topic badge

12.03 Partitioning and ordering

Worksheet
Partitioning and ordering
1

Consider the number 327.

a

State the hundreds part.

b

State the tens part.

c

State the units part.

d

Hence, express 327 in expanded form.

2

Consider the number 8364.

a

State the thousands part.

b

State the hundreds part.

c

State the tens part.

d

State the units part.

e

Hence, express 8364 in expanded form.

3

Determine whether each of the following groups of coins is ordered from lowest to highest value:

a
b
c
d
e
f
Algorithms
4

To make \$1.35 using the fewest number of coins follow the steps below:

a

Select the coin with the highest value that goes into \$1.35 and then find the remaining amount by subtracting the value of the coin from \$1.35:

A
B
C
D
b

Select the coin with the highest value that goes into the answer from part (a) and then find the remaining amount by subtracting the value of the coin from the answer from part (a):

A
B
C
D
c

Select the coin with the highest value that goes into the answer from part (b) and find the remaining amount by subtracting the value of the coin from the answer from part (b):

A
B
C
D
d

Which coin is needed to make the final amount?

A
B
C
D
5

To make \$4.25 using the fewest number of coins follow the steps below:

a

Select the coin with the highest value that goes into \$4.25 and then find the remaining amount by subtracting the value of the coin from \$4.25:

A
B
C
D
b

Select the coin with the highest value that goes into the answer from part (a) and then find the remaining amount by subtracting the value of the coin from the answer from part (a):

A
B
C
D
c

Select the coin with the highest value that goes into the answer from part (b) and find the remaining amount by subtracting the value of the coin from the answer from part (b):

A
B
C
D
d

Which coin is needed to make the final amount?

A
B
C
D
6

Consider the given algorithm for arranging the following four coins in order:

  1. Find the coin with the lowest value.

  2. Place this coin in the first position.

  3. Repeat this process for the remaining coins.

a

Following the algorithm, state which coin should go in the first position.

b

State which coin should go in the second position.

c

Sort the four coins according to the algorithm.

7

Consider the given algorithm for arranging the following three-digit numbers from smallest to largest:705, \, 281, \, 106

  1. Order the numbers from the lowest to highest hundreds digit.

  2. Is there more than one number with the same hundreds digit?

    • If no - STOP

    • If yes - Order them from the lowest to highest tens digit.

  3. Is there more than one number with the same hundreds and tens digits?

    • If no - STOP

    • If yes - Order them from the lowest to highest units digit.

  4. STOP

a

List the hundreds digit of each number from smallest to largest.

b

Will the algorithm STOP at step 2?

c

Hence, put the numbers 705, \, 281 and 106 in order from smallest to largest.

8

Consider the given algorithm for arranging the following four-digit numbers from smallest to largest:4475, \, 6857, \, 1183

  1. Order the numbers from the lowest to highest thousands digit.

  2. Is there more than one number with the same thousands digit?

    • If no - STOP

    • If yes - Order them from the lowest to highest hundreds digit.

  3. Is there more than one number with the same thousands and hundreds digits?

    • If no - STOP

    • If yes - Order them from the lowest to highest tens digit.

  4. Is there more than one number with the same thousands, hundreds and tens digits?

    • If no - STOP

    • If yes - Order them from the lowest to highest units digit.

  5. STOP

a

List the thousands digit of each number from smallest to largest.

b

Will the algorithm STOP at step 2?

c

Hence, put the numbers 4475, \, 6857 and 1183 in order from smallest to largest.

9

Consider the given algorithm for arranging the following three-digit numbers from lowest to highest:532, \, 492, \, 454

  1. Order the numbers from the lowest to highest hundreds digit.

  2. Is there more than one number with the same hundreds digit?

    • If no - STOP

    • If yes - Order them from the lowest to highest tens digit.

  3. Is there more than one number with the same hundreds and tens digits?

    • If no - STOP

    • If yes - Order them from the lowest to highest units digit.

  4. STOP

a

List the hundreds digit of each number from lowest to highest.

b

List the tens digit of the two numbers with the same hundreds digit from lowest to highest.

c

Which step will the algorithm STOP at?

d

Hence, put the numbers 532, \, 492 and 454 in order from lowest to highest.

10

Consider the given algorithm for arranging the following four-digit numbers from lowest to highest:1352, \, 1190, \, 9278

  1. Order the numbers from the lowest to highest thousands digit.

  2. Is there more than one number with the same thousands digit?

    • If no - STOP

    • If yes - Order them from the lowest to highest hundreds digit.

  3. Is there more than one number with the same thousands and hundreds digits?

    • If no - STOP

    • If yes - Order them from the lowest to highest tens digit.

  4. Is there more than one number with the same thousands, hundreds and tens digits?

    • If no - STOP

    • If yes - Order them from the lowest to highest units digit.

  5. STOP

a

List the thousands digit of each number from lowest to highest.

b

Will the algorithm STOP at step 2?

c

List the hundreds digit of the two numbers with the same thousands digit from lowest to highest.

d

Will the algorithm STOP at step 3?

e

Hence, put the numbers 1352, \, 1190 and 9278 in order from lowest to highest.

Sign up to access Worksheet
Get full access to our content with a Mathspace account

What is Mathspace

About Mathspace