

\bf{0}**Not placing****’s as placeholders.**

Subtracting the numbers 10 - 0.51

1. Subtract the numbers 1.04-0.23

1.01

0.81

81

0.91

Stack the numbers with the larger one on top, lining up the decimal points.

No 0 ’s are needed as placeholders. Subtract from right to left, regrouping when necessary.

Check if the answer is reasonable.

1.04 rounds to 1 and 0.23 rounds to 0.

The answer should be close to 1-0 = 1

It is, so 0.81 is reasonable.

2. Subtract the numbers 12.5-7.8

4.7

5.3

20.3

5.7

Stack the numbers with the larger one on top, lining up the decimal points.

No 0 ’s are needed for placeholders. Subtract from right to left, regrouping when necessary.

The answer in standard form is 4.7

Check to see if the answer is reasonable.

12.5 rounds to 13 and 7.8 rounds to 8.

The answer should be close to 13-8 = 5

It is, so 4.7 is reasonable.

3. Subtract the numbers 56.29-2.47

31.59

3.159

53.82

54.22

Stack the numbers with the larger one on top, lining up the decimal points.

No 0 ’s are needed for placeholders. Subtract from right to left, regrouping when necessary.

The answer is 53.82

Check to see if the answer is reasonable.

56.29 rounds to 56 and 2.47 rounds to 2.

The answer should be close to 56-2 = 54

It is, so 53.82 is reasonable.

4. Subtract the numbers 23.4-16.573

7.827

16.339

7.173

6.827

Stack the numbers with the larger one on top, lining up the decimal points and place values. Add 0 ’s as placeholders.

Subtract from right to left, regrouping when necessary.

The answer is 6.827

Check to see if the answer is reasonable.

23.4 rounds to 23 and 16.573 rounds to 17.

The answer should be close to 23-17 = 6

It is, so 6.827 is reasonable.

5. Subtract the numbers 8.29-5.9

2.39

3.2

2.4

3.28

Stack the numbers with the larger one on top, lining up the decimal points and place values. Add 0 ’s as placeholders.

Subtract from right to left, regrouping when necessary.

Check to see if the answer is reasonable.

8.29 rounds to 8 and 5.9 rounds to 6.

The answer should be close to 8-6 = 2

It is, so 2.39 is reasonable.

6. Subtract the numbers 24-11.27

11.03

11.30

12.37

12.73

Stack the numbers with the larger one on top, lining up the decimal points and place values. Add 0 ’s as placeholders.

Subtract from right to left, regrouping when necessary.

Check to see if the answer is reasonable.

11.27 rounds to 11.

The answer should be close to 24-11 = 13

It is, so 12.73 is reasonable.

They have similar procedures, such as lining up decimal points, place values, and adding 0 ’s as place holders. When you subtract decimals in 5th grade and 6th grade it’s important to stack the decimal numbers so that the larger number is on top. When you add decimals, that step isn’t necessary.

Using estimation strategies such as rounding is a good practice when doing decimal operations. Whole numbers are easier to conceptualize than decimal numbers so it’s a good practice to determine if your answer is reasonable.

Following the Common Core recommendations, in 5th grade, students should work with tenths place, hundredths place and thousandths place. In 6th grade this is expanded to smaller numbers. Check your state’s specific standards for further clarification.

- Multiplying decimals
- Dividing decimals
- Adding and subtracting integers
- Ordering decimals
- Fractions

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