The challenge is based on the Working Mathematically content of the NSW BOS Mathematics Syllabus, vol 1.
Whole number (G)
Week 1
Question one
Draw a picture which represents the following square numbers
a. 1
b. 4
c. 9
d. 36
Draw a picture which represents the following triangle numbers
e. 1
f. 3
g. 6
h. 15
i. 28
Question two
Square Numbers
In the multiplication square above can you:
- Can you locate the square numbers?
- Can you see a pattern?
- Can you continue the square number pattern through to 15? (eg. 13 x 13 =?) Record your number sentences and answers.
Triangle numbers
In the multiplication square below, the first seven triangle numbers 1, 3, 6, 10, 15, 21, 28 have been identified.
- Can you see a pattern?
- Can you predict the positions of the next triangle numbers? Check to see if you're right.
- Can you explain why triangle numbers take up these positions in a multiplication square?
Time (E)
Week 2
Question one
With each question please show your working.
Download the bus timetable (PDF 235.4 KB)
a. We set out by bus at 09:45 on the 15th of September and travelled until we arrived at our destination at 22:20 on the 16th of September. How long did the bus journey take?
b. If there was a breakdown and it delayed the trip by 3 hrs and 26 mins, what time would you arrive at your destination?
Question two
You will find below the Sydney Bus Lines timetable for the Mosman to City & Milsons Point, Route 227, 228, 229,230,243,244,245,246,247,248,249.Public transport timetables reflect a 24hour time format, therefore, it is important that we can understand it.
Please note the stop names, are listed in bold, and the street they are located on is noted next to them.
Eg. Beauty Point, Pearl Bay Avenue. The name of the bus stop (where you get on and get off the bus, is named Beauty Point. It is located on Pearl Bay Avenue.
- What time can you catch the earliest bus? Please also note, the bus route number, and the bus stop name.
- What time can you catch the latest bus? Please also note, the bus route number, and the bus stop name.
- If you live on Avenue Road and needed to arrive in North Sydney by 07:30 what bus stop, time and bus route would you need to catch?
- How long would the journey take?
- You forgot to set your alarm and end up running 15 minutes late. What time does the next bus come? What time will you arrive in North Sydney?
- You have won 4 tickets to go to a secret 5SOS concert at Luna Park located at Milsons Point on Friday night. You have asked 3 of your friends to attend the concert with you. You have all decided to catch the bus to the concert which starts at 20:30. List latest times you can leave from each station: Mosman Wharf, Mosman Junction, Cremorne Jn Military Rd& Spofforth St, and Clifton Gardens.
- What will the friend catching the bus from Clifton Gardens have to do at Neutral Bay Jn Military& Wycombe Rds?
FRACTION (E)
WEEK 3
Question one
The graphic designers of the Woolworths catalogue have made a serious error on one of the pages of the latest catalogues.
Download the catalogue here (PDF 60 KB)
All the products in the page below have been advertised with
the incorrect price reductions. The items are on special, but they are all 1/3 of the price off!
You need to work out the normal price, and then work out 1/3 off the regular price!
Juliette is an artist who has four new artworks to frame. She has contacted a local
Art Framer with the perimeter of each painting to be framed.
The dimension of the artworks include painting 1 - fifty-eight centimeters by twenty-seven centimeters, painting 2 - one hundred and thirteen millimeters by two hundred and eighty-six millimeters, painting 3 – one hundred and thirty-eight centimeters by two hundred and eighty-two centimeters, and painting 4 – four hundred and eighty six centimetres by three hundred and sixteen centimetres. The type of wood Juliette has chosen for the four frames are, the same.
- Can you help the Art Framer, by working out the perimeter of each painting?
- To make Juliette's frames, what is the total length of wood measurement, the Art Framer will have to order?
Addition (H) and 3D space
Week 5
This week we see Charlotte, an Art Curator who works at the Art Gallery where Julliette's paintings will be exhibited. It is Charlotte's job to select where in the Art Gallery, artwork is hung. Julliette's 4 paintings (from last week's maths challenge), form a collection and will be exhibited on one wall in the Art Gallery. Charlotte has 4 different walls where the collection can be displayed.
The four wall options Charlotte has to choose from are, wall 1 - nine hundred and three millimetres by six hundred and sixty one millimetres, wall 2 – nine hundred and seventy two centimetres by three hundred and two centimetres, wall 3 – six hundred and ninety six millimetres by eight hundred and twenty six millimetres, and wall 4 – seven hundred and eighty four centimetres by five hundred and ninety seven centimetres.
Which wall will accommodate Juliette's collection?
- You need to work out the perimeter of each wall
- Draw a to scale (a scale must be included), a diagram justifying your answer.
- Remember: you will need your answers from last week's maths challenge to solve this question
3D Space T4Wk5_Student Worksheet S3 (pdf 141 KB)
If you would like to brush up on your 3D shapes visit this website: 3D Shapes - Refresher
Activity Two
You are required to create and record (sketch/photograph/video etc.), your own construction of a pyramid, prism, sphere and cone using a variety of materials eg. playdough, paper/ cardboard nets, connector cubes, found in your classroom.
Please attach your evidence and hand into your teacher.
Substraction (H)
Week 6
T4Wk6_Student Worksheet S3 (PDF 141KB)
Your mission:
You have to plan a food budget using $50. The food is to feed 1 person for one week.
Mission Rules:
You can work with another person. In life, we can live with other people and share the cost of food. If you do this, that means you have $100 to spend but remember you then have to budget to feed 2 people for a week.
You should buy healthy options.
- Think about buying "in bulk"
- You must use the attached Coles Supermarket catalog as your price reference.
- You cannot buy more than 2 of the same type of item
eg. 2 packets of Twisties, and 2 packets of Burger Rings = 4 packets of chips
1 packet of Twisties and 1 packet of Burger Rings = 2 packets of chips
You will be handed in to your teacher:
1. A draft itemised shopping list, with the prices noted; and
- You will need to show that you have added this up without a calculator (yes, it means showing your working!).
- Note and corrections that you may need to make. If you need to remove items off the list, please write and summary on this, and recalculate.
2. A final itemised shopping list, which is within your budget.
Multiplication (E) and Area (D)
Week 8
The above is a plan of Joe's wheat paddock. He needs to work out how much seed he needs to plant this coming season.
Download the image of Joe's Wheat Paddock in PDF form.
You need to work out the total area of the paddock, and then calculate how many bags of seed are needed per hectare. You must also consider rainfall or irrigation when planting a seed. The following table indicates how many bags of seed are needed for different conditions.
Poor Conditions (little/ no rainfall or no irrigation)
Average Conditions (good rainfall, no irrigation)
Perfect Conditions (good rainfall, with irrigation)
Bags of seed per ha
9 bags/ha
6 bags/ha
4 bags/ha
Cost of seed per 25Kg bag: $22 or $495 per tonne
Questions:
What is the total area of the paddock? Express in hectares
- How many bags of seed would Joe need if he were to plant for
- Poor conditions
- Average conditions
- Perfect conditions
- How much would it cost if Joe planned to plant for average conditions?
- Extension: Would it be more affordable to purchase the seed "by the bag" or "by the tonne"?
Division (C) and Volume and Capacity (D)
Week 8
You are a student at Pigpimples School of Witchcraft and Wizardry, and you have been given an assignment in your potions class.
Question 1:
You must formulate a magic potion which must have 6 different ingredients, and can only be 1800 milliliters in total. Unfortunately, if one of those ingredient portions equals 300 milliliters the potion will explode. If they use more than 6 ingredients or if their ingredients don't add to 1800 milliliters the potion will also explode.
Use the jug below to illustrate your ingredients and measurements. You must indicate an exact measurement of each ingredient. REMEMBER to add a scale to your measuring cup.
Question 2:
Your potion has been hailed a grand success, and the Potions Master, Professor Snapple wants to teach it to the first year Pigpimples students. The only problem is, the first year students are only allowed to handle potions quantities which equal 1000 millimeters or less. You must convert your current 1800millitre potion recipe into a 1000millitre potion recipe.