Adding and subtracting fractions

Image is a screenshot from the Cool Math 4 Kids site.

When adding or subtracting fractions the first thing you need to do is make sure that the denominators (bottom numbers) are the same. If all the denominators are the same you can simply add or subtract the numerators (top numbers) and then simplify the answer if required. If the denominators are different, you need to find a common multiple and convert both fractions, so that the denominators are the same. Activities 4 and 5 below show how this is done:

1. Adding Fractions from Cool Maths 4 Kids.

2. Three simple steps to adding fractions from “Maths is Fun”.

3. BBC Bitesize – fractions activities – Choose the fractions activities from BBC Bitesize (Equivalent fractions and ordering and comparing fractions).

4. Adding fractions with different denominators from “Maths Playground”.

5. Adding fractions with different denominators from YouTube – Maths Made Simple Series.

Equivalent fractions

Learning intention: Students will be able to identify and name equivalent fractions (halves, thirds, quarters, fifths and sixths) and describe how they are calculated.

Success criteria: Students will successfully identify equivalent fractions on their fraction walls and name equivalent fractions on a number line.

Maths Playground – Visual fractions (the visuals are good, but the program doesn’t always allow the right answer?)

Maths is Fun – Equivalent fractions

Maths Games – Matching equivalent fractions

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.

Multiples, Factors and Primes

Image Source

Learning Intention: Students will understand what Multiples, Factors and Prime Numbers are and why they are useful.

Success criteria: Students will be able to recognise multiples, factors and prime numbers and calculate the Highest Common Factors (HCF) and Lowest Common Multiples (LCM) of given numbers.

Substitution in Algebra

Learning Intention: Students will understand that substitution into formulae is a valuable mathematical process that is useful in many real-life situations.

Success Criteria: Students will work through a series of substitution exercises and identify useful formula for converting units of measurement (eg. Celcius to Fahrenheit; ounces to grams; miles to kilometers; calories to kilojoules). Students will use the formulae to calculate the height of a person knowing the length of their femur bone.

Forensic scientists are responsible for piecing together information about crimes, such as identifying victims and perpetrators from DNA evidence, fingerprints and bones. One formula that scientists use is to calculate the height of a person(h) from the length of their thigh bone – called a femur(f) in centimeters. The formula is as follows:

height = 69.09 + 2.24 x femur OR h = 69.09 + 2.24f

Walking along the beach, your dog retrieves a human thigh bone! It is 45cm long. How tall was the person this bone belonged to?

A fellow blogger, Malyn Mawby, has written a great post about how she used the Vitruvian Man to teach a lesson incorporating ratio, percentages and algebra. Do your body parts match the ratio of the Vitruvian Man?

Use the Internet to research at least five of the following and give an example of each.

1. Calories to kilojoules
2. Miles to kilometers
3. Celcius to Fahrenheit
4. Ounces (oz) to grams
5. Pounds (lbs) to kilograms
6. Acres to hectares
7. Inches to centimeters
8. Australian dollars to British sterling
9. Feet to metres
10. Time in Hawkesdale to time in Greenwich, UK.

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.