Hey teacher – there’s letters in my Maths!


Learning Intention: Students should understand that pronumerals represent variable numbers in expressions and equations. They will also understand what “like” and “unlike” terms are and some of the simple algebraic conventions that mathematicians use.

Success Criteria: You will complete a series of tasks, including identifying like and unlike terms and simplifying expressions.

This week we will continue our introduction to algebra. You have already done lots of algebra without knowing it – recognizing and continuing number patterns, finding the missing angle or number and substituting values into equations.

A = the number of letters in your first name (Britt = 5)
B = the number of letters in your family name (Gow = 3)

What does A + B = ? (Britt Gow = 8) See if you can find someone in the class with the same answer as you. Did you both have the same equation?

Now see if you can make A and B equal your age. I am 46 years old, so
8A + 2B = 46. Are there other ways you can make the answer equal your age?

How could you make A and B equal today’s date? Can you make A and B equal your birthdate (day of the month you were born).

Some more algebra for beginners:

Shape times Shape is an activity where you discover which shapes represent which numbers, using a series of multiplication problems.

BBC Bitesize has an introduction to algebra using formulae.

Maths is Fun also has an introduction to algebra which includes a brief explanation with some examples.

Students then need to be able to recognise like and unlike terms. There are some more practise questions at MCA Online: Like and Unlike TermsAlgebra for Children is another site that may assist you to work with like and unlike terms.

Later in the term we will access some more difficult problems:

As each of you have netbooks to use at school and at home, you may like to access the National Library of Virtual Manipulatives site, which has a great range of interactive tasks for year 6 to 8 Algebra. I like the “Coin Problem”;“Factor Tree” and “Function Machine”.

This virtual manipulative from the National  Library, Algebra Scales, helps you to solve equations using a balance scales. This one is a little more difficult, Algebra Scales using negative numbers. Remember to do the same thing to both sides of the equation.

Monday 22nd October

Learning Intention: You will consolidate your understanding of how to calculate the volume of three dimensional prisms.

Success Criteria: By completing the set exercises you will demonstrate your understanding of how to calculate the volume of prisms.

James, Emily, Liam and Jeremy  – please work on page 344 “Discover – Volume and capacity”.

All other students are to work on page 346 “Explore – Volume and capacity”.

Fencing a paddock


Learning Intention: Students will understand the difference between area and perimeter and that if you double the area of a paddock, you do not necessarily double the perimeter.

Success Criteria: Using a fixed quantity of fencing, students will model different areas of paddock. With a fixed area of paddock, students will find different perimeters.

A farmer has 3.6 kilometres of fencing. Convert to metres and design five different paddocks using all the fencing. Calculate the area of each paddock. Which has the greatest area?

A farmer needs a paddock of 2400 metres square. Design four different paddocks with this area. What is the perimeter of each of these paddocks?

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!

 

Length, Area and Volume


Learning Intention: Students will understand the similarities and differences between types of measurement – length, area and volume.

Success Criteria: You will be able to measure and calculate length, area and volume of squares, rectangles, triangles and their prisms. You will create a Venn diagram to compare length, area and volume.

For the first 60 seconds of class list all the units of measurement you can think of.

Last term we learnt about measuring the perimeter and area of two dimensional shapes. With the pre-service teacher, Mrs Bos, we measured the perimeter and area of the playgrounds in the school.
This term we will start by looking at three dimensional shapes – cubes, rectangular and triangular prisms. If you look at the shape of your text book, you will see it has six surfaces – three pairs of rectangles with the same area. There are three measurements you need – length, width and depth. Calculate the surface area of this rectangular prism using these three measurements. Now calculate the volume of your textbook using these three measurements – length x width x depth.

Learning Intentions for this unit

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1. Classify triangles according to their side and angle properties and describe quadrilaterals.

2. Establish the formulas for areas of triangles, rectangles and parallelograms and use these in problem solving.

3. Demonstrate that the angle sum of a triangle is 180 degrees and use this to find the angle sum of a quadrilateral.

Tripods, tricycles and triceratops!

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Learning Intention: To learn to work independently and improve student understanding of angles and triangles, specifically how they are classified.

Success criteria: You will complete all of the activities listed below before next Wednesday.

Sorry I am not at school today – you probably heard my voice failing due to a sore throat this week! While most of our class are at the MWC Winter Sports today (good luck footballers and netballers!) you have a few choices:

1. Page 236 from “Oxford Big Ideas 7″ – Classifying triangles.

2. Mathsmate (Term 3, week 3) due tomorrow

3. Mathletics – I have set three new activities for each student about angles and triangles.

4. Go to the National Library of Virtual Manipulatives and choose “Congruent Triangles”. You need to use the sides and angles to create two triangles that look the same.

Angles Assessment

Building in Perth (author’s photo)

1. Can you find an acute, right, obtuse, straight and reflex angle in the image above?

2. Fold an A4 sheet of paper into six sections. In each section draw one of the following angles, estimate it’s size and then measure it. Make sure you label each drawing.

(a) obtuse

(b) right

(c) acute

(d) reflex

(e) complementary angles

(f) supplementary angles

 

 

Measuring Angles, triangles by side length and angle size.

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Learning Intention: You will understand that angles are measured in degrees and be able to name and identify different types of angles and triangles. You will be able to use a protractor effectively and be able to estimate angle sizes.

Success Criteria: You will be able to estimate, draw, measure and identify angles measured in degrees. You will be able to identify, name and draw triangles by side length and by angle size.

This term we will start by measuring angles, using a “rotogram” and then a protractor. You will all need your geometry kit this semester – compass, sharp grey lead pencil, protractor and a good ruler.

What are acute, right, obtuse, straight and reflex angles?
What are equilateral, isosceles and scalene triangles?
What are acute, right and obtuse triangles?
Can you have an equilateral right angled triangle or an obtuse equilateral triangle?
Can you have an obtuse isosceles triangle or a right-angled isosceles triangle?

Task 1: Work in a group of three. Each person should draw and cut out six copies of an equilateral, isosceles or scalene triangle, using different coloured paper. Share your shapes so that each person in the group has two of each type of triangle. Now, tear off the corners of one of each type of triangle and match up the corners to demonstrate the sum of the angles in a triangle.

Task 2: Do the same for acute, obtuse and right angled triangles. Do you think the sum of the angles in a triangle will always be the same? Can you explain why? Do you think the same would be true for quadrilaterals, pentagons and hexagons etc?

The Maths Masters have written a very interesting article in The Age about the triangles in Federation Square.
Read more