Minds On
Creating expressions
Create an expression to represent the following mathematical relationships:
- one less than a number
- one more than a number
- double a number
- half of a number
- three more than double a number
- three less than double a number
- three more than half a number
- three less than half a number
Substitute the number 5 to check that your expression is correct. Record your responses digitally, orally or in print.
Press ‘Answer’ to reveal the answers to the problems.
Action
Patterns in integer relationships
Task 1
Find the pattern in the following chart.
Record your thinking by using the Pattern Chart in your notebook or in the following fillable and printable document.
Use your knowledge of addition to complete the columns.
Start at 3 each time, and add different values, from 4 to (5).
| Starting Number | Operation: addition () |
Add to | Result |
|---|---|---|---|
| 3 | 4 | 3 4 7 | |
| 3 | 3 | 3 3 6 | |
| 3 | 2 | 3 2 | |
| 3 | 1 | 3 1 | |
| 3 | 0 | 3 0 | |
| 3 | 1 | 3 ( 1) | |
| 3 | 2 | 3 ( 2) | |
| 3 | 3 | ||
| 3 | |||
| 3 |
Press the ‘Activity’ button to access Pattern Chart.
Now, complete the following fillable and printable Pattern Chart 2 document in your notebook or using another method of your choice.
For this chart, we will be starting at 1 and adding various values from 4 to (5).
| Starting Number |
Operation: addition () |
Add to | Result |
|---|---|---|---|
| 1 | 4 | 1 4 | |
| 1 | 3 | ||
| 1 | 2 | ||
| 1 | 1 | ||
| 1 | 0 | ||
| 1 | 1 | 1 ( 1) | |
| 1 | 2 | 1 ( 2) | |
| 1 | 3 | ||
| 1 | |||
| 1 | |||
Press the ‘Activity’ button to access Pattern Chart 2.
- What pattern do you notice? How did you use this pattern when you got past getting zero as a result?
- Create a rule or strategy that you can use for adding a positive number to a negative number.
Task 2
Examine the pattern in the following data.
Use your knowledge of addition and subtraction to find the results. Record your ideas digitally, orally or in print.
Start at 5, subtract values from 4 to ( 5).
Complete the Pattern Chart 3 in your notebook or using the following fillable and printable document.
| Starting Number |
Operation: subtraction ( ) |
Subtract | Result |
|---|---|---|---|
| 5 | 4 | 5 4 | |
| 5 | 3 | ||
| 5 | 2 | ||
| 5 | 1 | ||
| 5 | 0 | ||
| 5 | 1 | 5 − (−) 1 = + 6 | |
| 5 | 2 | 5 ( 2) | |
| 5 | 3 | ||
| 5 | 4 | ||
| 5 | 5 |
Press the ‘Activity’ button to access Pattern Chart 3.
Now, complete the following fillable and printable Pattern Chart 4 document in your notebook or using another method of your choice.
For this chart, we will be starting at 2 and subtracting various values from 4 to ( 5).
| Starting Number |
Operation: subtraction ( ) |
Subtract | Result |
|---|---|---|---|
| 2 | 4 | 2 4 | |
| 2 | 3 | ||
| 2 | 2 | ||
| 2 | 1 | ||
| 2 | 0 | ||
| 2 | 1 | 2 ( 1) | |
| 2 | 2 | 2 ( 2) | |
| 2 | 3 | ||
| 2 | |||
| 2 |
Press the ‘Activity’ button to access Pattern Chart 4.
- What pattern did you notice when you completed the results after the zero? How does this pattern compare to the patterns in Task 1?
- Create a rule or strategy that you can use for subtracting a negative number from a positive number.
- What pattern did you use to help you subtract a larger number from a smaller number?
Record your thinking digitally, orally or in print.
Task 3
- Place the following set of integers in order from smallest to largest.
2, 5, 20, 0, 125, 120, 120, 3, 1, 2, 5 - The temperature one morning was 6C. It rose 13 degrees by the end of the day. What was the high temperature? Record a number statement and the answer.
Press ‘Answer’ to reveal the answers to the problems.
- 125, 120, 5, 2, 1, 0, 2, 3, 5, 20, 120
- 6 13 +7. So, the high temperature by the end of the day was +7°C.
Consolidation
Who is the better golfer?
Two golfers are comparing their golf scores over and under par.
Each claims to be the better golfer.
Your task is to use your knowledge of integers and statistics to help make the decision of “Who is the better golfer?”
Note: All scores are relative to PAR on each hole. Therefore, 1 is one over par (bogey) and 1 is one under par (birdie).
Golfer B’s score on the 6th hole was the result of hitting his ball into the marsh.
Comparison to Par card:
| Hole | Golfer A | Golfer B |
|---|---|---|
| 1 | 0 | 1 |
| 2 | 1 | 1 |
| 3 | 2 | 0 |
| 4 | 3 | 1 |
| 5 | 1 | 1 |
| 6 | 2 | 8 |
| 7 | 3 | 2 |
| 8 | 0 | 1 |
| 9 | 1 | 2 |
| PAR ( / ) |
1. Who won the round? (low score wins) (Blank)
2. Who won the greatest number of holes? (Blank)
3. Using the information gathered, decide who you believe is the better player. Justify your choice.
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel...
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.