Pango+2012

We are learning to solve multiplication and division problems that involve fractions.

The garden club decide to plant 3/4 of a planter box with carrots. The planter box is 4m x 5m.

You need to make two 4m x 5m garden boxes, use your squares to make your scale.

Cut out 3/4 of one of your garden boxes.

The garden club decide that they no longer want to plant that many carrots, so they decide that they will only plant 4/5 of the 3/4 of garden.

You now need to divide the 3/4 garden into fifths and cut out 4/5.

Let's compare the carrot patch to the whole garden. What fraction of the garden is a carrot patch? 3/4 x 4/5= 3/5

Find the equivalent decimal: 6/8 8/24 19/100 1/8 18/27

What do we do if we're multiplying straight fractions?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5/6 x 4/7= 20/42 = 10/21

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">What do you notice about this equation?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Solve these problems <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">2/8 x 3/4= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">1/2 x 3/4= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">4/9 x 11/12

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Find the equivalent fraction: <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">1.5 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">0.7 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">0.02 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">0.25

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">What do we do if we need to multiply a whole number by a fraction?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Mrs Carter was given some left over party food by the garden club. The cakes were already cut and she was given 4/9 of 12 cakes. What is our equation?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">12 x 4/9= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">How could we solve this? <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">What would a good estimate be?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">12/1 x 4/9=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;"> Mrs Carter was also given some left over spinach muffins. There were 14 packs of muffins. They were in packs of 12. Each pack was 2/3 full. How many muffins was Mrs Carter given?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">We are learning to solve difficult ratio problems.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Ratios show a multiplicative relationship between two quantities of the same measure. For example, 2:7 might mean 2 litres of blueberry to 7 litres of orange to make a fruit juice. This would make a total of 9 litres. <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">It could also mean 2 cups of blueberry to 7 cups of orange which would make 9 cups of fruit juice.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Let's solve this problem together. You will need to consider equivalent fractions and percentages to solve this.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">You get an after school job at the juice factory. Here are three mixtures of orange and mango juice. Which mixture will taste most strongly of orange?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Recipe A: 3 litres orange:5 litres mango <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Recipe B: 4 litres orange:7 litres mango <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Recipe C: 5 litres orange:8 litres mango

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Let's look at the tables and graphs below, what do they tell us? <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Let's use excel to solve these problems... <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Mixture A: <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">3:5 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5:6 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">4:9

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Mixture B: <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">4:6 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">3:4 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">3:7

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Mixture C: <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">6:12 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">7:8 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5:8

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Practice: Figure out which ratio of blue:yellow gives the darkest green, use the excel sheet to solve the first two problems.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">A: 4:2 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">B: 7:4 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">C: 6:12

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Which ratio of blue:red gives the darkest purple?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">A: 3:7 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">B: 2:5 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">C: 4:12

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Which ratio of blue:white gives the darkest blue?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">A: 7:9

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">B: 5:7

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">C: 2:3

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">We are learning to <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;"> solve simple equations of the form ax = b and use ratios to solve problems.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">The 'Beanie' problem... <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">It takes 8 balls of wool to make 2 beanies. How many balls of wool would you need to make 9 beanies?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Can you find four different methods to solve this problem? <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Method 1: Using multiplication.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Method 2: Using a table.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Method 3: Using multiplication and even numbers... <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">9= 8+1 <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">8= 4x2

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Method 4: Ratio. <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">//New number of balls// :8= 9:2

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Today our Beanie problem is a bit harder...

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">It takes 4 balls of wool to make 7 beanies. How many balls of wool would it take to make 19 beanies?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Can we use the same strategies to solve this problem? <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Which strategy do you prefer?

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 200%;">Rectangular tables are joined together for banquets as in the following diagram of 3 tables.



How many people can sit around a row of 9 tables?

How many tables would be needed for a party of 30 people?

A giant street party has 49 tables in a row. How many people can sit round this?

My street has 258 people living in it. How long would the row of tables need to be?

Make a table showing the number of people versus the number of tables. How will you label your table?

What pattern do you notice? Can you explain the formula?

We are going to draw a graph that shows the number of people versus the number of tables for up to 10 tables. What type of graph do you think will be the most appropriate? Why? What do we need to remember about this drawing this type of graph? How will you label your graph?

Matchsticks are used to make a pattern of cubes as in the following diagram.



Use matches to represent 1 cube, 2 cubes, etc up to 5 cubes.

Make a table showing the number of matches versus the number of cubes. Draw a graph showing the number of matches versus the number of squares for up to 10 cubes. Use your graph to find how many matches are used for 7 cubes. Use your graph to find how many cubes could be made with 49 matches.

What is the relationship between the number of matches and the number of cubes? Write your rule as an equation.

Julie has written m = 9 + 5(x-1), Alan has written m = 3x + 4 +5x, Joy has written 9x – 4(x-1) and Jenna has written m = 4 + 5x. Who is correct?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Write down a number on a piece of paper and turn the paper over. <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;"> Multiple your number by 5. <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;"> Divide the result by 5.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">What’s the effect of multiplying a number by 4 and then dividing by 4? <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;"> Does this always happen no matter what the number?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Does this happen for all numbers?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">What if we use a number that is a small integer (less than 20), a large integer, a decimal, or a fraction.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">5y = 17 <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">leads to 5y/5 = 17/5, <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">and so y = 17/5 =

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">If Joan had five times her bus money she’d have $15. How much is her bus money?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">How can we solve this problem using 3 completely different strategies?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Use two strategies to solve this problem, one strategy must be an algebraic startegy.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Mrs Tansely raised $210 to buy each member of her hockey team a T-shirt with the teams name on it. The hockey team has three reserves. How much was each shirt?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Jan had enough money to buy herself and three friends a giant bouncy ball each. If she spent $14, how much did each giant bouncy ball cost? (All giant bouncy balls were the same price.)

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">WALT: use scale factors to investigate areas and volumes being enlarged.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">**If you take any 2D shape, and enlarge it by a scale factor of //f//, by what scale factor has it been enlarged by**?

<span style="color: #7900ff; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">A 'dilation' refers to a shape that has been enlarged. Solve these problems about dilations.


 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">If you take any 3D object, and enlarge it by a scale factor of //f,// by what scale factor has the surface area and volume been enlarged? **

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Problem... <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Draw two different sized squares. The larger square must have double the area of the smaller square.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">//How did you know what dimensions to use for the base and height of your two squares?//

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Take a square and enlarge it using scale factor of 's'. **<span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 200%;">The scale factor for area **<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;"> is found by **<span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 200%;">squaring the scale factor for length **<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">. Thus the scale factor for area is s2.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">If this is reversed, a method is provided for solving the problem being investigated. The scale factor for area is 2. **<span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 200%;">The scale factor for length **<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;"> is found by **<span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 200%;">taking the square root of 2 **<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">. Thus the scale factor for length is √2.


 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Construct two squares on scrap paper that have an area of 25cm <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%; vertical-align: super;">2 <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">.
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Fold and cut these squares along the diagonal lines so that you have a total of 8 triangles.
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">Use all of these triangles to make a single square.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">//What is the area for the larger square?// <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">//What is the length of the larger square? Why?// <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">//How is this connected to our original problem from this morning?//

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">//Could we do something similar by starting with 4 individual squares?// <span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;">//What if we started with 3 squares?//

<span style="font-family: 'Comic Sans MS',cursive; font-size: 200%;"> Follow up activity...

Draw a small poster that shows two different sized balls (soccer balls or netballs, for instance). The larger ball needs to have double the volume of the smaller ball.

Explain how advertising agents could fool us, using diagrams such as these, into gaining the wrong impression from a picture used in an advertisement. Construct and draw an advertisement for some product or service that illustrates how scale factors can be used to mislead.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Take a look at these hands. By what scale factor do you think they have been enlarged by? <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">We can consider this by thinking if it took one jar of paint to paint my hand, how many jars should you need to paint the other hands? <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Will it be the same scale factor for enlargement?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">How can we solve such a difficult problem?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">How should a difficult problem such as our original one be approached?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">How can we simplify this problem?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Square?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Triangle?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Construct a circle with a radius of 4cm. <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">What is the area of this circle? <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">If we enlarge the radius by a scale factor of 2, how will the area of the circle be affected? <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Can you explain why? <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Construct the circle and check.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">We are going to divide our original circle into 16 sectors, to create a rectangle. Can you figure out the area of this new shape?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">What would happen if we double the amount of sectors? Can we use our second circle to check?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">If you take any 3D object, and enlarge it by a scale factor of //f,// by what scale factor has the surface area and volume been enlarged?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;"> Will the surface area of this ball be **twice** that of the smaller one?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">We need to clarify what scale factor is in relation to the volume of a cuboid or a sphere. <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;"> Use cubes to explain your ideas about how the surface area and volume are affected when enlarged by a scale factor of //f.//

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">ONE MINUTE TETRAHEDRON CHALLENGE <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">You have one minute and 8 tetrahedrons to enlarge the original tetrahedron by a scale factor of 2.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">WALT: apply Pythagoras Theorem.



<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Give these problems a try.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">WALT: do simple division by a whole number with tenths in the answer.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5.2/4= 1.3

//<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">=1 r 1.2 or 1 r 12 tenths //

//<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">=12 tenths / 4 = 3 tenths so... //

//<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5.2/4=1.3 //

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">1.6/4=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">19.2/3=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">21.6/4=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">41.2/4=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">2.1/7=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">We are learning to multiply a whole number by a decimal fraction.

2 x 4.7 is the same as 2 times 47 tenths. 2 x 47/10 = /10= 9.4 2 x 4.7=

3 x 1.4= is the same as... 3 x 14/10 = 42/10 3 x 1.4= 4.2

Try these problems...

10 x 0.6=6 4 x 4.5= 3 x 4.2= 8 x 8.1=

//**<span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We are learning to solve multiplication and division problems using standard written form. **//

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">546/7 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">927/3 <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">422/6

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Lets try with decimals...

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5.2/4= 1.3 //<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">=1 r 1.2 or 1 r 12 tenths // //<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">=12 tenths / 4 = 3 tenths so... // //<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5.2/4=1.3 //

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">1.6/4= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">19.2/3= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">21.6/4= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">41.2/4= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">2.1/7=

//**<span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">WALT: identify the lowest common multiple of two numbers. **//

**What you need:**


 * A deck of cards with the face cards, 10s and jokers removed (aces count as).
 * A classmate.

**What to do:**


 * Shuffle the cards into two even piles. Each player turns over one card, the first player to call out the lowest common multiple wins the cards.
 * Multiples are numbers you get when you multiply the number by another number, for example, the multiples of 7 are 7, 14, 21, 28, 35, 42…
 * Identify one common multiple of the two numbers. The easiest way to do this is to multiply the two numbers together. For example, if the two numbers are 4 and 6, one common multiple is 24 (4x6).

**Challenge:**
 * Modify this game so that the players must identify the lowest common denominator of two fractions. Think about how you could make this easier or harder for the players.

//**<span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">WALT: solve addition and subtraction problems involving fractions. **//

//** What is the simplest equivalent fraction? **//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**7/21**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**9/27**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**25/100**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**3/81**//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**Solve these simple problems...**//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**2/5 + 4/5= 1 1/5 = 6/5**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**2/10 + 2/10 + 2/10= 6/10 = 3/5**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**4/8 + 6/8= 10/8= 1 2/8= 1 1/4**//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;"> //**7/8- 4/8= 3/8**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**2/3 - 1/3= 1/3**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**14/20 - 6/20= 8/20 =2/5**//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**Now try these...**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**3/4 - 1/2=**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**4/9 + 2/3=**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**3/15 + 4/5=**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**15/20 - 1/5=**//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**Challenge...**// <span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">//**Peps had two pizzas, her dog Mo ate part of both pizzas. She was left with 3/4 of one pizza and 1/6 of another pizza.**//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">She has tried to figure this out and at first she thought she had 4/10 of pizza, but she realised this was wrong straight away. How did she know she was wrong? **//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">Peps figured she needed the two fractions to have a common denominator, so to help her we need to find the common denominator and understand lowest common multiples. **//



//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">What are the common multiples of 6 and 4? **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">Which is the least common multiple? **//

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">Our answer must be... **//

<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">


 * // Try to find the LCD (lowest common denominator). //**

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">Simplify these fractions... **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">8/10 = 4/5 **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">8/20 = 2/5 **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">6/12 = 1/2 **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">9/18 = 1/2 **//

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">Find the lowest common multiples of these numbers... **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">6 & 8 =24 **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">3 & 4 = 12 **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">4 & 6 = 12 **//

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">What is the lowest common denominator? **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">3/5 & 2/3 = 15 **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">4/12 & 2/4 = 12 **// //**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">3/6 & 2/9 = 18 **//

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">Let's use our prior knowledge to solve these problems. **//

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">3/5 + 2/3= **//

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">4/12 + 2/4= **//

//**<span style="color: #000080; font-family: Tahoma,Geneva,sans-serif; font-size: 180%;">3/6 + 2/9= **//

<span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">8/12 2/3

<span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">4/16 1/4

<span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">75/100 3/4

<span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">5/25 1/5

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Solve these simple fraction problems...
 * //__<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">1 __<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> + __2__= //**
 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">5 5 //**


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">__2__ + __2__ + __2__= //**
 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">8 8 8 //**


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Steph has 1/4 of a pizza and Tom has 3/8 of pizza. Steph thinks they have 4/12 of pizza and Tom thinks they have 5/8 of pizza. Who is right? //**


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Meggy wants to find 1/2 + 1/6. //**
 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Why can't we just add the numbers together directly? //**


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How will we solve this problem? //**


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Try these on your own... //**


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> 3/9 + 1/3= //**
 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">5/6 + 1/12= //**
 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">6/8 + 1/2= //**

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">What is the simplest equivalent fraction?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">6/24

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">12/16

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">25/100

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">12/32

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Solve these simple fraction problems...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">4/8 + 2/8= <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">1/3 + 1/3 + 1/3 + 1/3= <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">1/5 + 3/5=


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Jo has 6/8 of a cake and Frank has 3/24 of cake. Jo thinks they have 9/32 of cake and Frank thinks they have 7/8 of cake. Who is right, Jo, Frank, or neither of them? //**


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Try these on your own... //**


 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">5/8 + 4/16= //**
 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">1/9 + 2/3= //**
 * //<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">3/4 + 1/8= //**

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We are learning to solve addition and subtraction problems involving decimals using mental strategies. **//

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Using equal additions...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> To solve subtractions problems by equal additions that turn one of the numbers into a tidy number.

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">55.1 - 39.8= <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We could turn this problem into... <span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">55- 39.7= <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">or <span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">55.3 - 40=

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Let's look at how we have changed these problems...

<span style="color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">55 - 39.7= -0.1 -0.1 <span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">55.3 - 40= +0.2 +0.2

<span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;">Let's try this one together... <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">37.3 - 19.6=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;">Use equal additions to solve the following problems... <span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;">96.8 - 27.5 = <span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;">37.7 - 18.4 = <span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;">24.5 - 6.88 =

<span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;">Use equal additions to solve these word problems mentally...

<span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;">Liz has 35.4L of water in her watering can, she uses 14.6L to water her flowers. How many litres of water is left in her watering can?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;"> Kate's trousers were 50.2cm long, she measures them after putting them in the dryer. They are now 47.6cm long. How many cm did her trousers shrink?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 32px;">Sammy has 26.7mls of eye drops left in the bottle. Each drop is 0.8mls. If she puts two drops in each eye how many mls does she have left in the bottle?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Using written algorithms...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Adding using standard written form is easy. How can we use what we know about adding to figure out, and understand how to use an algorithm when subtracting?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Lets solve this addition problem... 1 1 <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> 27.5 __<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> +8.7 __ <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> 36.2

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">What do we need to remember?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How could we use our prior knowledge to solve this if we turned it into a subtraction problem? 1 16 1 <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"><span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px; text-decoration: line-through;"> 27 .5 __<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> -8.7 __ <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> 18.8

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Try and solve these problems...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> 82.8 <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> __-14.9__

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> 74.4 __<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> -27.32 __

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> 45.02 __<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> -16.55 __

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Algorithms again...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Turn this word problem into an algorithm...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Nick has 16.03m of wire, he uses 8.45m to repair a pig pen. How much wire does he have left?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Try these problems...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">It takes Frank 5.25 minutes to run around the block. On his second attempt it takes him 4.75 minutes. What is the difference between his two times?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Harry has 80.13 litres of paint. He uses 46.45 litres painting the fence. How much paint does he have left?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Lets check how we have set up the algorithms in our book.

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Using tidy numbers...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Try these...
 * 1) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">34.6 + 27.8 =
 * 2) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">24.9 + 203.7=
 * 3) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">6.5 - 1.98 =
 * 4) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">8.54 - 3.9=

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Now try these...
 * 1) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">351.7 + 38.8=
 * 2) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">54.33 + 23.98=
 * 3) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">45.66 - 5.97=
 * 4) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">9.8 - 3.98=
 * 5) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">54.33 + 23.98=
 * 6) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">38.99 + 110.56=
 * 7) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">9.8 - 3.98=
 * 8) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">5.46 - 2.999=
 * 9) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">436.9 + 12.8=
 * 10) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">298.9 + 236.5=
 * 11) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">23.756 - 4.9=
 * 12) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">3.284 - 0.98=
 * 13) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">19.6 - 5.997=

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">//Check your answers with a calculator when you are finished.//

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Using Place Value Partitioning...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">3.45 + 6.658= <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">3 + 6 + 0.4 + 0.6 + 0.05+ 0.05 + 0.008=

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We can also check the answers by using standard written form...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> 3.45 <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> __+6.658__

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Now try these...
 * 1) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">6.34 + 4.646=
 * 2) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">8.436 + 3.85=
 * 3) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">14.6 - 5.58=
 * 4) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">15.3 - 4.85=

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Are your answers correct? Use standard written form to check them.

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Now try these...
 * 1) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">4.56 + 32.7=
 * 2) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">24.66 + 3.886=
 * 3) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">24.64 - 6.75=
 * 4) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">53.83 - 8.37=
 * 5) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">14.354 + 3.7=
 * 6) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">43.8 + 3.478=
 * 7) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">34.6 - 20.54=
 * 8) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">27.8 - 13.08=
 * 9) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">45.46 - 3.5=
 * 10) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">62.6 - 5.78=
 * 11) <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">35.41 - 6.62=

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">//Check your answers using standard written form when you are finished.//