Explore · MATH-5B-C09-L08-OPEN
Mentally calculate 2.76 + 1.25 by making a whole number.
Singapore Math 5B · Original independent course
Mental Calculation
Watch for: Compensation applied in the wrong direction.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C09-L08-PREREQ
Compute 2.5 + 1.5 mentally.
Show worked answer (after attempting)
Answer: 4
Add 0.5 and 0.5 to make one whole; 2 + 1 + 1 = 4.
Understand the idea
Explain efficient mental strategies for decimal addition, subtraction and scaling; estimate for reasonableness. The essential earlier idea is: Place-value decomposition and integer mental arithmetic.. The model below will always use the actual quantities from the worked problem. Check compensation applied in the wrong direction when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C09-L08-Q01
Mentally calculate 2.75 + 1.25 by making a whole number.
Solution: 4
Preserve the total while grouping or compensating: 2.75 + 1.25 = 4. Check with reverse operation.
Worked example 2 · MATH-5B-C09-L08-Q02
Estimate then calculate 6.98 + 2.02 by compensation.
Solution: 9
Preserve the total while grouping or compensating: 6.98 + 2.02 = 9. Check with reverse operation.
Worked example 3 · MATH-5B-C09-L08-Q03
Calculate 8.4 − 0.7 mentally; explain a friendly-number strategy.
Solution: 7.7
Preserve the total while grouping or compensating: 8.4 − 0.7 = 7.7. Check with reverse operation.
Check understanding
1 · MATH-5B-C09-L08-Q04
Mentally calculate 2.76 + 1.25 by making a whole number.
Show worked answer (after attempting)
Answer: 4.01
Preserve the total while grouping or compensating: 2.76 + 1.25 = 4.01. Check with reverse operation.
2 · MATH-5B-C09-L08-Q05
Estimate then calculate 6.99 + 2.02 by compensation.
Show worked answer (after attempting)
Answer: 9.01
Preserve the total while grouping or compensating: 6.99 + 2.02 = 9.01. Check with reverse operation.
3 · MATH-5B-C09-L08-Q06
Calculate 8.41 − 0.7 mentally; explain a friendly-number strategy.
Show worked answer (after attempting)
Answer: 7.71
Preserve the total while grouping or compensating: 8.41 − 0.7 = 7.71. Check with reverse operation.
Guided practice
1 · MATH-5B-C09-L08-Q07
Mentally calculate 2.77 + 1.25 by making a whole number.
Show worked answer (after attempting)
Answer: 4.02
Preserve the total while grouping or compensating: 2.77 + 1.25 = 4.02. Check with reverse operation.
2 · MATH-5B-C09-L08-Q08
Estimate then calculate 7 + 2.02 by compensation.
Show worked answer (after attempting)
Answer: 9.02
Preserve the total while grouping or compensating: 7 + 2.02 = 9.02. Check with reverse operation.
3 · MATH-5B-C09-L08-Q09
Calculate 8.42 − 0.7 mentally; explain a friendly-number strategy.
Show worked answer (after attempting)
Answer: 7.72
Preserve the total while grouping or compensating: 8.42 − 0.7 = 7.72. Check with reverse operation.
4 · MATH-5B-C09-L08-Q10
Mentally calculate 2.78 + 1.25 by making a whole number.
Show worked answer (after attempting)
Answer: 4.03
Preserve the total while grouping or compensating: 2.78 + 1.25 = 4.03. Check with reverse operation.
Independent practice
1 · MATH-5B-C09-L08-Q11
Estimate then calculate 7.01 + 2.02 by compensation.
Show worked answer (after attempting)
Answer: 9.03
Preserve the total while grouping or compensating: 7.01 + 2.02 = 9.03. Check with reverse operation.
2 · MATH-5B-C09-L08-Q12
Calculate 8.43 − 0.7 mentally; explain a friendly-number strategy.
Show worked answer (after attempting)
Answer: 7.73
Preserve the total while grouping or compensating: 8.43 − 0.7 = 7.73. Check with reverse operation.
3 · MATH-5B-C09-L08-Q13
Mentally calculate 2.79 + 1.25 by making a whole number.
Show worked answer (after attempting)
Answer: 4.04
Preserve the total while grouping or compensating: 2.79 + 1.25 = 4.04. Check with reverse operation.
4 · MATH-5B-C09-L08-Q14
Estimate then calculate 7.02 + 2.02 by compensation.
Show worked answer (after attempting)
Answer: 9.04
Preserve the total while grouping or compensating: 7.02 + 2.02 = 9.04. Check with reverse operation.
5 · MATH-5B-C09-L08-Q15
Calculate 8.44 − 0.7 mentally; explain a friendly-number strategy.
Show worked answer (after attempting)
Answer: 7.74
Preserve the total while grouping or compensating: 8.44 − 0.7 = 7.74. Check with reverse operation.
6 · MATH-5B-C09-L08-Q16
Mentally calculate 2.8 + 1.25 by making a whole number.
Show worked answer (after attempting)
Answer: 4.05
Preserve the total while grouping or compensating: 2.8 + 1.25 = 4.05. Check with reverse operation.
7 · MATH-5B-C09-L08-Q17
Estimate then calculate 7.03 + 2.02 by compensation.
Show worked answer (after attempting)
Answer: 9.05
Preserve the total while grouping or compensating: 7.03 + 2.02 = 9.05. Check with reverse operation.
8 · MATH-5B-C09-L08-Q18
Calculate 8.45 − 0.7 mentally; explain a friendly-number strategy.
Show worked answer (after attempting)
Answer: 7.75
Preserve the total while grouping or compensating: 8.45 − 0.7 = 7.75. Check with reverse operation.
Challenge and error analysis
1 · MATH-5B-C09-L08-ERR1
The assigned question is: “Estimate then calculate 7.06 + 2.02 by compensation.” A learner wrote: “7.06 + 2.02 = 9.18. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 9.08
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 9.08. Recompute from the given data: Preserve the total while grouping or compensating: 7.06 + 2.02 = 9.08. Check with reverse operation.
2 · MATH-5B-C09-L08-ERR2
The assigned question is: “Calculate 8.48 − 0.7 mentally; explain a friendly-number strategy.” A learner wrote: “8.48 − 0.7 = 8.78. I used this intermediate value to finish the assigned problem.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 7.78
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 7.78. Recompute from the given data: Preserve the total while grouping or compensating: 8.48 − 0.7 = 7.78. Check with reverse operation.
Exit check
Exit · MATH-5B-C09-L08-Q19
Mentally calculate 2.81 + 1.25 by making a whole number.
Show worked answer (after attempting)
Answer: 4.06
Preserve the total while grouping or compensating: 2.81 + 1.25 = 4.06. Check with reverse operation.