2. Develop a flow diagram for each of the following patterns (NOTE: only show three input numbers and their corresponding output numbers for each flow diagram)
a. Rashida’s vetkoek b. Felicity’s cold drinks
c. The squares in the building block pattern d. The rectangles in the building block pattern e. The circles in the building block pattern f. The height of Helen’s sunflower
g. The cost of a phone call on Shaheeda’s phone.
3. Compare your answers for Activity 3 with a partner.
Activity 4:
Electricity balance
Work alone
The Bantwana Bami ECD Centre buys pre-paid electricity units at the start of each month. Each day Shaheeda checks the balance to see if the Centre is using electricity according to the budget. One of the parents has drawn the following flow diagram to help Shaheeda know what the daily balance should be.
Notice in the flow diagram you must first multiply the day of the month by -30 (negative thirty) and then add your answer to 990. The day of the month ×-30 corresponds to the amount of electricity used. The 990 is the number of units we started with. It may seem clumsy to do it in this order but that is a limitation of the flow diagram.
Day of the month Expected balance 1
It is deliberately unusual! We do not want learners to believe that the values in all number patterns always increase in value. We use the context of topping up the electricity dispenser at the start of the months to watch how the units go down at a constant rate to give a negative gradient. Because the gradient is negative, the first operation in the flow diagram involves multiplying by a negative number.
Learners may be uncomfortable with this and may need some scaffolding. Don’t make a fuss of the negative number itself.
Use the context to help learners see the negative as a directional indicator – i.e. -30 because we have “used up”
30 units each day. How many units do we use in 3 days?
The answer is 90 and therefore we must subtract 90 from the amount we started with.
1. Use the flow diagram to calculate the balance on the first three days of the month.
2. What is the balance on the 10thday of the month?
3. On the 17thday of the month the teachers reads the actual balance on the meter and sees that the balance is 510. Has the Centre been using too much electricity or have they been saving? Explain your answer.
4. Compare the electricity flow diagram with the flow diagrams that you developed for the earlier patterns in Activity 3. Which of the earlier patterns is the electricity budget example most like? Explain.
5. Predict what the electricity budget pattern will look like in a table and on a graph.
Activity 5:
Comparing answers and predictions
Work in pairs
1. Compare your answers for Activity 4, especially your answers to Questions 4 and 5.
2. Make a table of values for the expected electricity unit balance.
3. In your journal draw a graph for the expected electricity unit balance for each day of the month. Did you join the points on your graph? Why?
4. Were you correct with your predictions regarding the properties of the table and graph? discuss
Stop and Think
Think about your work in this unit and answer the following questions:
1. List the four different ways that we have used to represent a pattern so far.
2. Identify as many “patterns within patterns” that you have observed. We will be summarising these in the next unit and it would be useful for you to think about this before we do so.
What have you learned?
Flow diagrams are another way of representing the relational relationship in numeric patterns. Flow diagrams “show” the relational rule quite clearly.
There are two different types of situations that we have studied in this module so far:
• Situations that can be described using a flow diagram with a single operator,
• Situations that can be described using a flow diagram with two operators.
The points on the graphs of the patterns that we have studied in this module so far can all be joined by a straight line.
The numbers in the numeric patterns that you have worked with so far can all be created by adding or subtracting the same number to the previous number.
Time needed 155 minutes
MODULE FOUR Unit Three: More number patterns
Journal Reflection
Think about what you have learned. Write down all your thoughts, ideas and questions about your learning in your journal. Use these questions to guide you:
a. What did you learn from this unit about flow diagrams?
b. Write down one or two questions that you still have about the similarities between tables, graphs, flow diagrams and rules.
c. How will you use what you learned about graphs in your every day life and work?
Self-assessment Checklist
Reflect on the outcomes that were set for this unit. Think about what you know, what you can do and how you can use what you have learned. Use the key in the table and tick the column next to each outcome to show how well you think you can do these things now.
I can:
Tick as follows: 4=Very well 3=Well 2=Fairly well 1=Not well. 4 3 2 1 1. Draw graphs to describe situations
2. Convert between different representations of a numeric pattern including: tables, graphs, flow diagrams and verbal descriptions of the rules
3. Answer questions about a situation based on the graphs, tables of values and/or verbal descriptions of the situation 4. Describe situations using graphs, tables, flow
diagrams and rules
5. Identify the common features of tables, graphs, flow diagrams and rules that describe similar situations.