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.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
All four operations are extended to decimals to hundredths in fifth grade, and the emphasis is on reasoning, not memorized rules. For addition and subtraction, students combine or take away like units: tenths with tenths and hundredths with hundredths, which is why lining up place values matters, not 'lining up the decimal points' as a magic step.
For multiplication and division, students use models and place value to make sense of answers. 0.3 × 0.4 can be shown on a hundredths grid as a 3 by 4 block of squares, which is 12 hundredths, or 0.12. Dividing 2.4 by 0.6 asks how many groups of 6 tenths fit into 24 tenths, which is 4. Students relate each strategy to a written method and explain their reasoning, so the later standard algorithms in sixth grade rest on understanding. Estimation is a constant check: 4.9 × 3.1 should be close to 5 × 3 = 15.
Adding 3.5 + 1.25 by right-aligning the digits gives 1.60. Aligning by place value (3.50 + 1.25) gives the correct 4.75.
Students expect 0.5 × 8 to be more than 8. Multiplying by a number less than 1 gives a smaller result: half of 8 is 4.
The rule 'count the decimal places' works, but students who use it without estimating can place the point wrongly when zeros are involved, for example writing 0.2 × 0.5 = 0.010 and then misreading it.
6 ÷ 0.5 is 12, larger than 6, because there are 12 halves in 6. Asking 'how many groups of 0.5 fit in 6?' corrects the expectation.
Find 2.3 × 1.4 using an area model and check with an estimate.
Answer: 2.3 × 1.4 = 3.22.
Hundredths grids and base-ten blocks with a flat as one whole make decimal operations concrete. After modeling, ask students to write the matching equation and compare it with the written method, so the place value reasoning carries over to the algorithm.
Assessment items often use money and metric measurement, ask for an exact decimal answer, or ask students to identify an error in someone's decimal calculation.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 7.35
Write 2.6 as 2.60 so the places line up: 4.75 + 2.60 = 7.35.
Answer: 5.52
Write 9 as 9.00, then subtract: 9.00 - 3.48 = 5.52.
Answer: A) 0.18
6 tenths times 3 tenths is 18 hundredths, which is 0.18. On a hundredths grid it is a 6 by 3 block of squares.
Answer: 8
7.2 is 72 tenths and 0.9 is 9 tenths. 72 tenths ÷ 9 tenths = 8, so 7.2 ÷ 0.9 = 8.
Answer: C) $8.10
6 × $1.35 = 6 × $1 + 6 × $0.35 = $6 + $2.10 = $8.10.
Answer: 1.2 (also accepted: 1.2 m)
4.8 ÷ 4: 4 ones ÷ 4 = 1 and 8 tenths ÷ 4 = 2 tenths. Each piece is 1.2 m.
Answer: A) 5 × 0.8
Multiplying 5 by a number less than 1 gives less than 5: 5 × 0.8 = 4. The others give 6, 5 and 12.5.
A full lesson with slides, activities and an exit ticket on operations with decimals to hundredths, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.NBT.B.7 with an answer key, ready in about a minute.
Make a worksheet →Turn operations with decimals to hundredths into a quiz students answer online that marks itself, with a class summary for you.
Build a test →No. 5.NBT.B.7 asks for models, drawings and place value strategies related to a written method. Fluency with standard algorithms for decimal operations is a sixth grade expectation (6.NS.B.3).
Operations are with decimals to hundredths, which keeps models such as hundredths grids practical.