Part A: Introduction to word formulas
assignment 1Ordering photos at two websites
Take a really good look at the websites on page 1, before you answer the questions. When you order photos on the internet, you have to pay:
- A price per photo
- A price for sending the package by mail
Put a circle around these prices on both of the websites, so you can find them back easily!
a)How much do you have to pay for 10 photos of size 6 by 4 inches at Fotoinsight?
______
And at Fastlab? ______
b)Fill in the table:
c)Which website is cheaper for 5 photos? ______
d)Which website is cheaper for 25 photos? ______
e)For how many photos does it not matter which website you choose? ______
f)a.For how many photos is Fastlab cheaper? more / less than ______
b.And for how many is Fotoinsight cheaper? more / less than ______
g)Are 20 photos exactly 2 x as expensive as 10 photos? Why or why not?
______
h)Explain in your own words how you calculate the price of 60 photos at Fotoinsight:
______
i)
If you want to tell how you calculate the price of the photos in general, you can make a word formula. A word formula is like a recipe for cooking a meal, it tells you exactly what you have to do.
j)What is the word fomula for Fastlab?
______
k)Explain in your own words how you can make a word formula for any website, when you know the costs per photo and the costs per package?
______
Part B: Making linear formulas with arrows
assignment 2Getting to know the applet “Algebra Arrows”
In this assignment you are going to work with the program Algebra Arrows.
It helps you to make formulas. The computer can calculate the table and show the graph for you, so you do not have to spend a lot of time on calculating and drawing.
First example
The first example is about a painterscompany. You have to pay the company for a job:
- € 25 for each hour the painter works,
- € 30 once, for coming to your house
a)
The price of the job depends on the number of hours the painter works.
Make an arrow string with the applet Algebra Arrows, which starts with a white box hours.
Instructions:
- Drag the boxes to the working-space (White blocks for start and end, yellow blocks for calculations)
- Click on the boxes to type numbers and words in the boxes.
- Connect the boxes with the arrows (an arrow starts at the small triangle on the right of a box)
Connect the last arrow. In the last box appears the formula!
Write this formula down:
______
b)Explore what you can do with the applet. Take your time for this!
Make sure that you know:
- How to make a Table, how to change a table and how you can walk up and down through the table.
- How to draw a Graph, how to change a graph and how you can move the table in the window. (You have to connect the formula to the graph)
c)
Be careful with Clear! It is not clever to clear your work each time you have finished an assignment. Oftenly you can use your work again, by changing some numbers and words.
When you still have your drawing of question a, you can change it into:
without adding any new box. How did you do this?
______
Now you know enough to use the applet Algebra Arrows to work with formulas!
assignment 3Startnumber and Slope
When you open a savingsaccount you often get a free Startamount, in this example € 20. When you put € 15 in the account each month, the amount increases (goes up and up) equally. (We leave out the interest (NL: rente) in this example)
We are going to make the formula for this account with Algebra Arrows.
a)Calculate the savings-amounts for the first three months.
These are: ____, _____, _____
Make an arrow string, starting with:
You add the start-amount of € 20 at the end of the calculation.
Write down the formula that appears in the last white box: ______
b)Open the table. Move the list of months and the list of amounts next to each other. You now have a good view on which amount belongs to which month.
The savings-amount goes up with the same month-amount each month.
Put a circle around this month-amount in your formula of question a.
Where can you find the month-amount in the table?
______
Where can you find the start-amount in the table?
______
c)You can find the month-amount and start-amount in the graphtoo.
In this graph you can find the month-amount as one of the sides of the small triangle. Give this side a colour.
d)
Draw a line with the right height above 0 to point out the start-amount. (Use another color)
e)Take a look at the graph again and complete the following sentences:
The startnumber is called STARTnumber, because
______
______
The slope is called HELLING in Dutch, because
______
______
assignment 4From graph to formula and table
In the last assignment you have seen how you can find the startnumber and slope of the formula in the table and graph. This will help you with the next two problems.
a)This graph was drawn with Algebra Arrows. At 5 days the line goes trough 100.
Make this graph yourself, you have to choose the right startnumber and slopefirst!
b)How do you find the startnumber in the graph?
______
______
How do you find the slope?
______
What is the formula for these numbers?
______
What could this graph be about? Make your own story!:
______
c)
In this table you find the length of a candle after it has been burning a couple of hours. You have to find the formula that belongs to the table.
You can do this by using strings of arrows, like you used in assignment 2. This is really possible!
Try to make such an arrow string. If you can’t find the right string, you may read the text below:
Write down your formula: ______
Draw the graph. What is the big difference between this graph and the graphs you have seen in the other assignments? ______
Summary linear formulas
You made linear formulas with arrow strings. The computer made the table and graph for you.
Linear formulas consist of arrow strings with a white start-box, two calculation-boxes and a white end-box:
a)Write down the name of the number you have to put in each box in its balloon. Use the words that you have learnt in the 3 assignments.
b)Tables that belong to linear formulas have a special property. You see three tables on the right. One of them is not from a linear formula. Which one is that?
______
c)In one of the other tables it is easy to find the slope. With the other one, you have to be careful.
Write down the slopes of these two tables. How did you find them?
table:______slope:______how:______
table:______slope:______how:______
d)Above the first colums of the tables are not words, but letters. We do this to make the formulas shorter. Give the formulas of the two tables of question c:
______
e)Summarize in your own words what a linear formula looks like and how you can find the startnumber and the slope.
______
f)Why do you think that these formulas are called linear?
______
Test yourself
Do the following exercises from Numbers and Space. When you have finished them, check your answers. If you did not understand a question, you have to read the theory and practice some more exercises.
D-toets 7 theory par 6.3 (dl2), exercises 50, 51, her 9
D-toets 8 theory par 6.4 (dl1), exercises 54, 55, her 10
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