Cumulative semester review

Write 6,407 in words.

In 8,353, what is the value of the second 3 (reading left to right)?

Write 5,090 as a sum of thousands, hundreds, tens, and ones.

How many hundreds equal 3,200? Explain your grouping.

Order these from least to greatest: 7,205; 7,025; 7,250; 7,052.

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?

Continue the pattern for two more terms: 5,875; 5,625; 5,375; __; __.

Round 6,521 to the nearest thousand.

Round 4,349 to the nearest hundred.

Round 8,765 to the nearest ten.

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.

Give a four-digit number that rounds to 3,500 to the nearest hundred and 4,000 to the nearest thousand; justify your example.

Find 438 + 250 by splitting 250 into hundreds and tens.

Compute 598 + 167 using compensation; show why the adjusted sum must be corrected.

Find 763 − 240 mentally; record useful jumps.

Use equal adjustment to calculate 803 − 298. Show both adjusted numbers.

What must be added to 674 to make 1,000?

Without using column addition, calculate 397 + 205.

Two teams together earned 94 points. One scored 18 more than the other. Find both scores and describe a bar model.

A museum counted 1,248 visitors over the weekend. If 375 came on Saturday, how many visited on Sunday?

Maya has 235 beads. She has 47 fewer than Niko. How many beads does Niko have?

A library had 1,420 books. It received 235 more, then lent out 189. How many remain?

Two students calculate 702 − 299. One writes 703 − 300. The other writes 702 − 300 and adds 1. Are both valid? Find the answer.

Ava has 36 more stickers than Ben. Ava gives Ben 8. Who has more afterward, and by how many?

Calculate 2,768 + 1,457. Show at least one place-value exchange.

Calculate 4,503 − 1,278. Show why borrowing is required.

Solve 6,000 − 2,487 and explain how you regroup across zeros.

Estimate 3,462 + 2,153 by rounding each addend to the nearest hundred.

Estimate 6,187 − 2,741 by rounding to the nearest thousand, then calculate the exact difference.

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.

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.

Which is more reasonable for 2,908 + 3,096: 5,000 or 6,000? Justify before finding the exact sum.

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.

Draw or describe an array showing 7 rows of 4 dots. How many dots are there?

Use the distributive property to find 9 × 7 by splitting 7 into 5 and 2.

Thirty-six pencils are shared equally among 6 boxes. How many pencils go in each box?

Explain why 0 ÷ 7 = 0 but 7 ÷ 0 is not defined.

Forty-seven counters are packed in bags of 6. How many full bags and how many counters left over?

Without adding individually, decide whether the sum of five odd whole numbers is odd or even. Explain.

There are 8 tables with 6 chairs at each. How many chairs are there?

Jules has four times as many marbles as Kai. Kai has 9. Describe the equal-unit bar model and find Jules’s number.

A baker makes 9 trays with 8 rolls each. She packs the rolls into bags of 5. How many full bags and loose rolls?

Thirty-eight children need seats in vans that each hold 8. How many vans are needed? Explain why the remainder matters.

Find 7 × 300 using hundreds, not repeated counting.

Calculate 23 × 3 using (20 + 3) × 3.

Calculate 42 × 6; show what happens when 4 tens × 6 = 24 tens.

Calculate 58 × 4 with place-value exchanges.

Calculate 67 × 8 and identify both exchanges.

A factory packs 4 boxes with 213 buttons each. How many buttons altogether?

Calculate 376 × 5; estimate first to check whether the result is reasonable.

A theater has 6 sections, each with 128 seats. If 49 seats are empty, how many people are seated?

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.

Calculate 840 ÷ 4 by interpreting the hundreds and tens.

Calculate 64 ÷ 2 using equal tens and ones.

Calculate 74 ÷ 2. Explain how regrouping a leftover ten works.

Divide 96 apples equally into 4 crates. How many apples per crate?

Calculate 438 ÷ 2. Explain how many hundreds each group receives.

Calculate 684 ÷ 4, showing the place values of each quotient digit.

Calculate 336 ÷ 4. Why does the quotient have two digits rather than three?

A school has 285 pencils. It places 5 pencils in each packet. How many packets can be made?

Five packages each contain 124 cards. The cards are then shared equally among four classes. How many does each class get?

The bar graph shows books borrowed by four classes. Which class borrowed the most?

Using the same graph, how many more books did Cedar borrow than Oak?

The table shows recycled cans by day. How many were recycled Monday through Wednesday altogether?

From the same table, which day was exactly 6 cans higher than Wednesday?

A picture graph uses one star to represent 5 votes. One team has 4 stars. How many votes did it earn?

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.