Communication
Explain in one or two sentences how you would add 1/4+1/6 so a classmate can follow your steps.
Find a common denominator, 12: 1/4 = 3/12, 1/6 = 2/12; add to get 5/12.
Find the sum: 1/3+1/6. Show the result.
1/3+1/6 = 2/6+1/6 = 3/6 = 1/2.
What is the first step when adding 2/9+1/3? Perform the step and finish the addition.
First step: rewrite 1/3 = 3/9; then 2/9+3/9 = 5/9
On a number line, which is larger: 0.60 or 3/5? Model and explain briefly.
They are equal: 0.6 = 6/10 = 3/5 0.60.
Write a clear, step-by-step explanation for why you must find a common denominator before adding 2/5+3/8.
You need a common denominator to add like parts: for 2/5+3/8 use 40, convert: 16/40+15/40=31/40.
Solve: 5.6+0.75 and show your answer.
5.6+0.75 = 6.35
Compute: 0.48−0.275. Show your work and final answer.
0.48−0.275 = 0.205.
A carton holds 2/3 litre of juice. Two students each drink 0.25 litres. How much juice remains? Show work and give your answer as a fraction.
Total drank 0.5 or 1/2. Subtract 2/3-1/2 = 1/6
A student made this explanation: “To subtract decimals, line up the decimal points and subtract.” Add one more sentence to this explanation that describes what to do if you need to borrow. Use the example 3.02−1.47 in your answer.
Line up decimals, borrow from tenths to hundredths when needed. For 3.02−1.473.02−1.47 borrow: 3.02−1.47 = 1.55.
Mariana adds 5/12 + 1/8 and gets a sum of 6/20. Identify the error and give the correct sum.
Error: she did not find a common denominator correctly. Common denominator is 24: 5/12 = 10/24, 1/8 = 3/24; sum 13/24
Add and simplify: 7/10+3/25.
Convert to denominator of 50: 7/10 = 35/50, 3/25 = 6/50; sum 41/50
You run 3.5 miles on Monday and 7/4 miles on Tuesday. How many miles did you run in total? Show answer as a decimal and as a mixed number.
3.5+7/4 = 3.5+1.75 = 5.25 miles; as mixed number 5 & 1/4
Describe (in 2–3 sentences) how you would communicate your thinking when converting a mixed number to an improper fraction, using 2 & 3/5 as an example.
Multiply whole by denominator, add numerator and keep the denominator the same. 13/5
A recipe needs 3/4 cup of oil. You have already poured 0.5 cup. How much more oil is needed? Give your answer as a decimal and as a fraction in simplest form.
Remaining oil: 3/4−0.5 = 3/4−1/2 = 1/4 = 0.25 cup.
Subtract and simplify if needed: 11/12 − 0.25. Show all steps.
11/12 - 1/4 = 11/12 - 3/12 = 8/12 = 2/3
A classroom project requires 5/6 kg of clay per model. If the class makes 8 models, how much clay is needed in total? Give your answer as a mixed number and as a decimal.
Total clay: 8×5/6 = 40/6 = 20/3 = 6 & 2/3 kg; decimal 6.666…≈6.667 (rounded to thousandths)
Given the problem 4.25−7/20, write a concise explanation (3–4 sentences) showing both a decimal method and a fraction method, and state which you think is easier and why.
Decimal method: convert 7/20=0.35, then 4.25−0.35 = 3.90. Fraction method: convert 4.25=17/4, find common denominator with 7/20, etc. Decimal is quicker here.
Solve and show work: 7.125 − 9/40. Express the final answer as a decimal.
Convert 9/40 = 0.225; 7.125−0.225 = 6.900 or 6.9
Convert and compute: Add 2.4 + 5/8. Show the conversion you use and give the final answer.
Convert 5/8 = 0.625; 2.4+0.625 = 3.025
Real-world task: A bag contains 2.75 kg of flour. A baker uses 3/8 kg for one batch, then 0.9 kg for another. How much flour remains? Show step-by-step work and give the final amount as a decimal rounded to the nearest hundredth.
Convert 3/8 = 0.375; used total 0.375+0.9=1.275; remainder 2.75−1.275=1.475 kg (rounded to hundredth 1.48).