# Square numbers, square roots and Multo

Problem solving strategy board from Maths300

Over the last few weeks you have learned about the following concepts:

• numbers less than zero, called negative numbers
• factors
• multiples
• prime numbers (only two factors, one and themselves)
• Composite numbers (any number with more than two factors)
• Square numbers (numbers with an odd number of factors)
• Square root (the symbol over a number that indicates you calculate the number that is multiplied by itself to get the original number)

We played the game “Multo” which helped to consolidate your knowledge of number facts and made you think about which numbers were most frequently called (common multiples and not prime numbers greater than 7).

Remember you can access Mathsmate Skill Builder sheets at their website if you need help with your Mathsmate. You should also be accessing Mathletics to complete three activities each week. I have found that the Google Chrome or Mozilla Firefox browsers seem to access Mathletics from home better than Windows Explorer.

# Surface Area and Volume

Your homework this week is to take a photo of a rectangular prism in your home and label it with the measurements that will enable students to calculate the surface area and the volume of the prism. Some examples include a refrigerator, a freezer, a blanket box or a chest of drawers. What is the surface area of the freezer above? Remember you need to use all three measurements of height, width and depth and double for back and front, both sides and top and bottom. Please send your homework to brittgow(at)gmail(dot)com and don’t forget your Mathsmate for Friday!

# Interpreting Graphs

Graph created in Excel by Jakob Linke, Year 7

Learning Intention: This week you will continue to work with line graphs, bar charts, pie charts and scatter plots. Your learning intention is to understand how to describe various graphs in words. You need to be able to interpret the information given.

Success Criteria: You will be able to look at the scale, axes, labels and title of different graphs and be able to describe what they mean. You will be able to match a graph to it’s description and draw a sketch graph from a sentence. These are the activities planned:

1. Find a graph with data in a magazine or newspaper. Cut it out and paste it into your books. Look carefully at the title, axes, labels and scale. Write a few sentences describing what the graph shows.

2. “Which graph is which” worksheet. You will be given nine small graphs and have to match scenarios to the shape of the graph.

3. Maths300: Temperature Graphs. Match the average maximum and minimum temperatures to Australia’s capital cities.

5. Which kind of graph would best represent the following situations?

• Height of a plant growing over time?
• The various heights of different plants of the same species in a greenhouse, over time?
• Thousands of plants in a crop to determine which genotype was the fastest growing?
• Percentage of different species of plants in an area of forest?

6. “Purchasing pantyhose” and “Blood Bank” graphs

7. Go to the Melbourne Grand Prix map and note the speed and distance from the start as each car makes it’s way around the track. Draw a graph that shows distance from the starting line on the horizontal axis and speed on the vertical axis.

# Your choice

Today your task is to identify an area of difficulty – use your Mathsmate sheets or Mathletics activities – and write yourself a goal. For example, “Today I will work out how to simplify ratios” or “I need to practise converting fractions to percentages”. You can print out the Skill Builders from Mathsmate or use the corresponding activities on Mathletics to practise. Ten minutes before the bell, leave a comment below about your goal and what you achieved.

# Twelve days of Christmas in Maths!

The “Twelve days of Christmas” is a popular song, with some intriguing mathematics embedded in the lyrics.

1. How many gifts were given in total?
2. What was the total cost of the gifts?
3. If one gift was returned each day following Christmas, what day would it be when there be no gifts left?

Judy Anne Brown created this lesson plan in 1997 with some interesting explorations of Pascal’s triangle. Sol explained the mathematics of the problem in 2007 at “Wild About Math!” and another author wrote about the song and tetrahedral numbers at “The Math Less Travelled“. Create your own 12 days of Christmas image with free Christmas clip art from KidsLearnCentral.

# Plan your Dream Holiday!

Image source

Your task this week is to plan your dream holiday, including a schedule of places, times and dates, flights and activities as well as all the costs. You should present your work in a spreadsheet that includes meals, accommodation, flight costs, entry fees to attractions and spending money for souvenirs and gifts.

Questions to consider:

(1) Where are you travelling to? Do you need a visa and/or a passport?

(2) What dates and time of year do you plan to travel? What season will it be?

(3) Who is travelling? By yourself, with family or friends?

(4) How long will you be away for?

(5) What sort of accommodation would you like? Resort, caravan park, motel, hotel, camping? How much will it cost per night?

(6) What mode of transport will you use? Plane, car, boat, bus, train? How much will your tickets cost?

(7) How much money do you think you need each day for food? Breakfast, lunch, dinner and snacks.

(8) What attractions would you like visit while you are there? How much does it cost?

(9) What time is transport available and how much will a return ticket cost?

(10) How much spending money will you need to take per day?

# Clothing Combinations and Dinner Menus

Problem 1: Imagine you had three different pairs of pants in your wardrobe and four different tops. How many different combinations could you wear? How can you work it out for any number of articles of clothing? Now add two hats. How many outfits could you put together? To make the most out of your wardrobe (that is, most combinations) would you add another pair of pants, top or hat?

Problem 2: Three bus captains are to be chosen by putting 11 names in a hat – How many different combinations are possible?

Problem 3: At a buffet dinner, you have a choice of two soups (pumpkin or spring vegetable), four different main courses (chicken, lamb, beef or vegetarian) and three desserts (fruit salad, chocolate mousse or cheesecake). How many different combinations of three course meals could there be?

Problem 4: Your “combination” lock on your locker (really should be called a “permutation” lock, because the order of the numbers does matter!) has three numbers, each from zero to 39. What is the total number of possible lock combinations?

Problem 5: In a group of school students, 26 people barrack for Geelong and 32 like playing cricket. How many people might there be in the group? (You may like to use a Venn diagram or a table to help with this question. – Thanks to Peter Sullivan for this question).

Problem 6: At a party there were 50 people; 35 ate some of the fish, 30 ate some of the chicken dish and 5 ate nothing. Draw a diagram to show this information. Work out:

• what fraction of the people at the party ate only fish?
• what fraction of the people at the party ate only chicken?
• what fraction of the people at the party ate both fish and chicken?
• what fraction of the people at the party did not eat chicken?

More about Combinations and Permutations from Dr. Maths at the Maths Forum.

And even more about Combinations and Permutations from Maths is Fun!

Write a comment below to tell me the answer to the problem you liked best and tell me why you thought that was the most interesting problem.

# Assessment of Area and Perimeter

The assessment task for this unit of work is for you to draw the plans for a house, labelling the dimensions of each room and calculating the area of each room. The plans must be scale drawings, so you may like to have 1cm = 1m or 1:100. Your house should include at least two bedrooms, kitchen, lounge/living area, bathroom and laundry. Make sure you have allowances for door openings, wardrobes and hallways, if required. You can download an assessment rubric for this task at the Year 7 Wiki – Maths – Measurement Page.

# Circumference of a circle and Pi

Image Source

Today, 6/7G learnt about the ratio between the radius, diameter and circumference of a circle. We started with three lengths of string – 1m, 2m and 3m in length. Our task was to draw a circle, using half the length of the string as the radius of the circle, on the concrete with chalk. Then we used the string to measure how many times the string (diameter of the circle) went around the circumference.

Each group found that the circumference was ‘three and a bit’ times the diameter of the circle. More acurately, that ratio is ‘pi’ and is represented by the symbol below. Even thousands of years ago the Egyptians knew about this ratio, although they didn’t call it ‘pi’. The Babylonians, Indians, Greeks and Chinese mathematicians were fascinated by the irrational number, pi. You can read more about the magic of pi and Pi day. You may even like to celebrate Pi day next March (3rd month) 14th by making a ‘pi’ pie!

# Welcome to Technomaths

This is an aerial picture of Hawkesdale P12 College captured from Google Earth, showing the prerimeter of our school stadium. If you go to the ‘tools’ tab and click ‘ruler’ you can select ‘line’ or ‘path’ , which highlights and measures between points you mark. You can measure in centimeters, meters and kilometers. This shows that the roof area of the stadium measures 25 m wide and 30m long.

What is the perimeter of the stadium roof?

What is the area of the stadium roof?

Each square metre of roof area catches 1mm (1 cubic cm) of rainfall. So, to work out how much rain the stadium roof will catch you need to multiply the roof area by the monthly or annual rainfall. Using the new Bureau of Meterology “Climate Data Online” website you can find out the monthly and annual rainfall in Hawkesdale since 1884. Using the summary statistics for all years, leave me a comment about how much rain you would expect to collect this month or this year, showing your working.