Semester 4A — Practice Examination

Write 56,091 in words and expanded form. State the value of the 6. Show your work and briefly explain or check your reasoning.

Calculate 596,785 + 48,679, showing two place-value exchanges and a reasonable estimate. Show your work and briefly explain or check your reasoning.

Write four positive multiples of 18 greater than 50, and decide whether 0 is a multiple of 18. Show your work and briefly explain or check your reasoning.

Calculate 18 × 45 mentally using a distributive decomposition and a second doubling/halving method. Explain why both methods preserve the product.

Compute 864 ÷ 8 using friendly multiples. Verify that (864 × 2) ÷ (8 × 2) has the same quotient, and explain why.

Write two fractions equivalent to 5/8, and justify one with a partition model. Show your work and briefly explain or check your reasoning.

Compute 11/12 − 5/12 and express the result in simplest form. Show your work and briefly explain or check your reasoning.

Find 1/8 of 96 stickers. Describe the eight equal groups. Show your work and briefly explain or check your reasoning.

Read the line graph. What is the total increase in water collected from Tuesday to Friday? Show your work and briefly explain or check your reasoning.

Write 806,050 in expanded form. How many hundred-thousands are represented in 1,000,000? Show your work and briefly explain or check your reasoning.

Calculate 600,004 − 258,677. Check using addition. Show your work and briefly explain or check your reasoning.

Find the least positive common multiple of 9 and 15. Explain your method. Show your work and briefly explain or check your reasoning.

Write the place-value partial products for 312 × 3 and combine them. Show your work and briefly explain or check your reasoning.

A student estimates 3,237 ÷ 8 as about 40. Explain why that is unreasonable, then give a better estimate and calculate the quotient with remainder. Show your work and briefly explain or check your reasoning.

A student says 5/8 is greatest because 8 is the largest denominator. Explain the error, order 5/8, 3/4, and 2/3 from greatest to least, and locate them on a number line from 0 to 1.

A student calculates 5/8 − 1/4 = 4/4 by subtracting numerators and denominators. Explain the error and calculate correctly. Show your work and briefly explain or check your reasoning.

Calculate 5 × 2/7. Explain its repeated-addition meaning. Show your work and briefly explain or check your reasoning.

Draw a line graph for temperatures at 9 a.m., 10 a.m., 11 a.m., noon: 16°C, 18°C, 22°C, 20°C. Give a title, labeled axes and a consistent vertical scale.

Continue 84,600; 85,200; 85,800; __; __. Explain the change at each step. Show your work and briefly explain or check your reasoning.

Find 68,997 + 5,608 using an adjusted addend; explain why your adjustment works. Show your work and briefly explain or check your reasoning.

Write all positive factors of 42 and organize them into factor pairs. Show your work and briefly explain or check your reasoning.

Compute 698 × 7 and explain why the result is near 4,900. Show your work and briefly explain or check your reasoning.

Compute 5,742 ÷ 6 and verify using multiplication. Show your work and briefly explain or check your reasoning.

Convert 17/6 to a mixed number and explain what the remainder tells you. Show your work and briefly explain or check your reasoning.

Calculate 4 5/6 + 1/3 in simplest form. Show your work and briefly explain or check your reasoning.

Calculate 8 × 3/10 and simplify the answer. Show your work and briefly explain or check your reasoning.

Construct a labeled line plot for pages read by seven students: 4, 6, 6, 6, 8, 8, 10. State the total number of observations and the most common value.

Order 702,400; 720,040; 702,040; 719,999 from greatest to least. Show their approximate locations on an evenly scaled number line from 700,000 to 730,000, explaining the first differing place.

Use counting up or equal adjustment to calculate 73,004 − 39,997. Show your work and briefly explain or check your reasoning.

Is 51 prime? Decide, showing a nontrivial factor pair. Classify 0 and 1 as prime, composite, or neither, explaining why.

Calculate 68 × 40. Explain the factor of ten. Show your work and briefly explain or check your reasoning.

A museum has 1,174 brochures and places 8 in each packet. How many complete packets can it make, and how many brochures remain? Show your work and briefly explain or check your reasoning.

Convert 38/12 to a mixed number in simplest form. Show your work and briefly explain or check your reasoning.

Calculate 3 2/5 + 1 7/10 with all intermediate conversions. Show your work and briefly explain or check your reasoning.

There are 72 books. Five-eighths are novels. How many are novels? Show your work and briefly explain or check your reasoning.

Read the line plot. Find the range of the observations and the number of observations.

Round 43,650 independently to the nearest ten and the nearest thousand (start with the original number each time). Show your work and briefly explain or check your reasoning.

A charity raised $18,450, spent $7,895 on supplies and received another $2,650. How much money does it have now? Show your work and briefly explain or check your reasoning.

Find the greatest common factor of 30 and 45. Use it to explain how many identical packs can be made from 30 pencils and 45 erasers without leftovers. Show your work and briefly explain or check your reasoning.

Use a 2×2 area model to calculate 47 × 32. Label the four products. Show your work and briefly explain or check your reasoning.

A charity has 2,350 notebooks. It packs 7 in each complete bag and sets aside leftovers. Afterward it receives 15 more notebooks. How many complete bags were made originally and how many notebooks are outside the bags afterward? Show your work and briefly explain or check your reasoning.

Convert 5 2/9 to an improper fraction and justify the result. Show your work and briefly explain or check your reasoning.

Calculate 7 1/6 − 5/6 in simplest form. Show your work and briefly explain or check your reasoning.

Find 45 × 2/5 by partitioning first and scaling second. Show your work and briefly explain or check your reasoning.

Round 749,950 independently to the nearest thousand and nearest hundred thousand. Show your work and briefly explain or check your reasoning.

A warehouse held 40,005 cartons, shipped 18,999, then received 7,495 more. How many are there now? Show your work and briefly explain or check your reasoning.

What is the smallest positive number divisible by both 12 and 18? Explain using multiples or factors. Show your work and briefly explain or check your reasoning.

A student writes 79 × 56 = 474 + 395, treating the 5 as five ones. Identify the mistake, show the correct tens partial product, and connect a four-part area model with a written multiplication calculation.

There are 2,510 stickers packed in packets of 6. How many complete packets can be made, and how many stickers remain? Show your work and briefly explain or check your reasoning.

Five identical sandwiches are shared equally among three children. Express each share as an improper fraction and a mixed number. Show your work and briefly explain or check your reasoning.

Calculate 8 1/4 − 3 7/8 and explain why a whole must be renamed. Show your work and briefly explain or check your reasoning.

Compute 48 × 7/8 using two valid orders of operations. Show your work and briefly explain or check your reasoning.

Calculate 72,000 ÷ 1,000 and 45 × 10,000. Explain why neither operation changes the order of the nonzero digits. Show your work and briefly explain or check your reasoning.

A garden has 37 rows of 28 seedlings. Find the total using two different decompositions. Show your work and briefly explain or check your reasoning.

A student says 13/4 represents exactly 3 wholes. Explain and give the mixed number. Show your work and briefly explain or check your reasoning.

Calculate 4 1/6 + 2 3/4 and simplify. Show your work and briefly explain or check your reasoning.

A club has 96 tickets. Three-eighths are sold in the morning. How many tickets are sold in the morning? Show your work and briefly explain or check your reasoning.

A town counted 598,499 people. Round independently to the nearest thousand and nearest ten thousand. Explain both. Show your work and briefly explain or check your reasoning.

A gardener picks 144 flowers, gives 1/3 to neighbors, and sells 3/4 of the remainder. How many flowers are left? Explain why selling 3/4 of the original 144 would be a mistake. Show your work and briefly explain or check your reasoning.

A school orders 180 markers. Three-fifths are given to students. Of what remains, one-half is stored. How many are neither given away nor stored? Show your work and briefly explain or check your reasoning.