New Zealand
Level 6 - NCEA Level 1

# Solve problems using an algorithm

Lesson

Here is another algorithm - this time a little more complex:

Algorithm Steps Example
Think of any two numbers from $1$1 to $9$9. $3$3 and $5$5
Make two $2$2-digit numbers by putting them in either order. $53$53 and $35$35
Subtract the smaller number from the larger number. $53-35=18$5335=18
Divide the result by $9$9. $18\div9=2$18÷​9=2
Finally, add the smaller starting number. $2+3=5$2+3=5

In the example, we chose the numbers $3$3 and $5$5 to start with. In the last step of the algorithm, we added the smaller of these numbers, $3$3, and got a result which was the larger number, $5$5.

Does this always happen? Try it yourself with two different numbers!

#### Worked Examples

##### Question 1

We are going to add these two numbers together, using the addition algorithm below:

$37+46$37+46

 1 Add the units. 2 Is the result at least $10$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$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.
1. Which two numbers will be added in step 1?

$7$7$\text{and}$and$6$6

A

$3$3$\text{and}$and$4$4

B

$7$7$\text{and}$and$6$6

A

$3$3$\text{and}$and$4$4

B
2. Complete step 1: Add the units.

3. What do we need to do at step 2?

GO TO step 3.

A

First regroup into tens and units, then GO TO step 3.

B

GO TO step 3.

A

First regroup into tens and units, then GO TO step 3.

B
4. Regroup $13$13 into tens and units:

$13=\editable{}+\editable{}$13=+

5. Now complete step 3: Add the tens.

6. What do we need to do at step 4?

GO TO step 5.

A

First regroup into hundreds and tens, then GO TO step 5.

B

GO TO step 5.

A

First regroup into hundreds and tens, then GO TO step 5.

B
7. Complete step 5: Write the final answer by adding the hundreds, tens and units.

##### Question 2

We are going to add these two numbers together, using the addition algorithm below:

$89+65$89+65

 1 Add the units. 2 Is the result at least $10$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$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.
1. Complete step 1: Add the units.

2. What do we need to do at step 2?

GO TO step 3.

A

First regroup into tens and units, then GO TO step 3.

B

GO TO step 3.

A

First regroup into tens and units, then GO TO step 3.

B
3. Regroup $14$14 into tens and units:

$14=\editable{}+\editable{}$14=+

4. Now complete step 3: Add the tens.

5. What do we need to do at step 4?

GO TO step 5.

A

First regroup into hundreds and tens, then GO TO step 5.

B

GO TO step 5.

A

First regroup into hundreds and tens, then GO TO step 5.

B
6. Regroup $150$150 into hundreds and tens:

$150=\editable{}+\editable{}$150=+

7. Now complete step 5: Write the final answer by adding the hundreds, tens and units.

##### Question 3

We are going to subtract these two numbers, using the subtraction algorithm below:

$91-26$9126

 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.
1. Fill in the blanks below:

The units digit of the first number is $\editable{}$.

The units digit of the second number is $\editable{}$.

2. What do we need to do at step 1?

GO TO step 2.

A

Regroup the tens part of $91$91, then GO TO step 2.

B

GO TO step 2.

A

Regroup the tens part of $91$91, then GO TO step 2.

B
3. Fill in the blanks below:

We can regroup the tens part of $91$91 as $90=\editable{}+10$90=+10, in order to give $10$10 to the units part, which will become $1+10=\editable{}$1+10=.

4. Complete step 2: Subtract the units of the second number from the units of the first number.

5. Complete step 3: Subtract the tens of the second number from the remaining tens of the first number.

6. Complete step 4: Write the final answer by adding the results of steps 2 and 3.