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Unit 1 – Practice Problems
1
UNIT 1 – PRACTICE PROBLEMS
1. Use Base-10 blocks to represent the following numbers.
Number Picture Number of Base – 10 Blocks
a) 23 ____ flats + ______ rods + ______ units
b) 40 ____ flats + ______ rods + ______ units
c) 254 ____ flats + ______ rods + ______ units
d) 108 ____ flats + ______ rods + ______ units
e) 7 ____ flats + ______ rods + ______ units
f) 18 ____ flats + ______ rods + ______ units
g) 110 ____ flats + ______ rods + ______ units
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2. Represent the following quantities using the least amount of base blocks. Write the corresponding number
of ones, tens and hundreds used.
Given Quantity Picture of Regrouping Number of Base – 10 Blocks
a) 23 units
____ flats + ______ rods + ______ units
____ 100’s + _____ 10’s + ______ 1’s
b) 31 rods
____ flats + ______ rods + ______ units
____ 100’s + _____ 10’s + ______ 1’s
c) 14 rods + 21 units
____ flats + ______ rods + ______ units
____ 100’s + _____ 10’s + ______ 1’s
d) 28 rods + 30 units
____ flats + ______ rods + ______ units
____ 100’s + _____ 10’s + ______ 1’s
e) 3 flats + 16 rods +
13 units
____ flats + ______ rods + ______ units
____ 100’s + _____ 10’s + ______ 1’s
f) 2 flats + 8 rods +
64 units
____ flats + ______ rods + ______ units
____ 100’s + _____ 10’s + ______ 1’s
g) 234 units
____ flats + ______ rods + ______ units
____ 100’s + _____ 10’s + ______ 1’s
h) 2 flats + 30 rods +
22 units
____ flats + ______ rods + ______ units
____ 100’s + _____ 10’s + ______ 1’s
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3. Write the following numbers in expanded form, place value form (in a chart) and word name form.
a) 513
Expanded Form: __________________________________________
Place Value Form:
Word Name: ______________________________________________
b) 27
Expanded Form: __________________________________________
Place Value Form:
Word Name: ______________________________________________
c) 801
Expanded Form: __________________________________________
Place Value Form:
Word Name: ______________________________________________
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4. Write the following numbers in numerical form, expanded form and place value form (in a chart).
a) One hundred eighty-three
Number: __________________________________________
Expanded Form: __________________________________________
Place Value Form:
b) Four hundred thirty-two
Number: __________________________________________
Expanded Form: ________________________________________________
Place Value Form:
c) Nine hundred one
Number: __________________________________________
Expanded Form: __________________________________________
Place Value Form:
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5. Write the following numbers in place value form, numerical form, and word name form.
a) 600 + 30 + 5
Place Value Form:
Number: __________________________________________
Word Name: ______________________________________________
b) 700 + 40 + 0
Place Value Form:
Number: __________________________________________
Word Name: ______________________________________________
c) 100 + 20 + 5
Place Value Form:
Number: __________________________________________
Word Name: ______________________________________________
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6. Answer the problems below. Be sure to include sketches of your base block representations.
a) Represent 372 with base blocks.
b) What two flat numbers does 372 lie between? ____________________________
c) To what number of flats is 372 closest? ________________________________
d) What two rod numbers does 372 lie between? ________________________________
e) What number of rods is 372 closest? ________________________________
7. Answer the problems below. Be sure to include sketches of your base block representations.
a) Represent 237 with base blocks.
b) What two flat numbers does 237 lie between? ____________________________
c) To what number of flats is 237 closest? ________________________________
d) What two rod numbers does 237 lie between? ________________________________
e) What number of rods is 237 closest? ________________________________
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8. Round using the place value method.
a) Round 283 to the nearest hundred b) Round 352 to the nearest hundred
c) Round 106 to the nearest ten d) Round 349 to the nearest hundred
e) Round 52 to the nearest ten f) Round 819 to the nearest ten
g) Round 437 to the nearest hundred h) Round 86 to the nearest hundred
i) Round 182 to the nearest hundred j) Round 23 to the nearest hundred
k) Round 409 to the nearest ten l) Round 409 to the nearest hundred
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9. Melinda had three new pairs of shoes. She bought two more pairs of shoes. How many new pairs of shoes
does she have now?
10. Melinda had three new pairs of shoes. She bought some more pairs of shoes. Now she has five new pairs of
shoes. How many pairs of shoes did Melinda buy?
11. Melinda had some new pairs of shoes. She bought two more pairs of shoes. Now she has five new pairs of
shoes. How many new pairs of shoes did Melinda have before she bought some more?
12. Connie had five pens at the beginning of the semester. She lost two of the pens during the first week. How
many pens does Connie have left?
13. Connie had five pens at the beginning of the semester. She lost some of the pens during the first week. Now
she has three pens left. How many pens did Connie lose?
14. Connie had some pens at the beginning of the semester. She lost two of the pens during the first week. Now
she has three pens. How many pens did Connie have at the beginning of the semester?
15. There are four seniors and three juniors on the debate team. How many students are on the debate team?
16. There are seven students on the debate team. Four of the students are seniors and the rest are juniors. How
many juniors are on the debate team?
17. Paul and Ed are going to lunch. Paul has $10 and Ed has $8. How much more money does Paul have than
Ed?
18. Ed has $8. Paul has $2 more than Ed. How much money does Paul have?
19. Paul has $2 more than Ed. Paul has $10. How much does Ed have?
20. An instructor wanted to give 2 pencils to each student taking the final exam in the Introductory Algebra
class. There are 25 students in the class. How many pencils did the instructor need?
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21. Linda is taking her relatives on a hiking trip. She has 15 bottles of water that need to be placed into three
different coolers. How many bottles will Linda put into each cooler if she wants the same number of bottles
in each cooler?
22. A group of 30 incoming freshmen students is going to be divided into teams of five students to go on a
campus tour. How many teams are there?
23. Packages of markers cost 75 cents each. How many cents does 4 packages cost?
24. Mary Ellen spent $100 on four concert tickets. How much did each ticket cost?
25. Sara enrolled at a local college. She spent $640 dollars on tuition. Each credit hour costs $80. How many
credit hours will Sara be taking?
26. Ronna has to read 2 books for her fine arts class. She has to read 3 times as many for her English class.
How many books does Ronna have to read for her English class?
27. Sandy solved 12 word problems. This is 3 times as many as Nancy. How many word problems did Nancy
solve?
28. Sandy solved 12 word problems. Nancy solved 4 word problems. How many times greater is the number
of word problems Sandy solved compared with the number of word problems Nancy solved?
29. Leon has a rectangular dining room that is tiled. Leon counts 12 tiles along one wall and 10 tiles along an
adjacent wall. How many tiles cover the floor of the dining room?
30. There are 24 desks in the classroom. Lisa notices that there are 4 rows. How many desks are in each row?
31. Roberto has four shirts and three pairs of slacks packed for his vacation trip. How many different outfits
does Roberto have?
32. The local diner has 15 different ice cream sundaes consisting of one scoop of ice cream and a syrup. The
diner has five different ice cream flavors. How many different types of syrup does the diner offer?
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For 33 – 36: Round as indicated.
33. The Math Club raised $127 with their bake sale. Round this to the nearest ten.
34. Kevin earned $98 delivering pizza. Round this to the nearest ten.
35. The weekend trip cost $412 per person. Round to the nearest hundred.
36. There were 26,577 tickets sold for the football game. Round this to the nearest hundred.
37. Represent the following numbers with base blocks and order the numbers from least to greatest.
231, 321, 123, 132
38. Represent the following numbers with base blocks and order the numbers from least to greatest.
205, 52, 25, 205
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39. Order the numbers below from smallest to largest. Use the place value chart to organize your work.
231, 321, 123, 132, 213, 312
100’s 10’s 1’s
40. Order the numbers below from smallest to largest. Use the place value chart to organize your work.
57, 830, 208, 350, 83, 808, 698, 901
100’s 10’s 1’s
41. Sally has 97 stickers, Betty Lou has 88 stickers and Peggy Sue has 79 stickers. Who has the most? Who
has the least?
42. Cameron is comparing the sticker price of cars on the lot. The red Mustang costs $34,799. The orange
Camaro costs $35,500. The black Nissan 370Z costs $35,499. Which car costs the most? Which costs the
least?
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43. Place the numbers below in the place value chart. Use the chart to assist you in writing the word name for
the number.
a) 38,113
Word Name: ______________________________________________________
b) 7,108,090
Word Name: ________________________________________________________
c) 32,018,911,002
Word Name: ________________________________________________________
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44. The population of the United States is constantly changing. According the website www.worldometers.info
when I last checked, the population of the U.S. was listed as 323,352,941. Round this number to the nearest
thousand.
45. The national debt is also constantly changing. The website www.usdebtclock.org shows real time estimates
of the national debt. At one point, the estimate of the debt was $17,882,815,724,883. Round this number to
the nearest billion dollars.
46. Scientists don’t know exactly how many cells are in the human body, but they estimate that there are about
37,200,000,000,000 cells. What place value are they rounding to?
47. Place the number 413,163,092,107 in the place value chart below and answer the corresponding questions.
a) Determine the place value for the digit 6 and write what it represents as a word and a number.
b) Determine the digit in the ten thousand’s place and write what it represents as a word and a number.
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48. Complete the table below.
Problem Represent with Blocks Represent with Algorithm
a) 315 + 204
b) 503 − 328
49. Jorge earned 37 points on a quiz. He makes corrections for extra credit and earns 8 more points. What is
the total amount of points Jorge earned? Show all of your work and write your answer in a complete
sentence.
50. Lisa tweeted 19 times in January and 33 times in February. How many times did she tweet in total? Show
all of your work and write your answer in a complete sentence.
51. Vincent earns $80 on Monday and he earns $35 on Tuesday. How much total money does Vincent earn?
Show all of your work and write your answer in a complete sentence.
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52. On a road trip, Anna drove 420 miles on the first day and 380 miles on the second day. How many miles
did she drive in all? Show all of your work and write your answer in a complete sentence.
53. Katherine is 14 years younger than Joe. If Joe is 48 years old, how old is Katherine? Show all of your work,
and write your answer in a complete sentence.
54. Amy deposited $650 into her checking account one month and withdrew $220 to pay bills and expenses.
How much money does she have left over after paying her bills? Show all of your work, and write your
answer in a complete sentence.
55. It took Alice 45 minutes to drive to work this morning. On the way home, she ran into traffic and it took her
86 minutes. How much longer did the return trip take? Show all of your work, and write your answer in a
complete sentence.
56. The temperature was 77 oF and it drops 9 degrees. What is the new temperature? Show all of your work, and
write your answer in a complete sentence.
57. Tally sprinted 1000 meters in 210 seconds on her first try and in 187 seconds on her second try. How much
faster was her second try? Show all of your work, and write your answer in a complete sentence.
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58. Consider the multiplication problem 18 ∙ 27.
a) Draw the outline of the rectangle that represents the multiplication problem 18 ∙ 27 on the grid below.
b) Use base blocks to represent the area in the gridded rectangle. Determine the number of flats, rods and
units that make up the rectangle and simplify your results by regrouping. Write your final answer in
place value form.
Number of Base Blocks Regrouping of Base Blocks Product
Flats:_________
Rods:_________
Units:_________
Flats:_________
Rods:_________
Units:_________
Result: 18 ∙ 27 =
c) Represent this multiplication using the standard algorithm.
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59. Use base blocks to determine the 732 ÷ 4.
a) Represent 732 with base blocks.
b) Use the four bins below to show how you partitioned the base blocks into 4 equally sized groups.
Group 1 Group 2 Group 3 Group 4
Result: 732 ÷ 4 =
c) Find 732 ÷ 4 using the Standard Algorithm for division.
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60. Sean buys a package of 20 chocolate chip cookies from the bakery and wants to divide them equally to each
of the five members of his family. How many cookies will each person get?
a. Draw a picture to represent this situation.
b. How many cookies will each person get?
61. Amber buys a package of 18 eggs, and wants to make 3-egg omelets. How many 3-egg omelets can she
make?
a. Draw a picture to represent this situation
b. How many 3-egg omelets can she make?
62. Sara hiked uphill for 3 hours. Each hour, her elevation increased by 40 meters. Compute her change in
elevation in meters relative to her starting point. Show all of your work, and write your answer in a
complete sentence.
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63. A baby gained 8 ounces per month for 4 months. Find the baby's total change in weight relative to her
original weight. Show all of your work, and write your answer in a complete sentence.
64. Tally bought 20 packages of hot dog buns for her fair booth. Each package contained 9 buns. How many hot
dog buns is this in total? Show all of your work, and write your answer in a complete sentence.
65. Daphne paid $66 each month for one year for internet service. How much did she pay in total? Show all of
your work, and write your answer in a complete sentence.
66. Together, 6 friends have 30 dollars. If they share the money equally, how much does each friend get? Show
all of your work, and write your answer in a complete sentence.
67. Jorge bikes to school each day. If he can travel 36 miles in 4 hours, how fast does he travel in one hour?
Show all of your work, and write your answer in a complete sentence.
68. Yvonne bought a total of 880 t-shirts. If there were 8 t-shirts per package. How many packages did Yvonne
buy? Show all of your work, and write your answer in a complete sentence.
Unit 1 – Practice Problems
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69. Complete the table below
Symbolic Form Division Sign 18 ÷ 6
Symbolic Form Fraction
Divided by Language
Into Language
Copies of Language
Fraction Language
Dividend
Divisor
Quotient
70. Write the following in symbolic form, then evaluate.
a) The sum of twelve and six b) The product of twelve and six
b) The quotient of twelve and six d) Twelve minus six.
e) Twelve divided by 6 f) Six times twelve
g) Six less than twelve h) The difference between six and twelve
