Ma+2012

We are learning to...
 * use and understand tables;
 * identify a general rule.



How many red squares do we need for the first red factory? The second? The third?

How many red squares will we need for the tenth factory? What if we needed to find out how many squares would be needed for the hundredth or the 124?

What can you say about the number of squares that you will need for any factory in this sequence?

What if our factory looked like this?



How would we find out how many tiles of each colour we would need? What would the rule be?
 * Factory || 1 || 2 || 3 || 4 || 5 ||
 * Purple tiles || 1 || 2 || 3 || 4 || 5 ||
 * Red tiles || 6 || 10 || 14 || 18 || 22 ||
 * Total tiles || 7 || 12 || 17 || 22 || 27 ||

Let's review what we have learned...



Create a table that shows the number of tiles for the 1st 10 factories. What is the pattern? What is the rule? Use the rule to find out how many tiles you would need if you joined the 14th and 15th factory together. How many tiles would you need to build the: 50th factory? 100th factory? 82nd factory?

//**WALT: find percentages of amounts. **//

//**Today we are looking at how finding 10% of a number can help us to solve other problems. **//

//**We find 10% by dividing a number by 10. **//

//** 10% of 60 is... **// //**60 divided by 10= 6 so... **// //**10% of 60 is 6. **//

//**Find 10% of... **// //**80 **// //**54 **// //**12 **//

//**Let's use this information to find 20% of... **// //**80 **// //**54 **// //**12 **//

//**Challenge... **// //**Find 10% of 40 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Find 5% of 40 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Find 1% of 40 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Find 16% of 40 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">"Percent" means out of 100. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">45% means 45 out of 100. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">When do see percentages in our daily lives? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">In a game of netball, Tea gets 37 shots of his 50 shots. I take 24 shots and get in 18. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Who is the better shot? **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How do you know? **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How can we figure out the percentages for each person? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Look at the following fractions, use the hundred strip to figure out what their equivalent percentage is. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">16/32 **// //**<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;">9/36 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">10/25 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">4/20 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Let's use our strips again, but this time we are going to turn over the percentage strip so we have to use imaging. **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">8/20 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">32/40 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">15/25 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">20/32 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">4/16 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">14/36 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Players in a soccer team compared their stats at the end of the season, they each have a fraction that shows how many goals they scored out of their total number of attempts. Find the percentage for each player and identify the most accurate goal scorer. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Alan 18/24 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Nic 8/32 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Matt 25/40 **// //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Scott 18/27 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Richie said he got 24 out of 16 and Dan said he got 55 out of 20. What are the percentages for these to players? What do you think about their stats? **//

//**<span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We are learning to use our knowledge of fractions to solve problems involving proportions. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">The word <span style="color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> proportion <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">is used to compare part of a group with the whole group. We normally use fractions or percentages to express proportions. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">For example, at Outram school there is a class with 18 girls and 12 boys. What proportion of the class are girls? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Can you give an answer as a fraction and as a percentage? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Find the equivalent fraction and/or percentage: **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">0.5 **//

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

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">0.25 **//

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

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">At a pet shop, there were 24 pets for sale. 25% were puppies, 1/3 were turtles, 12.5% were birds, 1/6 were rats and mice and the rest were kittens. **//


 * //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How many of each sort were on sale in the pet shop? **//
 * //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">What proportion of the pets were kittens? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Find the equivalent fraction and/or percentage: **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">6/8 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">5/20 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">9/27 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">0.33 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">0.66 **//

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

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">75% **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">There are 560 people who attend Te Kuiti Primary school. 50% of the school are girls. 40% of the boys went to the skate park at least once during the holidays. 2/7 of them took scooters or bikes. The rest of them took skateboards. **//


 * //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How many of the boys took a scooter or a bike to the skate park? **//
 * //**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">What proportion of the whole school took a skateboard to the skate park? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Today we are going to use our knowledge of Proportions to solve harder problems. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Let's try this one together: **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Room 4 goes shopping, we can buy 8 cushions for $6.00, if we have $15 how many cushions could we buy? **//

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

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> At Technology it takes 6m of cloth to make 8 pencil cases. How many metres of cloth would it take to make 20? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Find the equivalent fraction, decimal and/ or percentage... **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">0.8 **//

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

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">29% **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">110% **//

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

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">0.333 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Let's try another tricky word problem... **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How can we use our knowledge of proportions to help us solve this problem? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">If I have 32 weeks to pay for a new cell phone that cost $80, how much should I have paid after 12 weeks? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Find the equivalent fraction, decimal and/ or percentage... **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">0.02 **//

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

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">42% **//

//**<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;">21/63 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">0.75 **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">To make 800grams of muesli, you need 400 grams of oats, 250 grams of bran flakes and 150 grams of dried fruit. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How much rolled oats would you need to make 160 grams of muesli? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">A country at the Olympics earned 6 bronze medals, 8 silver medals and 10 gold medals. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">What proportion of the medals were bronze? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">What proportion of the medals were silver? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">What proportion of the medals were gold? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Give your answers as a fraction and as a percentage. Do your percentages add up to 100% **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">A country sent 32 athletes to the Olympics. 25% of these athletes won a medal in their event. **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How many of these athletes won a medal? **//

//**<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How many of these athletes did not win a medal? **//

<span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">We are learning to add and subtract integers (positive and negative numbers).

<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;">-5 - -8= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">+12 - -7= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">+4 - -1= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">-6 - +3= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">+8 - -5= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">-3 - -1= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">-3 - -2= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">+3 + -1= <span style="font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">+3 + -2=

<span style="background-color: #000000; color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We are learning to use a range of strategies to solve multiplication and division problems.

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Write these problems up twice as algorithms:

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">273 X 9= <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">1029 X 7= <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">3248 X 4=

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Can you explain how these two strategies work and how they are different?

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Yesterday we looked at the two ways we can use algorithms to solve multiplication problems today we are going to look at using standard written form to solve division problems.

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Let's turn this problem into a division algorithm: <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">654/6

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Let's try another one: <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">231/4

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Can you explain in your own words ho

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Turn these problems into standard written form and solve them.

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">279/3 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">640/8 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">743/7

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Let's practice what we have learned... <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Turn these problems into algorithms and solve them:

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">290 X 8 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">569 /6 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">1234 X 9 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">4324/4 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">333 X 5 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">8686/6

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Could you solve some of these problems using a mental strategy?

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">We are learning to multiply a whole number by a decimal fraction.

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">How could we use our PK to solve a problem like this?

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">2.7 X 3=

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Could we turn this into an algorithm? <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Let's try writing it up... <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">2.7 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">__X3__

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">How can we solve this problem using a mental strategy we already use for whole numbers?

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">1.2 X 6=

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Solve these three problems by first using a mental strategy and then check by using an algorithm.

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">2.5 X 4= <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">7 X 3.5= <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">P X 0.5= 9

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

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Double and halve these numbers...

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">16

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">144

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">81

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">15

2 x 4.7 is the same as 2 times 47 tenths.

2 x 47/10 = 94/10= 9.4

2 x 4.7= 9.4

10 x 0.4=

3 x 4.5=

5 x 4.2=

9 x 8.1=

3 x 1.4=

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Abbey had 34 boxes of shoes. Each box has got 12 pairs of shoes inside. How many pairs of shoes does she have altogether?

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">10 x 12 = <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">20 x 12= <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">30 x 12= <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">14 x 2 = so the answer is

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">34 x = <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">34 x = <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">so the answer is

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Emma and Nikita are planning a party. They buy 7 boxes of glow sticks. Each box contains 28 glow sticks. How many glow sticks do they have altogether?

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Use different strategies to solve these problems...

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">29 X 11= 319 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">20 X 11= 220 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">9 X11= 99

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">29 X 10= 290 + 29

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">11X30= 330 -11=319

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">4 X 24= 96 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">4 X20=80 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">4X4=16

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">24 X2 then doubled it again

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">2 X48

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5X24=120 -24

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">302 X 5= 1510 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5X300=1500 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">5X2=10

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">302X10=3020/2

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">198 X 6= 1188 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">100X6 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">90X6 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">8X6

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">200X6=1200-(2X6)

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">190X6= 1140 + (6X8)

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Ella has so many clothes they can barely fit in her drawers. Her duchess has 6 drawers and she has 336 items of clothing. If she puts an equal amount of clothes into each draw, how many items of clothing will be in each draw? <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">56 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">300/6=50 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">36/6=6

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">? X6=300 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">?X6=36

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">Try these problems... <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">279/9=31 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">270/9=30 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">9/9=1

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">128/8= 16r3 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">8x10=80 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">8X5=40 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;"> = 120 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">+5 and 3 left over

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">150/6=25 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">60/6=10 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">90/6=15

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">60/5=10 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">120/5=20 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">30/6=5

<span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">196/7=28 <span style="color: #008000; font-family: 'Comic Sans MS',cursive; font-size: 25.6px;">7X30=210-7=203-7=

<span style="background-color: #000000; color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 32px;"> WALT:use a range of mental strategies to solve multiplication and division problems involving measurement.

How do we find the area of a shape? What is the formula for a square or rectangle?

Look at these shapes, let's use our multiplication and division strategies to figure out the area. This rugby field is 144m long (including the dead ball line) and is 70m wide. What is the area of this field?

What about this triangle?

18mm

18mm

How do we find the volume of shapes? What is the formula for a cube or rectangular prism?

Let's work this one out together... This building is 32m high, it is 12m wide and it has a depth of 12m. What is the volume of this building?



Try this one... This building is 13 stories high and is 37m high, it is 18m wide and it has a depth of 12m. What is the volume of this building?



<span style="background-color: #000000; color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We are learning to use a range of mental strategies to solve multiplication and division problems.

Each of these containers have 38 beans inside. How many beans are there altogether?



We know that there are 38 beans inside each container. It could look like this...

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

We could solve this problem in more than one way.

We could use our knowledge of basic facts and place value to solve this problem by multiplying 30 by 7 and 8 by 7 and two answers together.



Or we could round 38 up to 40. 40 lots of 7 are 280, but we have multiplied 7 lots of 2 too many and will need to take it away.



Let's try and solve this problem...

Nic has 26 buckets of paint. Each bucket holds 8L of paint. How many litres of paint does he have altogether?

Explain the strategy you used to solve this problem. Check to see if you're correct by using a different mental strategy.

Try and solve these problems...

6 x 78 = ?

7 x 306 = ?

Rasty has six bowls hidden around the house. Each bowl has 49 cat biscuits in it. How many cat biscuits does he have altogether?



Use another mental strategy to check if you are right.

Let's look at these strategies together.

Which of these problems would be best solved by using a double and half strategy? Why? What about compensation (rounding)? What about a place value strategy?

8 x 179 = ? 3 x 66 = ? 4 x 348 = ? 9 x 83 = ? 6 x 333 = ? 486 x 5 = ? 4 x 275 = ? 5 x 999 = ?

Solve these problems...

40 x 5=

39 x 9=

102 x 4=

28 x 16=

Doubling and halving Compensation Place value

<span style="background-color: #000000; color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 32px;">WALT round numbers to the nearest...

Betty’s Appliance Store prices TVs to the nearest $10. If the exact price is $567.78, what does Betty charge?



Let's use number lines to help us solve these problems...


 * A builder works out the price of building a house as $123,566.89. He quotes a price to the nearest $1,000. What is his price?


 * A school wants a new classroom and it is going to cost $345,902.89 to build. They want to fundraise to the nearest $1,000. How much money do they need to raise?


 * Emma needs $266,345.09 for a new Ferrari, she wants to save the amount to the nearest $100. How much does she need to save?


 * Max won NZ Masterchef, she won $794,856.23. The Masterchef man decided to round it up to the nearest $10,000. How much did she win?


 * Natalie wanted to buy a painting worth $5,624,509. The artist wants her to round that amount to the nearest $100,000. How much does the artist want for his painting?

**Rounding Cards**

**What to do:**
 * Shuffle the cards and deal out 4 in a row. This represents a 4-digit number (eg. 3836).
 * Round the number to the nearest 10
 * Round the number to the nearest 100
 * Round the number to the nearest 1000
 * You round to whichever number is closest, but if the digit being rounded is a 5 then you round up, rather than down. For example 4125 rounded to the nearest 10 is 4130, not 4120.
 * Now try with 6 cards, 7 cards and 8 cards.

**Let's solve these problems without our number lines...**

Jess has $9 099.99 in her bank account she deposits some money into her account to round this amount to the nearest $10. How much does she have in her account now?

Nic buys some potatoes, the bag weighs 795.078g. The supermarket rounds to the nearest 100g, how many grams is this?

Try rounding these numbers...
 * 94 756.2309 to the nearest 10 000
 * 999.999 to the nearest 1
 * 11.89 to the nearest 1
 * 10 890.8 to the nearest 100
 * 956.2709 to the nearest 10
 * 999 999.9 to the nearest 1

**Let's try "Rounding cards" with decimal numbers...**
 * Place your decimal card...

<span style="background-color: #000000; color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We are learning how the number on the left and right of the decimal point contribute to the size of the number and how decimals can be added and subtracted.

<span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Look at this!

<span style="color: #de7575; font-family: Arial,Helvetica,sans-serif; font-size: 200%;"><span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;"> L ook at the "chocolate bars" we have made.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">If there are 8 chocolate bars and 4 friends. How many chocolate bars would each friend get?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">What if there were six chocolate bars and only 5 friends, how many would each friend get? Use your "chocolate bars" to find out.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">Lets check our answers on the calculator.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">What if there were...

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">5 chocolate bars and 4 people?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">5 chocolate bars and 2 people?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">6 chocolate bars and 4 people?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">Henry has 3.4 candy bars, and Tania has 1.8 candy bars.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">Peter thinks that they will have 4.12 bars altogether. Use the Unifix cubes and calculator to find out if he is right. Can you explain why he is right or wrong?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">**__Figure these out...__**

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">Jody has 4.3 candy bars. She thinks that if she eats 2.7 candy bars, she will <span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">have 2.4 left. Is she right?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">Rangi-Marie thinks that 7 x 0.4 candy bars will be 0.28. Is she right?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">Timoti thinks that 5.2 ÷ 4 = 1.3 (5.2 bars shared among four people). Is he right?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 200%;">Try this activity

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Put these fractions in order from biggest to smallest...

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">0.3, 0.234, 0.24

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Sam has 6.7m of rope, and George has 5.4m of rope.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Sam thinks that they will have 11.11m altogether and George thinks they will have 12.1m of rope.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Who is wrong, Sam, George, or both of them?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Explain how you know this.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Mr Plow has 56.3g of steak, Rastas has 55.9g of steak. Mr Plow thinks they have 111.12g. Rastas thinks they have 111.2g.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Who is wrong, Mr Plow, Rastas, or both of them?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Explain how you know this.

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Solve this problem on your own...

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Hazel has 44.8cm of tape for her parcel, she needs another 16.8cm of tape to finish wrapping it. How much does she need altogether?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Put these decimals in order from smallest to biggest...

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">0.03, 0.2, 0.12

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">0.03, 0.12, 0.2

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">Jenna has $29.80 in her piggy bank and $142.70 in her bank account. How much does she have altogether?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">$172.50

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">She spends $37.90 on a new scooter. How much money does she have now?

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">$134.60

<span style="color: #f26161; font-family: Arial,Helvetica,sans-serif; font-size: 180%;">$58.90 is deposited into her bank account by her mum. How much money does she have now?

<span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Try this activity

<span style="background-color: #000000; color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We are learning to use standard written form to add and subtract.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">Identify the value of the underlined digit...

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">98,004 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">__6__00,844 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">9,1__8__0,445 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">3__8__7,487,001

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Lets solve this addition problem...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> 27.5 <span style="font-family: 'Comic Sans MS',cursive; font-size: 150%;">__ +8.7 __

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">What do we need to remember?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">How could we use our prior knowledge to solve this if we turned it into a subtraction problem?

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> 27.5 <span style="font-family: 'Comic Sans MS',cursive; font-size: 150%;">__ -8.7 __

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Try and solve these problems...

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> 82.8 <span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> __-14.9__

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> 74.4 <span style="font-family: 'Comic Sans MS',cursive; font-size: 150%;">__ -27.32 __

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;"> 45.02 <span style="font-family: 'Comic Sans MS',cursive; font-size: 150%;">__ -16.55 __

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Algorithms again...

<span style="background-color: #e28484; color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Turn this word problem into an algorithm...

<span style="background-color: #e28484; color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Nick has 16.03m of wire, he uses 8.45m to repair a pig pen. How much wire does he have left?

<span style="background-color: #e28484; color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Try these problems...

<span style="background-color: #e28484; color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">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="background-color: #e28484; color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">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: 150%;">Lets check how we have set up the algorithms in our book.

<span style="color: #000000; font-family: 'Comic Sans MS',cursive; font-size: 150%;">Try this link...

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">Identify the value of the underlined digit... <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">8__7__5,020 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">70,000

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">95.0__2__2 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">2 hundredths

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">16.__1__2 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">1 tenth

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">1__9__,060,543 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">9,000,000

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> Let's turn the following problems into algorithms...

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">87 + 49=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> 87 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">__+49__

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">95 + 77=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">134 - 22=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> 134 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">__- 22__ <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> 112

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">223- 18=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">184 - 96=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">Try this one on your own...

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">254 - 178=

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">Have you got all of your digits in the right place?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">How do decimals fit in?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> Let's use our strategy to solve decimal problems.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> 24.3 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">__+ 18.3__

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> 88.6 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;">__+33.5__

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> 185 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> __-96.8__

<span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> 843.2 <span style="font-family: 'Comic Sans MS',cursive; font-size: 160%;"> __-658.8__

<span style="background-color: #000000; color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 32px;">We are learning to look at the addition and subtraction of 3 or more numbers to calculate the easy combination first.

<span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Bradley had three piggy banks. The first contained $89 then second had $597 inside and the last one only had $11 inside. How much money did Bradley have altogether?

<span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Lets make this problem easy...

<span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Can you see an easy combination to calculate first? Lets solve it together.

<span style="background-color: #000000; color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Lets turn this into a word problem <span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">49 + 693 + 51 + 7= <span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Louise has four boxes of ice cream, one box has 49 hokey pokey ice creams, another has 693 chocolate ice creams, the third box has 51 bubble gum ice cream and the last box has 7 bacon ice creams. How many ice creams does Louise have altogether? 800

<span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">49 + 51= 100 <span style="background-color: #ffffff; color: #000080; font-family: 'Comic Sans MS',cursive; font-size: 32px;">693 + 7 = 700

<span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Turn these into word problems and then solve them...
 * 1) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">970 + 3213 + 30= 4213
 * 2) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">99 + 89 + 11 + 1=200
 * 3) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">678 + 234 - 78= 834
 * 4) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">234 - 89- 11= 234 - 100= 134
 * 5) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">992 + 3,456 + 8= 4,456
 * 6) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">2,345 + 5 +995 -345=2000 + 1000 = 3000

<span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Roger is saving money to buy a new electric guitar. <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">How much has he saved altogether?
 * Month || Money saved ||
 * 1 || $ 88 ||
 * 2 || $174 ||
 * 3 || $236 ||
 * 4 || $84 ||

<span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Now turn these two problems into word problems and solve them... <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">34 + 77 + 123 + 68= <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">487 + 93 + 112 + 14=

<span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">Turn these into word problems and then solve them...


 * 1) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">870 + 4513 + 33=
 * 2) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">199 + 809 + 11 + 1=
 * 3) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">688 + 244 - 70=
 * 4) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">865 - 189- 11=
 * 5) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">823 + 780 + 8=
 * 6) <span style="background-color: #ffffff; color: #800000; font-family: 'Comic Sans MS',cursive; font-size: 32px;">3,445 + 5 +995 -345