3A-R-0011 point
Write 6,407 in words.
Reveal worked solution
Answer: six thousand four hundred seven
Read the 6 thousands, 4 hundreds, 0 tens, and 7 ones.
Semester 3A · Review · ORIGINAL PUBLIC PRACTICE
Cumulative semester review
67 original questions with worked explanations, drawn from the frozen Chapters 1–7 instructional objectives.
Work on paper. This is an original, untimed, public practice resource. Do not use the results alone to make placement decisions. It covers Chapters 1–7 only; fractions, time, money, and measurement belong to later material.
How to use this cumulative review
The review is organized by topic to make weak areas easier to revisit. Try one or two chapters at a time, then revisit the areas you miss using the corresponding lessons. Challenge and explanation tasks are intentional: show a model, equation, or reason where requested.
| Content area | Questions | Points |
|---|---|---|
| Chapter 1: Numbers to 10,000 | 12 | 22 |
| Chapter 2: Addition & Subtraction I | 12 | 29 |
| Chapter 3: Addition & Subtraction II | 9 | 26 |
| Chapter 4: Multiplication & Division | 10 | 25 |
| Chapter 5: Multiplication | 9 | 25 |
| Chapter 6: Division | 9 | 25 |
| Chapter 7: Graphs & Tables | 6 | 13 |
CHAPTER 1
Numbers to 10,000
12 questions · 22 points · attempt before revealing explanations.
3A-R-0022 points
In 8,353, what is the value of the second 3 (reading left to right)?
Reveal worked solution
Answer: 3 ones
The second 3 is in the ones place, so its value is 3. The first 3 is 300.
3A-R-0032 points
Write 5,090 as a sum of thousands, hundreds, tens, and ones.
Reveal worked solution
Answer: 5,000 + 90
Five thousands, zero hundreds, nine tens, zero ones: 5,000 + 90.
3A-R-0042 points
How many hundreds equal 3,200? Explain your grouping.
Reveal worked solution
Answer: 32 hundreds
Each hundred is 100, and 3,200 ÷ 100 = 32; 3 thousands become 30 hundreds plus 2.
3A-R-0052 points
Order these from least to greatest: 7,205; 7,025; 7,250; 7,052.
Reveal worked solution
Answer: 7,025; 7,052; 7,205; 7,250
All have 7 thousands. Compare the hundreds next (0 before 2), then the tens.
3A-R-0062 points
On a number line marked 2,000, 2,200, 2,400, 2,600 at equal distances, what value lies halfway between 2,200 and 2,400?
Reveal worked solution
Answer: 2,300
Half of the 200-unit gap is 100; 2,200 + 100 = 2,300.
3A-R-0072 points
Continue the pattern for two more terms: 5,875; 5,625; 5,375; __; __.
Reveal worked solution
Answer: 5,125; 4,875
Each step subtracts 250, so continue twice.
3A-R-0081 point
Round 6,521 to the nearest thousand.
Reveal worked solution
Answer: 7,000
The hundreds digit is 5, and 6,521 is above the midpoint 6,500.
3A-R-0091 point
Round 4,349 to the nearest hundred.
Reveal worked solution
Answer: 4,300
4,349 is 49 away from 4,300 and 51 away from 4,400.
3A-R-0101 point
Round 8,765 to the nearest ten.
Reveal worked solution
Answer: 8,770
The ones digit is 5, so round up to the next multiple of 10.
3A-R-0113 points
A student rounds 5,449 first to 5,400 (nearest hundred), then to 5,000 (nearest thousand). Is 5,000 also the correct result from rounding 5,449 directly to the nearest thousand? Explain.
Reveal worked solution
Answer: Yes, 5,000
5,449 is below the 5,500 midpoint, so direct rounding gives 5,000. The two-step procedure agrees here, but two-step rounding is not always safe.
3A-R-0123 points
Give a four-digit number that rounds to 3,500 to the nearest hundred and 4,000 to the nearest thousand; justify your example.
Reveal worked solution
Answer: Example: 3,500
3,500 is already a multiple of 100 and sits at the midpoint between 3,000 and 4,000, so under the standard half-up rule it rounds to 4,000. Values 3,500–3,549 also work.
CHAPTER 2
Addition & Subtraction I
12 questions · 29 points · attempt before revealing explanations.
3A-R-0132 points
Find 438 + 250 by splitting 250 into hundreds and tens.
Reveal worked solution
Answer: 688
438 + 200 = 638; 638 + 50 = 688.
3A-R-0142 points
Compute 598 + 167 using compensation; show why the adjusted sum must be corrected.
Reveal worked solution
Answer: 765
(600 + 167) − 2 = 767 − 2 = 765. We added 2 extra to 598, so subtract it.
3A-R-0152 points
Find 763 − 240 mentally; record useful jumps.
Reveal worked solution
Answer: 523
763 − 200 = 563; then 563 − 40 = 523.
3A-R-0162 points
Use equal adjustment to calculate 803 − 298. Show both adjusted numbers.
Reveal worked solution
Answer: 505
Add 2 to both: 805 − 300 = 505. Equal shifts preserve the difference.
3A-R-0172 points
What must be added to 674 to make 1,000?
Reveal worked solution
Answer: 326
674 + 26 = 700; another 300 reaches 1,000, so 326.
3A-R-0182 points
Without using column addition, calculate 397 + 205.
Reveal worked solution
Answer: 602
Think 400 + 205 − 3 = 602.
3A-R-0194 points
Two teams together earned 94 points. One scored 18 more than the other. Find both scores and describe a bar model.
Reveal worked solution
Answer: 38 and 56
Remove the 18 extra points: 94 − 18 = 76. Two equal bars each represent 38; the larger is 38 + 18 = 56.
3A-R-0202 points
A museum counted 1,248 visitors over the weekend. If 375 came on Saturday, how many visited on Sunday?
Reveal worked solution
Answer: 873
The weekend total has two parts: Saturday and Sunday. Sunday = 1,248 − 375 = 873.
3A-R-0212 points
Maya has 235 beads. She has 47 fewer than Niko. How many beads does Niko have?
Reveal worked solution
Answer: 282
Niko has more, so add: 235 + 47 = 282.
3A-R-0223 points
A library had 1,420 books. It received 235 more, then lent out 189. How many remain?
Reveal worked solution
Answer: 1,466
Start 1,420 + 235 = 1,655. Then 1,655 − 189 = 1,466.
3A-R-0233 points
Two students calculate 702 − 299. One writes 703 − 300. The other writes 702 − 300 and adds 1. Are both valid? Find the answer.
Reveal worked solution
Answer: Both are valid; 403
Equal adjustment: 703 − 300 = 403. Compensation: 702 − 300 + 1 = 403. Both preserve the original difference.
3A-R-0243 points
Ava has 36 more stickers than Ben. Ava gives Ben 8. Who has more afterward, and by how many?
Reveal worked solution
Answer: Ava by 20
Giving 8 decreases Ava by 8 and increases Ben by 8, so the gap shrinks by 16: 36 − 16 = 20.
CHAPTER 3
Addition & Subtraction II
9 questions · 26 points · attempt before revealing explanations.
3A-R-0253 points
Calculate 2,768 + 1,457. Show at least one place-value exchange.
Reveal worked solution
Answer: 4,225
8 ones + 7 ones = 15 ones: write 5 ones, exchange 10 ones for 1 ten. Continue to get 4,225.
3A-R-0263 points
Calculate 4,503 − 1,278. Show why borrowing is required.
Reveal worked solution
Answer: 3,225
Regroup across the empty tens; 4,503 − 1,278 = 3,225. Add 1,278 back to check.
3A-R-0273 points
Solve 6,000 − 2,487 and explain how you regroup across zeros.
Reveal worked solution
Answer: 3,513
Rename 6,000 as 5 thousands, 9 hundreds, 9 tens and 10 ones, then subtract columns: 3,513.
3A-R-0282 points
Estimate 3,462 + 2,153 by rounding each addend to the nearest hundred.
Reveal worked solution
Answer: 5,700
3,462 → 3,500 and 2,153 → 2,200; sum 5,700.
3A-R-0293 points
Estimate 6,187 − 2,741 by rounding to the nearest thousand, then calculate the exact difference.
Reveal worked solution
Answer: Estimate 3,000; exact 3,446
6,187 → 6,000; 2,741 → 3,000; estimate = 3,000. Exact: 6,187 − 2,741 = 3,446.
3A-R-0303 points
A school collected 2,385 cans in September and 1,756 in October, then recycled 2,094. Estimate the number left by rounding each quantity to the nearest hundred, then calculate exactly.
Reveal worked solution
Answer: Estimate 2,100; exact 2,047
Estimate 2,400 + 1,800 − 2,100 = 2,100. Exact: 2,385 + 1,756 = 4,141; 4,141 − 2,094 = 2,047.
3A-R-0313 points
A learner says 4,002 − 1,978 = 3,976 because they subtracted the smaller digit from the larger in each column. Explain the error and find the correct answer.
Reveal worked solution
Answer: 2,024
Column subtraction must exchange place-value units, not always subtract smaller digit from larger. Correct: 4,002 − 1,978 = 2,024.
3A-R-0323 points
Which is more reasonable for 2,908 + 3,096: 5,000 or 6,000? Justify before finding the exact sum.
Reveal worked solution
Answer: 6,000; exact 6,004
Both numbers are near 3,000, so their sum is near 6,000. The exact sum is 6,004.
3A-R-0663 points
A class has 2,675 paper squares and another class brings 1,459. Estimate the total to the nearest hundred and then calculate it exactly.
Reveal worked solution
Answer: Estimate 4,200; exact 4,134
Round 2,675 → 2,700 and 1,459 → 1,500 for estimate 4,200. Exact: 2,675 + 1,459 = 4,134.
CHAPTER 4
Multiplication & Division
10 questions · 25 points · attempt before revealing explanations.
3A-R-0332 points
Draw or describe an array showing 7 rows of 4 dots. How many dots are there?
Reveal worked solution
Answer: 28 dots
Each of 7 rows has 4 dots, so 7 × 4 = 28. Any 7-by-4 array has 28 dots.
3A-R-0342 points
Use the distributive property to find 9 × 7 by splitting 7 into 5 and 2.
Reveal worked solution
Answer: 63
9 × (5 + 2) = 45 + 18 = 63.
3A-R-0352 points
Thirty-six pencils are shared equally among 6 boxes. How many pencils go in each box?
Reveal worked solution
Answer: 6 pencils
36 ÷ 6 = 6. Check 6 × 6 = 36.
3A-R-0363 points
Explain why 0 ÷ 7 = 0 but 7 ÷ 0 is not defined.
Reveal worked solution
Answer: 0 ÷ 7 = 0; 7 ÷ 0 is undefined
Zero objects can be shared among 7 groups as 0 each. No number multiplied by 0 yields 7, so dividing 7 by 0 is undefined.
3A-R-0372 points
Forty-seven counters are packed in bags of 6. How many full bags and how many counters left over?
Reveal worked solution
Answer: 7 full bags; 5 left over
6 × 7 = 42 and 47 − 42 = 5. The remainder 5 is smaller than 6.
3A-R-0383 points
Without adding individually, decide whether the sum of five odd whole numbers is odd or even. Explain.
Reveal worked solution
Answer: Odd
Pairing two odd numbers gives an even sum. Two pairs give even + even, and one unpaired odd makes the total odd.
3A-R-0392 points
There are 8 tables with 6 chairs at each. How many chairs are there?
Reveal worked solution
Answer: 48 chairs
8 equal groups of 6: 8 × 6 = 48.
3A-R-0403 points
Jules has four times as many marbles as Kai. Kai has 9. Describe the equal-unit bar model and find Jules’s number.
Reveal worked solution
Answer: 36 marbles
Kai has one 9-unit bar. Jules has four bars each the same length, totaling 4 × 9 = 36.
3A-R-0413 points
A baker makes 9 trays with 8 rolls each. She packs the rolls into bags of 5. How many full bags and loose rolls?
Reveal worked solution
Answer: 14 full bags; 2 loose rolls
9 × 8 = 72 rolls. 72 ÷ 5 = 14 remainder 2.
3A-R-0423 points
Thirty-eight children need seats in vans that each hold 8. How many vans are needed? Explain why the remainder matters.
Reveal worked solution
Answer: 5 vans
38 ÷ 8 = 4 remainder 6. Four vans cannot seat the remaining six children, so a fifth van is needed.
CHAPTER 5
Multiplication
9 questions · 25 points · attempt before revealing explanations.
3A-R-0432 points
Find 7 × 300 using hundreds, not repeated counting.
Reveal worked solution
Answer: 2,100
7 groups of 3 hundreds = 21 hundreds = 2,100.
3A-R-0442 points
Calculate 23 × 3 using (20 + 3) × 3.
Reveal worked solution
Answer: 69
20 × 3 = 60; 3 × 3 = 9; total 69.
3A-R-0453 points
Calculate 42 × 6; show what happens when 4 tens × 6 = 24 tens.
Reveal worked solution
Answer: 252
6 × 2 ones = 12 ones: write 2 ones and carry 1 ten. Then 6 × 4 tens plus 1 ten = 25 tens, giving 252.
3A-R-0463 points
Calculate 58 × 4 with place-value exchanges.
Reveal worked solution
Answer: 232
8 × 4 = 32 ones = 3 tens + 2 ones. 5 tens × 4 plus 3 tens = 23 tens = 232.
3A-R-0473 points
Calculate 67 × 8 and identify both exchanges.
Reveal worked solution
Answer: 536
8 × 7 ones = 56 ones, exchange 5 tens; 8 × 6 tens plus 5 tens = 53 tens, exchange 5 hundreds, yielding 536.
3A-R-0483 points
A factory packs 4 boxes with 213 buttons each. How many buttons altogether?
Reveal worked solution
Answer: 852
213 × 4 = (200 × 4) + (10 × 4) + (3 × 4) = 800 + 40 + 12 = 852.
3A-R-0493 points
Calculate 376 × 5; estimate first to check whether the result is reasonable.
Reveal worked solution
Answer: 1,880
376 × 5 = (300 + 70 + 6) × 5 = 1,500 + 350 + 30 = 1,880; roughly 400 × 5 = 2,000.
3A-R-0503 points
A theater has 6 sections, each with 128 seats. If 49 seats are empty, how many people are seated?
Reveal worked solution
Answer: 719 people
6 × 128 = 768 seats; 768 − 49 = 719 occupied seats.
3A-R-0513 points
Someone claims 46 × 7 = 282 by writing 6 × 7 = 42 as just 2 ones, then doing 4 × 7 = 28 tens. What exchange was omitted? Find the correct product.
Reveal worked solution
Answer: 322
The 4 tens carried from 42 ones must be added to 28 tens: 28 + 4 = 32 tens, so 46 × 7 = 322.
CHAPTER 6
Division
9 questions · 25 points · attempt before revealing explanations.
3A-R-0522 points
Calculate 840 ÷ 4 by interpreting the hundreds and tens.
Reveal worked solution
Answer: 210
840 is 84 tens. 84 tens ÷ 4 = 21 tens = 210.
3A-R-0532 points
Calculate 64 ÷ 2 using equal tens and ones.
Reveal worked solution
Answer: 32
Split 6 tens into 3 tens for each group, and 4 ones into 2 ones each: 32.
3A-R-0543 points
Calculate 74 ÷ 2. Explain how regrouping a leftover ten works.
Reveal worked solution
Answer: 37
Give each group 3 tens, leaving 1 ten; exchange that for 10 ones and combine with 4 ones. 14 ones ÷ 2 = 7 each, so 37.
3A-R-0552 points
Divide 96 apples equally into 4 crates. How many apples per crate?
Reveal worked solution
Answer: 24 apples
96 ÷ 4 = 24; check 4 × 24 = 96.
3A-R-0563 points
Calculate 438 ÷ 2. Explain how many hundreds each group receives.
Reveal worked solution
Answer: 219
4 hundreds ÷ 2 = 2 hundreds per group, then 3 tens leave 1 ten to exchange; result 219.
3A-R-0573 points
Calculate 684 ÷ 4, showing the place values of each quotient digit.
Reveal worked solution
Answer: 171
6 hundreds ÷ 4 gives 1 hundred and 2 hundreds left; exchange to get 28 tens, giving 7 tens, then 4 ones ÷ 4 gives 1 one. Quotient 171.
3A-R-0583 points
Calculate 336 ÷ 4. Why does the quotient have two digits rather than three?
Reveal worked solution
Answer: 84
3 hundreds cannot make 4 full groups of 1 hundred, so exchange them into tens. 33 tens ÷ 4 gives 8 tens and 1 ten left, then 16 ones ÷ 4 = 4 ones. Quotient 84.
3A-R-0593 points
A school has 285 pencils. It places 5 pencils in each packet. How many packets can be made?
Reveal worked solution
Answer: 57 packets
285 ÷ 5 = 57; check 57 × 5 = 285.
3A-R-0674 points
Five packages each contain 124 cards. The cards are then shared equally among four classes. How many does each class get?
Reveal worked solution
Answer: 155 cards
5 × 124 = 620 cards, and 620 ÷ 4 = 155 cards per class.
CHAPTER 7
Graphs & Tables
6 questions · 13 points · attempt before revealing explanations.
3A-R-0602 points
The bar graph shows books borrowed by four classes. Which class borrowed the most?
| Oak | 10 |
|---|---|
| Pine | 14 |
| Cedar | 18 |
| Maple | 12 |
Reveal worked solution
Answer: Cedar
Cedar has a bar reaching 18, taller than Oak 10, Pine 14, and Maple 12.
3A-R-0612 points
Using the same graph, how many more books did Cedar borrow than Oak?
| Oak | 10 |
|---|---|
| Pine | 14 |
| Cedar | 18 |
| Maple | 12 |
Reveal worked solution
Answer: 8 books
Cedar borrowed 18 and Oak borrowed 10: 18 − 10 = 8.
3A-R-0622 points
The table shows recycled cans by day. How many were recycled Monday through Wednesday altogether?
| Category | Cans |
|---|---|
| Monday | 18 |
| Tuesday | 24 |
| Wednesday | 15 |
| Thursday | 21 |
Reveal worked solution
Answer: 57 cans
18 + 24 + 15 = 57.
3A-R-0632 points
From the same table, which day was exactly 6 cans higher than Wednesday?
| Category | Cans |
|---|---|
| Monday | 18 |
| Tuesday | 24 |
| Wednesday | 15 |
| Thursday | 21 |
Reveal worked solution
Answer: Thursday
Wednesday 15; Monday 18 (3 higher), Tuesday 24 (9 higher), Thursday 21 (6 higher). Correct day is Thursday.
3A-R-0642 points
A picture graph uses one star to represent 5 votes. One team has 4 stars. How many votes did it earn?
Reveal worked solution
Answer: 20 votes
4 symbols × 5 votes per symbol = 20. A picture graph key is part of the data.
3A-R-0653 points
Two bar graphs display the same survey data. One vertical axis begins at 0; the other begins at 10. Could the pictures make the same difference look different? Explain.
Reveal worked solution
Answer: Yes
Truncating the axis at 10 can exaggerate the visual difference; check axis labels and numerical scale before comparing bars.