Mango Shop

Mango Shop

For today's lesson, you may wish to use this worksheet.

I own a shop where I sell mangoes at $5. If I start the day with $3 in my tin, what is the relationship between the number of customers I have had and how much money is in my tin?

1. How would you approach the problem above in a systematic way?  

2. What are different ways you could present your findings?  You may wish to present your findings using Desmos or Geogebra.  

3. What if we now change to

• (a) start with $7, charge $3; 

• (b) start with $5, charge $4; 

• (c) start with $6, charge $4; 

• (d) start with $7, charge $4; 

• (e) start with $4, charge $3; 

4. How could you...

1. • Make a downward sloping graph? What does it mean?

   • Make a graph starting below the x-axis? What does it mean?

   • Make a graph that is between (a) and (d)?  Is it half-way between?  Why/ why not?

   • Make a horizontal graph? What does it mean?

   • Make a vertical graph? What does it mean? 

5. How does the starting amount and the cost per mango affect the graph? 

6. How does the cost affect the steepness? 

7. What about downward-sloping graphs?

Further Practice

Some of the essential skills introduced in this lesson are "plotting linear (straight line) graphs", "gradient", "y-intercept" and "y=mx+c".  You may also wish to look at "parallel lines", "perpendicular lines", "intersection of lines" etc.  The relevant skills can be found on DrFrostMaths, CorbettMaths, MyiMaths and Eedi.  Watch any video and/or go through any online lesson as you see fit.  

Desmos

• Put the Point on the Line - place points on an imaginary line, the activity, then estimate and calculate the slope.

• Match My Line - can you match my line?

• Land the Plane - can you land the plane?

• Marble slides: Lines - transform lines so that the marbles go through the stars.

• Lego Prices - use sliders to explore the relationship between price and number of pieces for various Star Wars LEGO sets and to make several predictions based on that model. No, not all points will land on the straight line in real life!

• Parallel Lines - explore connections between equations of parallel lines in slope-intercept form.

• Polygraphs: Lines - can you describe these lines to each other using the most accurate mathematical language?

• Card Sort: Linear Functions - can you put the cards in groups of three. Why might you have grouped the cards in a particular way?

• Two Truths and a Lie: Lines - can you create a line and write two true and one false statement about it?

Transum

• Plotting Graphs - practise plotting a graph given the equation.

• Equation of a Straight Line - do this online exercise about the equation y=mx+c and the features of a straight line graph.

• Gradient of a Line - practise the skill of finding the gradients of straight lines from their graphs.

• Graph Match - practise matching the graphs with their equations or descriptions. A self-marking, drag-and-drop mathematical

• Equation of a Line Through Points - practise matching the equations of the straight line graphs to the clues about gradients and points.

• Straight Line Graphs - here is a video and a challenge to get you to reproduce the images given using your graph plotting software.

• Parallel Graphs - group the equations that are parallel to each other.

• Perpendicular Matching - play this game to match perpendicular lines. 

Extension

nRich

To further investigate about parallel and straight line graphs, try these activities on nRich.

Don Steward

Here are some more challenging ones by Don Steward.