Test Prep: 5.NBT & 5.NF Mixed Practice
The value of a digit based on its position in a number. Each place is 10× the place to its right.
The Least Common Denominator — the smallest number that is a multiple of both denominators.
A division strategy where you subtract easy multiples of the divisor step by step, then add up how many you subtracted.
An SBA question where you write your own answer instead of picking from choices. You must show work AND explain your thinking.
Multiplying by a fraction to make something bigger or smaller. If the fraction is less than 1, the product gets smaller.
What is 3.45 × 10² ?
❌ This moves the decimal LEFT 2 places — that's dividing by 100, not multiplying.
❌ This only moved the decimal 1 place right — that's × 10¹, not × 10².
✅ 10² = 100. Move the decimal RIGHT 2 places: 3.45 → 34.5 → 345
❌ This moved the decimal 3 places — that would be × 10³.
Which expression equals 34 of 20?
❌ "Of" in math means MULTIPLY, not add. This gives 20.75, not 34 of 20.
✅ "34 of 20" means 34 × 20 = 604 = 15. "Of" always means multiply!
❌ Dividing by 34 gives 2623 — that's MORE than 20. "Of" means multiply, not divide.
❌ This splits 34 into 20 pieces = a very tiny fraction. That's not "34 of 20."
Which is the best estimate for 1,847 ÷ 31?
❌ 6 × 31 = 186. Way too small — we need about 1,847!
✅ Round: 1,847 ≈ 1,800 and 31 ≈ 30. Then 1,800 ÷ 30 = 60. (Exact answer is 59 R 18.)
❌ 600 × 31 = 18,600. Way too big — that's 10× too much!
❌ 6,000 × 31 = 186,000. WAY too big — the dividend is only 1,847!
💡 BUDGET YOUR TIME
If a problem is taking more than 2 minutes, FLAG IT and move on. You can always come back. Don't let one hard question eat up time you need for 5 easier questions.
How to use it: The test scores right answers — it doesn't care which order you answered them. Easy points first, hard points last.
In the number 45.678, the digit 6 is in the ___ place. It represents ___.
What place is the 6 in? What is its value?
The 6 is in the tenths place.
It represents 610 or 0.6
How does the value of the 5 in 3.52 compare to the value of the 5 in 35.2?
The 5 is in the tenths place
Value = 0.5
The 5 is in the ones place
Value = 5
The 5 in 3.52 is 110 as much as the 5 in 35.2.
0.5 is one-tenth of 5. Each place to the RIGHT is ÷ 10.
💡 Use J/K to compare the two numbers
346 × 57 = ?
Step by step — click to reveal each step:
2,184 ÷ 42 = ?
943 students need to ride buses to the field trip. Each bus holds 38 students. How many buses are needed?
When there's a remainder in a division word problem, you don't always round up. Think of 3 examples:
1. When do you round UP? (like the bus problem)
2. When do you round DOWN? (drop the remainder)
3. When is the remainder the actual answer?
Sentence starter: "You round up when ___ because ___"
Fill in: 2.7 × ___ = 27,000
Move the decimal ___ places ___
÷ 100 = move decimal 2 places LEFT
12.5 → 1.25 → 0.125
Move the decimal ___ places ___
× 1,000 = move decimal 3 places RIGHT
0.043 → 0.43 → 4.3 → 43
Explain why 6.3 ÷ 10 = 0.63 using place value.
Write your explanation on your whiteboard. Use math vocabulary!
ANSWER: 6.3 ÷ 10 = 0.63
MATH: When you divide by 10, every digit moves one place to the RIGHT. The 6 moves from the ones place to the tenths place. The 3 moves from the tenths place to the hundredths place.
EXPLAIN: Each place value to the right is 110 as much, so dividing by 10 shifts every digit one place right — making the number 10 times smaller.
× by power of 10: Move decimal RIGHT (count the zeros)
÷ by power of 10: Move decimal LEFT (count the zeros)
Each place is 10× the place to its right and 110 the place to its left
Remainders in word problems: Think about the context — round UP (buses), round DOWN (full boxes), or the remainder IS the answer (leftover)
47 + 23 = ?
A cake recipe needs 34 cup of sugar. A cookie recipe needs 23 cup. How much MORE sugar does the cake recipe need?
23 × 58 = ?
60 students tried out for the basketball team. 35 made it. How many students made the team?
Is 712 × 8 greater or less than 8?
Explain WITHOUT computing.
LESS than 8
Why: 712 is LESS than 1 (7 < 12). When you multiply by a fraction less than 1, the product is smaller than the other factor.
Rule: Scaling by a number < 1 = shrinks. Scaling by a number > 1 = grows.
9 ÷ 13 = ?
Dividing by a fraction LESS than 1 makes the answer BIGGER!
12 ÷ 6 = ?
Unit fraction ÷ whole number = SMALLER fraction. You're splitting a slice into more pieces!
You have 5 cups of flour. Each loaf of bread takes 12 cup. How many loaves can you bake?
Problem: 13 ÷ 5 = ?
13 ÷ 5 = 53
"I flipped and multiplied"
❌ Marcus swapped the dividend and divisor. He did 5 ÷ 13 instead of 13 ÷ 5. His answer is BIGGER than the original — but dividing 13 into more pieces should make it SMALLER.
13 ÷ 5 = 115
"I split 13 into 5 equal parts"
✅ Tina correctly split 13 into 5 parts. Each part = 115. Unit fraction ÷ whole number = SMALLER fraction. You're splitting a slice into more pieces, so each piece gets tinier.
💡 Click to reveal, or use J/K keys
Add/Subtract fractions: Find the LCD first, then add/subtract numerators only
Multiply fractions: Multiply straight across (num × num, den × den), then simplify
Scaling: × by fraction < 1 = smaller result; × by fraction > 1 = bigger result
Divide whole ÷ fraction: Answer is BIGGER (how many pieces fit?)
Divide fraction ÷ whole: Answer is SMALLER (splitting into more pieces)
A store has 1,200 pencils. They pack 34 of them into boxes of 36. How many boxes do they fill?
Multiply 0.6 × 10³. Then divide your answer by 100. What do you get?
A ribbon is 58 of a yard long. You cut it into pieces that are 14 yard each. How many pieces?
Write a word problem where the answer is:
"You have 34 of a pizza left. You eat 12 of what's left. How much of the whole pizza did you eat?"
Answer: 34 × 12 = 38 of the whole pizza
Tara says 10 ÷ 15 = 2. Is she correct? Explain using words, numbers, AND a model.
ANSWER: No, Tara is wrong. The correct answer is 50.
MATH: 10 ÷ 15 means "how many 15-sized pieces fit in 10?" Each whole has 5 fifths, so 10 wholes have 10 × 5 = 50 fifths.
EXPLAIN: Tara confused ÷ 15 with × 15. Dividing by a fraction less than 1 makes the answer BIGGER, not smaller. 10 × 15 = 2, but 10 ÷ 15 = 50.
In the bottom of your notebook page, write one sentence explaining the most important thing you reviewed today about numbers and fractions. What's the #1 strategy you'll use on the SBA?
1,728 ÷ 36 = ?
Show your work!
36 × 40 = 1,440 → 1,728 − 1,440 = 288
36 × 8 = 288 → 288 − 288 = 0
48
56 − 38 = ?
Show how you found a common denominator.
LCD = 24
2024 − 924 = 1124
Kai says 8 ÷ 14 = 2.
Mia says 8 ÷ 14 = 32.
Who is correct? Explain.
Mia is correct.
8 ÷ 14 = "how many 14s fit in 8?" Each whole has 4 quarters, so 8 × 4 = 32. Kai multiplied instead of dividing.
A pool is 34 full. Then 13 of the water is drained. What fraction still has water?
Drained: 13 × 34 = 312 = 14
Remaining: 34 − 14 = 24 = 12