Topics
11. Coding and Algorithms
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CanadaON
Grade 8

11.01 Solve problems using an algorithm

Lesson
Worksheet
Practice
Worksheet
Solve problems using an algorithm
1

Below is an algorithm for adding two 2-digit numbers together:

  1. Add the units.

  2. If the result in step 1 is at least 10, regroup into tens and units.

  3. Add the tens, including any from step 2.

  4. Write the final answer by adding the units to the result of step 3.

a

If we use the algorithm to add 41 and 38, state what will happen at:

i

Step 1

ii

Step 2

iii

Step 3

b

If we use the algorithm to add 38 and 27, state what will happen at:

i

Step 1

ii

Step 2

iii

Step 3

2

Consider the addition algorithm below:

  1. Add the units.

  2. Is the result at least 10?

    • If no - GO TO Step 3.

    • If yes - regroup into tens and units, then GO TO Step 3.

  3. Add the tens.

  4. Is the result at least 100?

    • If no - GO TO Step 5.

    • If yes - regroup into hundreds and tens, then GO TO Step 5.

  5. Add the hundreds.

  6. Is the result at least 1000?

    • If no - GO TO Step 7.

    • If yes - regroup into thousands and hundreds, then GO TO Step 7.

  7. Write the final answer by adding the thousands, hundreds, tens and units.

a

If we use the algorithm to calculate 343 + 415, state what will happen at:

i

Step 2

ii

Step 4

iii

Step 6

iv

Step 7

b

If we use the algorithm to calculate 428 + 367, state what will happen at:

i

Step 2

ii

Step 4

iii

Step 6

iv

Step 7

3

Consider the addition algorithm below:

  1. Add the units.

  2. Is the result at least 10?

    • If no - GO TO Step 3.

    • If yes - regroup into tens and units, then GO TO Step 3.

  3. Add the tens.

  4. Is the result at least 100?

    • If no - GO TO Step 5.

    • If yes - regroup into hundreds and tens, then GO TO Step 5.

  5. Write the final answer by adding the hundreds, tens and units.

a

If we use the algorithm to calculate 43 + 56:

i

What two numbers will be added in step 1?

ii

What do we need to do at step 2?

iii

What do we need to do at step 4?

iv

Write the final answer.

b

If we use the algorithm to calculate 37 + 46:

i

What two numbers will be added in step 1?

ii

What do we need to do at step 2?

iii

What do we need to do at step 4?

iv

Write the final answer.

c

If we use the algorithm to calculate 62 + 93:

i

What two numbers will be added in step 1?

ii

What do we need to do at step 2?

iii

What do we need to do at step 4?

iv

Write the final answer.

d

If we use the algorithm to calculate 89 + 65:

i

What do we need to do at step 2?

ii

What do we need to do at step 4?

iii

Write the final answer.

4

Consider the subtraction algorithm below:

  1. Is the units digit of the first number less than the units digit of the second number?

    • If no - GO TO Step 2.

    • If yes - regroup the tens from the first number to give a ten to the units, then GO TO step 2.

  2. Subtract the units of the second number from the units of the first number.

  3. Subtract the tens of the second number from the remaining tens of the first number.

  4. Write the final answer by adding the results of steps 2 and 3.

a

If we use the algorithm to calculate 97 - 36:

i

What do we need to do at Step 1?

ii

What is the result from Step 2?

iii

What is the result from Step 3?

iv

Write the final answer.

b

If we use the algorithm to calculate 91 - 26:

i

What do we need to do at Step 1?

ii

What is the result from Step 2?

iii

What is the result from Step 3?

iv

Write the final answer.

5

Consider the multiplication algorithm below:

  1. Split the first number into tens and units.

  2. Multiply the second number by the units of the first number.

  3. Multiply the second number by the tens of the first number.

  4. Add the results of step 2 and step 3.

a

If we use the algorithm to calculate 35 \times 6, state the result of:

i

Step 1

ii

Step 2

iii

Step 3

iv

Step 4

b

If we use the algorithm to calculate 12 \times 82, state the result of:

i

Step 1

ii

Step 2

iii

Step 3

iv

Step 4

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Outcomes

8.C3.1

Solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves the analysis of data in order to inform and communicate decisions.

8.C3.2

Read and alter existing code involving the analysis of data in order to inform and communicate decisions, and describe how changes to the code affect the outcomes and the efficiency of the code.

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