Semester 4A — Cumulative Review

Write 73,408 in words and expanded form. Explain what the 7 means.

Explain how ten groups of 100,000 compare with one million. Write 1,000,000 − 100,000.

Continue 26,750; 26,500; 26,250; __; __. State the rule.

Order 405,090; 450,009; 405,900; 449,999 from least to greatest. Explain the first differing place, then show their approximate positions on a number line from 400,000 to 500,000.

Round 67,450 to the nearest hundred and to the nearest thousand. Why are the answers different?

Round 685,500 to the nearest ten thousand and nearest hundred thousand (separately).

Find 36 × 1,000 and 48,000 ÷ 100. Explain each place-value change.

A stadium records 695,480 visitors. Round independently to the nearest 1,000 and 100,000, then explain why the two estimates differ.

A child says “Adding one thousand always changes only the thousands digit.” Explain why this is false using 99,500.

Add 487,659 + 75,884. Show one regrouping and check by estimation.

Subtract 402,006 − 178,589. Explain how you regroup across zeros.

Use compensation to find 39,998 + 7,456 without long column addition.

Find 50,002 − 29,998 by adding the same number to both quantities.

A library had 7,650 books. It received 875 and donated 1,240. How many books remain? Give a bar-model or equation explanation.

A store sold 12,750 items in June, 9,865 in July, and 14,390 in August. How many more did it sell in August than July, and what was its three-month total?

A student claims 70,000−39,999 = 30,001 because it is the same as 70,000−40,000+1. Is the claim valid?

List the first five positive multiples of 14 and explain why 0 is also a multiple of 14.

Find the least positive common multiple of 8 and 12. Show two lists.

List all positive factors of 36 by writing factor pairs.

Classify 0, 1, 2, 21, and 29 as prime, composite, or neither. Explain each exception.

Find the greatest common factor of 24 and 40 and explain how it relates to equal-size grouping.

Find the least positive common multiple of 6 and 10, then the greatest common factor of 6 and 10. Explain why they differ.

A student says 1 is prime because it cannot be divided equally by any number except 1. What has been overlooked?

Compute 25 × 36 mentally in two ways: using the distributive property and using doubling/halving. Explain why the two methods agree.

Use partial products to calculate 212 × 4 without regrouping.

Compute 487 × 6 with regrouping and check the approximate size.

Calculate 47 × 30 by interpreting 30 as 3 tens.

Use four partial products to calculate 34 × 26.

Calculate 68 × 47 using a four-part area model and then a written partial-product algorithm. Explain how the two match; check with an estimate.

A rectangular tile design has 24 rows of 35 tiles. Find the total using a split model.

Explain why 46×20 is ten times 46×2, without saying “add a zero.”

Divide 936 ÷ 6 using convenient partial quotients. Then calculate (936 × 2) ÷ (6 × 2) and explain why both quotients are equal.

Estimate 2,848 ÷ 7 using compatible numbers. Then calculate the exact quotient.

Calculate 4,368 ÷ 7 and check by multiplication.

There are 1,258 crayons packed in boxes holding 9 each. How many full boxes can be filled and how many crayons remain?

A school has 1,245 tickets to share equally among 6 classes. Each class receives the same whole number; what remains? Then the school receives 23 additional tickets. How many tickets are not yet shared?

A school has 3,205 pencils to distribute in bundles of 8. How many full bundles and what remainder?

Explain why 4,080 ÷ 8 cannot be 51 using an inverse check.

Show why 3/4 and 9/12 represent equal parts of the same whole.

Order 2/3, 5/6, and 3/4 from smallest to largest. Mark their approximate positions on a number line from 0 to 1.

Express 13/5 as a mixed number and represent its full wholes and leftover fifths.

Convert 29/8 to simplest mixed-number form.

Convert 4 3/7 to an improper fraction and explain the numerator.

Three pizzas are shared equally by four students. What fraction of a pizza does each receive?

A ribbon is 3 1/4 meters long. Write the length as an improper fraction and in fourths.

A student says 3/5 > 3/4 because 5 > 4. Explain the error using equal-sized wholes.

Compute 7/10 + 8/10. Simplify the result and explain the unit being counted.

Calculate 2/3 + 1/6 using sixths.

Compute 2 3/4 + 1/2. Rename the fractional sum if necessary.

Compute 1 5/6 + 2 3/4; show a common denominator.

Compute 5 1/4 − 3/4 by regrouping one whole.

Compute 6 1/3 − 2 5/6 with a clearly shown exchange.

A recipe uses 1 3/4 cups of oats and 2 5/8 cups of flour. How much is that altogether?

A student adds 1/2 and 1/3 and writes 2/5. Explain what has gone wrong and calculate the correct sum.

Find 1/7 of 63 counters and explain why division represents one equal share.

Calculate 4 × 3/8 as repeated addition and simplify.

Compute 6 × 5/9. Explain how to simplify the improper result.

A jar has 40 beads. Three-fifths are green. How many beads are green?

Find 24 × 3/4 as three-quarters of a whole-number quantity.

Compute 36 × 5/6 two ways and show why the results agree.

A farm harvests 84 apples and sells 5/7 of them. How many apples are sold? Show a unit bar.

A baker has 120 rolls. She gives 1/4 away, then sells 2/3 of what remains. How many rolls are left?

A class has 120 pencils. Two-fifths are blue. Of the rest, one-third are green. How many are neither blue nor green?

A child claims that 3/4 of 32 is 32×4÷3. Explain and correct the error.

The graph shows library visitors on four days. How many more visited on Thursday than Monday?

Draw a line graph of plant height: Week 1 = 8 cm, Week 2 = 12 cm, Week 3 = 11 cm, Week 4 = 15 cm. Label both axes and choose a sensible scale.

Draw a line plot for seven reading times (minutes): 10, 15, 15, 20, 20, 20, 25. Label the units, then tell how many students read at least 20 minutes.

Read the line graph showing results over four equal days. What is the overall change from the first to last day? Does it increase every day?

A student draws a line graph with equal time intervals spaced unevenly on the horizontal axis. What should be changed?