Table of Contents
(Week 8/9)
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Table of Contents
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WALT - On top of every red slide you will find the WALT or what you are learning.
SUCCESS CRITERIA -
WALT : Solve addition and subtraction problems by splitting (partition) one number into smaller numbers.
SUCCESS CRITERIA:
Sometimes when we add or subtract numbers, it helps to break one of these numbers into parts.
55
40
2
42
+
55 + 40 = 95
95 + 2 = 97
55 65 75 85 95
+10
+10
+10
+10
While Superman was flying in New York City, He flew over 68 buildings and 24 parks. How many places did he fly over altogether?
Can someone help me solve these Maths problems?
Aunty Lisa made 88 cupcakes. Her naughty nephew and his friends ate 53. How many cupcakes did Aunty Lisa have left?
There were 165 students in the hall for a special assembly. 59 students came 15 minutes later. How many students attended this special assembly?
Think, Pair, Share.
I am having trouble counting in tens to solve these problems.
123 - 40 = 83
123 113 103 93 83
-10
-10
-10
-10
WALT - Solve addition and subtraction problems by choosing the best strategies.
SUCCESS CRITERIA - I must…..
Making ten
Changing one number into a tidy number.
Using place value
Counting forward or backwards in tens
Compensating
Algorithm
Partitioning / Splitting Numbers
Near doubles
Solve these problems and show your working please.
WALT : Solve Maths equations that have more than one operations using the order of operations rule. (BEDMAS / PEDMAS)
SUCCESS CRITERIA :
What have you learned from this video about the Order of Operations?
Does the order of your operations matters!
Using bedmas for unknown values
1. The school library had a used book sale. Paperbacks were $2 each and hardcover books were $3 each. There were 54 paperbacks and 163 hardcover books sold. How much money did the library raise?
2. Tamara has to go on a business trip. Including taxes, her round trip airfare is $400 and her room costs $150 per night. The cab fare from the airport to the hotel is $40. If Tamara stays for two nights, how much does the trip cost, not including the cost of food?
3. The football stadium has 32 560 seats. For the last game, 4 500 tickets were given away. The rest were sold at $10 each. How much money was received from ticket sales?
Using bedmas for unknown values
Robert bought 2 burgers for $3.50 each and 3 medium French fries for $1.20 each. Write a numerical expression to represent this situation and then find the cost.
Martha pays 20 dollars for materials to make earrings. She makes 10 earrings and sells 7 for 5 dollars and 3 for 2 dollars. Write a numerical expression to represent this situation and then find Martha's profit?
John bought 3 pants for 25 dollars each and paid with a one-hundred dollar bill. Write a numerical expression to represent this situation and then find how much money John gets back from the cashier?
The price of a shirt is 100 dollars. The store manager gives a discount of 50 dollars. A man and his brother bought 4 shirts and then share the cost with his brother. Write a numerical expression to represent this situation and then find the price paid by each brother.
Peter withdrew 1000 dollars from his bank account today. He uses 500 to fix his car. Then, he divide the money into 5 equal parts and gave away 4 parts and kept 1 part for himself. Finally, he took to wife to the restaurant and spent 60 dollars on meals. Write a numerical expression to represent this situation and then find how much money Peter has now?
Solve these problems. Please show your working.
Sam had baseball cards and 32 had spots. He gave 18 away. He now has 47 baseball cards left. How many baseball cards did he start with ?
There are three hundred thirty students at a school, and three hundred of them are boys. If each classroom holds thirty students, how many classrooms are needed at the school?
Paula repairs swimming pools and earns $15/h for the first 35 h she works in a week. For hours over 35 h, she earns 2 times as much. If she works 48 hours in a week, how much does she earn?
pedmas/bedmas () 2 x ÷ + -
Solve these problems. Please show your working.
Adam has $450. He spends $210 on food. Later he divides all the money into four parts out of which three parts were distributed and one part he keeps for himself. Then he found $50 on the road. Write the final expression and find the money he has left?
Linda bought 3 notebooks for $1.20 each, a box of pencils for $1.50, and a box of pens for $1.70.
Joan has ninety - six muffins, which he needs to box up into dozens. How many boxes does she need?
pedmas/bedmas () 2 x ÷ + -
(a) 11 − 4 + 13 × 2 = ?
(b) 5 − 45 ÷ 15 + 3 2 = ?
(c) 4 × 5 ÷ 2 + 7 − 4 × 4 = ?
(d) 42 ÷ 7 × 3 + 9 × 2 − 4 = ?
(e) 15 − (6 + 1) + 30 ÷ (3 × 2) = ?
(f) 17 − 2 3 + 4 × 5 = ?
(g) 72 ÷ (3 × 2) − (10 + 1) = ?
(h) 10 × (0.4 + 0.3) − 2 2 ÷ 5 0 = ?
(i) 10 × 0.4 + 0.3 − 2 2 ÷ 5 0 = ?
(j) 6 + (36 ÷ 9)3 ÷ 2 − 1 = ?
(k) (14 − 6) × ((30 + 5) ÷ 5) = ?
(g) 3 × 7 + 5 − 100 ÷ 20 × 4 = ?
Solving problems using
PEDMAS / BEDMAS
Solving unknown values using
PEDMAS / BEDMAS
WALT - Solve unknown values using PEDMAS / BEDMAS.
SUCCESS CRITERIA -
Content Page
Click on the picture below to write down important notes from the video.
Having BEDMAS means that we will all agree on the value of an unknown amount in an equation.
Do you agree or disagree?
Eg (25 – 5) ÷ 5 = __
Sometimes unknown values are represented as n or x
Using bedmas for unknown values
“I’m thinking of a number. We’ll call this number ‘n’. I add six to it. I double it. This is equal to twenty eight.”
Can you write this problem as an equation?
Using bedmas for unknown values
“I’m thinking of a number. We’ll call this number ‘n’. I add six to it. I double it. This is equal to twenty eight.”
(n + 5) x 2 = 28
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. We’ll call this number ‘n’. I add six to it. I double it. This is equal to twenty eight.”
(n + 5) x 2 = 28 ÷ 2
n + 5 = 14
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. We’ll call this number ‘n’. I add six to it. I double it. This is equal to twenty eight.”
(n + 5) x 2 = 28 ÷ 2
n + 5 = 14
n = 14 - 5
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. We’ll call this number ‘n’. I add six to it. I double it. This is equal to twenty eight.”
(n + 5) x 2 = 28 ÷ 2
n + 5 = 14
n = 14 - 5
n = 9
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. We’ll call this number ‘n’. I add six to it. I double it. This is equal to twenty eight.”
(n + 5) x 2 = 28 ÷ 2
n + 5 = 14
n = 14 - 5
n = 9 lets check using BEDMAS! (9 + 5) x 2 = 28
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract 10 from it. I divide this by nine. This is equal to ten.”
Using bedmas for unknown values
“I’m thinking of a number. I subtract 10 from it. I divide this by nine. This is equal to ten.”
(n – 10) ÷ 9 = 10
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract 10 from it. I divide this by nine. This is equal to ten.”
(n – 10) ÷ 9 = 10
(n – 10) ÷ 9 = 10 x 9
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract 10 from it. I divide this by nine. This is equal to ten.”
(n – 10) ÷ 9 = 10
(n – 10) ÷ 9 = 10 x 9
n – 10 = 90
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract 10 from it. I divide this by nine. This is equal to ten.”
(n – 10) ÷ 9 = 10
(n – 10) ÷ 9 = 10 x 9
n – 10 = 90
n = 90 + 10
n = 100 ... lets check using BEDMAS!(100 – 10) ÷ 9 = 10
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract two. I square it and I get twenty five.”
(n – 2)2 = 25
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract two. I square it and I get twenty five.”
(n – 2)2 = 25
(n – 2)2 = √25
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract two. I square it and I get twenty five.”
(n – 2)2 = 25
(n – 2)2 = √25
n - 2 = 5
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract two. I square it and I get twenty five.”
(n – 2)2 = 25
(n – 2)2 = √25
n - 2 = 5
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
“I’m thinking of a number. I subtract two. I square it and I get twenty five.”
(n – 2)2 = 25
(n – 2)2 = √25
n - 2 = 5
n = 7 ... lets check using BEDMAS! (7 – 2)2 = 25
We want to bring all numbers to the other side of the equation so that the unknown number is by itself!
If we want to do this, we need to do the opposite...
Using bedmas for unknown values
Term 1 Week 10
Introduction to Algebra!
Algebra is great fun - You get to solve puzzles!
A Puzzle…
What is the missing number?
- 2 = 4 Ok, the answer is 6, right? Because 6 - 2 = 4
Well, in algebra we don’t use blank boxes, we use a letter (usually an x or y, but any letter is fine). So we write
x - 2 = 4
It is really that simple. The letter ‘x’ just means “we don’t know this yet”, and is often called the unknown, or the variable.
And when we solve it, we write x = 6
Introduction to Algebra - Multiplication!
What’s the missing number?
x 4 = 8 The answer is 2, right? Because 2 x 4 = 8.
But because we don’t use blank boxes, we use a letter. So we might write:
x x 4 = 8
But the ‘x’ looks like the multiply ‘x’ and that can be very confusing. So in algebra, we don’t use the multiply symbol (x) between numbers and letters.
We put the number next to the letter to mean multiply: 4x = 8
Watch this video!
Now have a go! Choose which level you want to try
Single-Step Equations (+, -, x, ÷)
x - 4 = 12
Early Finishers…Multi-Step Equations
5x - 2 = 18
Early Finishers…
Keep Practicing!
Using symbols instead of numbers
Rewrite these equations before answering
6 + a = 19 a = 19 - 6
b + 43 = 60 b =
15 – c = 2 c =
d – 26 = 90 d =
e x 4 = 32 e =
7 x f = 77 f =
g ÷ 10 = 120 g =
300 ÷ h = 6 h =
Last week Dan had 32 dollars. He washed cars over the weekend and now has 86 dollars. How much money did he make washing cars ?
Sally spent half of her allowance going to the movies. She washed the family car and earned 6 dollars. What is her weekly allowance if she ended with 14 dollars ?
The sum of three consecutive even numbers is one hundred two. What is the smallest of the three numbers ?
Tim bought a soft drink for two dollars and eight candy bars. He spent a total of thirty - four dollars. How much did each candy bar cost ?
Floyd is an aspiring music artist. He has a record contract that pays him a base rate of $200 a month and an additional $12 for each album that he sells. Last month he earned a total of $644. How many albums did Floyd sold last month?
Solve these problems.
Algebra: Patterns and Relationships
WALT: to find a rule to give the number of blocks in a sequence
Link to lesson plan from nzmaths
First factory
Second factory
third factory
What will the fourth factory look like?
WALT: to find a rule to give the number of blocks in a sequence
Link to lesson plan from nzmaths
First factory
Second factory
third factory
How many blue squares do we need for the first factory? The second? The third?
How many blue tiles will we need for the tenth factory? The hundredth? The 3,298th?
What is the number pattern for the blue squares?
How many red squares do we need for the first factory? The second? The third?
Factory number | 1 | 2 | 3 | 4 | 5 |
Number of blue squares | 2 | 4 | 6 | 8 | 10 |
Number of orange squares | 9 | 15 | 21 | 27 | 33 |
Total number of squares | 11 | 19 | 27 | 35 | 43 |
First factory
Second factory
third factory
How many blue squares do we need for the first factory? The second? The third?
How many blue tiles will we need for the tenth factory? The hundredth? The 3,298th?
What is the number pattern for the blue squares?
How many red squares do we need for the first factory? The second? The third?
Factory number | 1 | 2 | 3 | 4 | 5 |
Number of blue squares | | | | | |
Number of orange squares | | | | | |
Total number of squares | | | | | |
First factory
Second factory
third factory
How many orange squares are in the first factory? The second? The Third?
How many orange squares will be in the fourth factory?
What is the number pattern for the orange squares?
What is the rule for calculating the number of orange squares
If we have to use exactly 33 orange squares in making a factory, how many blue squares would we need?
Factory number | 1 | 2 | 3 | 4 | 5 |
Number of blue squares | | | | | |
Number of orange squares | | | | | |
Total number of squares | | | | | |
First factory
Second factory
third factory
How many squares do we need altogether for the first factory? The second? The third?
Who can tell me how many squares we’ll need for the fourth factory?
What is the rule for figuring out the total number of squares?
If we had 35 squares, which numbered factory could we make?
Which of these numbers are not a number of squares for one of these factories: 43, 44, 45, 46?
Factory number | 1 | 2 | 3 | 4 | 5 |
Number of blue squares | | | | | |
Number of orange squares | | | | | |
Total number of squares | | | | | |
WALT: add and subtract integers
SC: I understand the rules for adding negative and positive numbers
What is Integers? What do you know about it?
Practice Time!
Ethan started the week with $3,000 in his bank account. At the end of the week, his balance was $4,000. Which integer represents the change in Ethan's bank account balance?
Justin ended round one of a game show with 300 points. In round two, he lost 100 points. What was his final score?
Katherine is very interested in cryogenics (the science of very low temperatures). With the help of her science teacher she is doing an experiment on the effect of low temperatures on bacteria. She cools one sample of bacteria to a temperature of -51°C and another to -76°C. What was the temperature difference in the two experiments?
On Tuesday the mailman delivers 3 checks for $5 each and 2 bills for $2 each. If you had a starting balance of $25, what is the ending balance?
You owe $225. on your credit card. You make a $55 payment and then purchase $87 worth of clothes at Kmart. What is the integer that represents the balance owed on the credit card?
I have -$6 on my eftpos card and I spent $13 at Laser Strike with my friends. How much money do I have now?
I have -$19. I washed my mums car, did the mowing and cleaned the toilets. I was paid $11. How much money do I have now?
I have $8. I bought my family 3 pizzas for $21 dollars. How much money do I have now?
The temperature on the mountains in New Zealand is -8℃. In the North Pole, the average temperature is 22℃ colder. What is the temperature in the North Pole?
I have -$13. I spent $22 at KMart. How much money do I have now?
The coldest temperature recorded in the South Pole is -82℃. The coldest temperature recorded in the North Pole is 45℃ warmer. What is the coldest temperature recorded in the North Pole?
Add (-10) + (+12). Add (+7) + (-11) + (+5).
Subtract (+6) – (–4). Subtract (–10) – (+3) – (–4).
Subtract (–10) – (+3) – (–4). Multiply (–5)(–2)(+3).
-24 divided by -6. 36 divided by 4 .
Marie is buying light bulbs for her Christmas decorations. She buys 12 but when she gets to the cash, she has to put back four because they are broken. How many light bulbs does Marie buy?
Annie monitors the temperature in her swimming pool on a daily basis. On Monday it was 250 C and then it dropped two degrees before climbing five degrees by Friday. What was the temperature of the pool on Friday?
Phil gets paid $500 every two weeks. After getting paid he had to pay $30 for repairs to his skateboard, but then received a cheque from his grandparents for his birthday. If his balance is $520, how much did he receive from his grandparents?
You are tracking the movements of an ant as he searches for food for a science project. You notice that he travels 10 m north of the colony and then moves 60 m south. How far away from the colony is the ant when he finally finds food?
You are selling drinks at the school dance. You have a cooler, which holds 35 cups. The canteen gets busy and you lose track of how many cups you sold. You check and see that there are 17 cups left in the cooler. How many drinks must you have sold?
Your school is having an open house. They decide to make bumper stickers with the school logo. The school budgeted $220 for the stickers. It costs $40 to make the design and another $2 for each sticker. How many stickers can the school buy?
I had $20 on my credit card. I spent $80. How much money do I have now?
Interest is 15%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I had $20 on my credit card. I spent $80. How much money do I have now?
20 - 80 = -60
Interest is 15%. How much will interest be?
10% of 60 = 6 5% = 3 3 + 6 = 9
What will the number problem be to show the total amount I pay?
-60 - 9 =
How much do I owe? -69
I had -$135 on my credit card. I repaid $85. How much money do I have now?
Interest is 25%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I had -$135 on my credit card. I repaid $85. How much money do I have now?
-135 + 85 = -50
Interest is 25%. How much will interest be?
10% of 50 = 5, 5%= 2.5 5+5+2.5 or 5x2 =10 + 2.5 = 12.5
What will the number problem be to show the total amount I pay?
-50 -12.5 =
How much do I owe? -62.5
I have -$75 on my credit card. I spent $25. How much money do I now have?
Interest is 45%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I have -$75 on my credit card. I spent $25. How much money do I now have?
-75 - 25 = -100
Interest is 45%. How much will interest be?
10% of 100 = 10 5% = 5 4x10 = 40 + 5 = 45
What will the number problem be to show the total amount I pay?
-100 - 45 =
How much do I owe? = -145
I have -$870 on my credit card. I repaid $35 on my credit card. How much money do I now have?
Interest is 10%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I have -$870 on my credit card. I repaid $35 on my credit card. How much money do I now have?
-870 + 35 = -835
Interest is 10%. How much will interest be?
10% of 835 = 83.5
What will the number problem be to show the total amount I pay?
-835 - 83.5
How much do I owe? 918.5
I have $65 on my credit card. I spent $180. How much money do I now have?
Interest is 30%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I have -$230 on my credit card. I spent $180. How much money do I now have?
Interest is 35%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I have $35 on my credit card. I spent $238. How much money do I now have?
Interest is 60%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I have -$170 on my credit card. I spent $562. How much money do I now have?
Interest is 15%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
EXPANDING ALGEBRAIC EXPRESSIONS
WALT : expand algebraic equations
SUCCESS CRITERIA : I must….
Expanding is when you remove brackets from an equation by multiplying.
Click on the image to learn a few important rules about expanding!
Have a go at expanding the examples in the YouTube clip
4(3x + 1)
4 x 3𝑥 + 4x1
12𝑥 + 4
4(3𝑥 + 1)
5(7 + 2𝑥)
2(3y + 4z)
2𝑥 (3𝑥 -2)
4𝑥(3𝑥 - 2y)
FOLLOW UP: EXPANDING ALGEBRAIC EXPRESSIONS
WALT: factorise algebraic expressions
SC: I can find factors of a number
When you have two sets of brackets, you need to expand and then simplify.
You simplify when you combine the ‘like’ terms
"Like terms" are terms whose variables (letters) and their exponents (such as the 2 in 𝑥2) are the same.
In other words, terms that are "like" each other.
Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.
Example: 5y and 2y are ‘like terms’. 5𝑥2 and 12𝑥2 are also like terms
What are ‘like terms’?
EXAMPLES
8𝑥yz and 10y𝑥z are like terms (because the both contain an y 𝑥 and z)
It doesn’t matter what order the letters are in, as long as they are exactly the same.
So we simplify them by adding them together.
8𝑥yz and 10y𝑥z
10𝑥yz (to make it easier we put the letters in alphabetical order)
Unlike terms have different powers and letters (variables)
Examples:
5𝑥 and 3𝑥2 are not like terms
5xy and 7yz are not like terms
We cannot add unlike terms together
WHAT are ‘unlike terms’?
Let’s have a go at simplifying
Example: 4𝑥3 + 3𝑥2 − 7 − 𝑥2 + 2
Step 1: highlight all like terms
4𝑥3 + 3𝑥2 − 7 − 𝑥2 + 2
Step 2: combine the like terms. Remember to take the operations
4𝑥3 + 3𝑥2 − 7 − 𝑥2 + 2 → 4𝑥3 + 3𝑥2 − 𝑥2 − 7 + 2
Step 3: Now you have simplified!
4𝑥3 + 2𝑥2 − 5
Quick Quiz!
Expand and Simplify: 2 + 3(𝑥+ 2)
2 + 3(𝑥+ 2)
2 + 3𝑥 + 6
= 3𝑥 + 8
Expand and Simplify: 8 + 5(a + 7b)
Expand and Simplify: 3(n + 1) + 2(n + 3)
Expand and Simplify: 3(n + 1) + 2(n + 3)
How do we find a percentage of a number?
WALT : Find a percentage of a number.
How do we find a percentage of a number?
What is 10% of 100?
How did you know this?
100÷10 = 10
What is 20% of 80?
How did you know this?
What is 20% of 80?
How did you know this?
80 ÷ 10 =8
8 x 2 = 16
What is 45% of 60?
How did you know this?
What is 45% of 60?
How did you know this?
60÷ 10 = 6 (10% is 6) then 5% = 3 (because half of 6 is 3)
6 x 4 = 24 + 3 = 28
WORD PROBLEMS with MONEY
I had $20 on my credit card. I spent $80. How much money do I have now?
Interest is 15%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I had $20 on my credit card. I spent $80. How much money do I have now?
20 - 80 = -60
Interest is 15%. How much will interest be?
10% of 60 = 6 5% = 3 3 + 6 = 9
What will the number problem be to show the total amount I pay?
-60 - 9 =
How much do I owe? -69
I had -$135 on my credit card. I repaid $85. How much money do I have now?
Interest is 25%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I had -$135 on my credit card. I repaid $85. How much money do I have now?
-135 + 85 = -50
Interest is 25%. How much will interest be?
10% of 50 = 5, 5%= 2.5 5+5+2.5 or 5x2 =10 + 2.5 = 12.5
What will the number problem be to show the total amount I pay?
-50 -12.5 =
How much do I owe? -62.5
I have -$75 on my credit card. I spent $25. How much money do I now have?
Interest is 45%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I have -$75 on my credit card. I spent $25. How much money do I now have?
-75 - 25 = -100
Interest is 45%. How much will interest be?
10% of 100 = 10 5% = 5 4x10 = 40 + 5 = 45
What will the number problem be to show the total amount I pay?
-100 - 45 =
How much do I owe? = -145
I have -$870 on my credit card. I repaid $35 on my credit card. How much money do I now have?
Interest is 10%. How much will interest be?
What will the number problem be to show the total amount I pay?
How much do I owe?
I have -$870 on my credit card. I repaid $35 on my credit card. How much money do I now have?
-870 + 35 = -835
Interest is 10%. How much will interest be?
10% of 835 = 83.5
What will the number problem be to show the total amount I pay?
-835 - 83.5
How much do I owe? 918.5
A test has 20 questions. If Peter gets 80% correct, how many questions did peter missed?
The number of correct answers is 80% of 20 or 80/100 × 20
80/100 × 20 = 0.80 × 20 = 16
Recall that 16 is called the percentage. It is the answer you get when you take the percent of a number
Since the test has 20 questions and he got 16 correct answers, the number of questions he missed is 20 − 16 = 4
Peter missed 4 questions
Multiplication with DeCIMALS
WALT: Solve multiplication problems with decimals using place value
SC: I can convert basic fractions and decimals. I can split numbers up into wholes and tenths
FACTORISING ALGEBRAIC EXPRESSIONS
WALT: factorise algebraic expressions
SC: I can find factors of a number
When we factorise, we find the hCF and the most common variables (letters)
Sometimes we will only have a common variable, and no HCF.
When we factorise, we find the hCF and the most common variables (letters)
Factorise:
2c2bd +cde
𝑥 + a𝑥
pqr + qrt + qsw
y𝑥2z3 + q𝑥z2
𝑥2 + 3az𝑥
When we factorise, we find the hCF and the most common variables (letters)
Factorise:
2c2bd +cde = cd (2cb + e)
𝑥 + a𝑥 = 𝑥 ( 1 + a)
pqr + qrt + qsw = q (pr + rt - sw) Q IS THE ONLY COMMON VARIABLE ACROSS ALL THREE PARTS
y𝑥2z3 + q𝑥z2 = 𝑥z2(y𝑥z + q)
𝑥2 + 3az𝑥 + 𝑥 = 𝑥( 𝑥 + 3az + 1)
When we factorise, we find the hCF and the most common variables (letters)
Factorise:
25p2 - 10p
6p4 - 12p
24m3 no - 16m4 o2p
When we factorise, we find the hCF and the most common variables (letters)
Factorise:
25p2 - 10p = 5p (5p - 2)
6p4 - 12p = 6p (p3 - 2)
24m3 no - 16m4 o2p = 8m3o (3n - 2mop)
Factorising Expressions - Double Brackets
If we factorise double brackets (𝑥 +/- ___) (𝑥 +/- ___)
WALT: factorise quadratic equations
SC: I can find factors of a number
Factorising Expressions - Double Brackets
If we factorise double brackets (𝑥 +/- ___) (𝑥 +/- ___)
Factorise: 𝑥2 + 9𝑥 + 14
First, we know that an 𝑥 will be in the first part of both brackets.
Factorising Expressions - Double Brackets
If we factorise double brackets (𝑥 +/- ___) (𝑥 +/- ___)
Factorise: 𝑥2 + 9𝑥 + 14
First, we know that an 𝑥 will be in the first part of both brackets.
Then, we look at the last number without any variables. We know that we get this answer by multiplying the two numbers in the brackets.
Then, figure out which two factors can be added/subtracted to equal the number with one variable.
(𝑥 + ) (𝑥 + )
2 and 40, 10 and 8,
𝑥2 + 18𝑥 + 80
𝑥2 + 6𝑥 + 8
𝑥2 + 6𝑥 + 8
(𝑥 + ) (𝑥 + )
2 and 12, 3 and 8, 6 and 4
𝑥2 + 11𝑥 + 24
𝑥2 + 𝑥 - 42
𝑥2 + 4𝑥 - 32
Factorising Expressions - Double Brackets
If we factorise double brackets (𝑥 +/- ___) (𝑥 +/- ___)
Factorise: 𝑥2 + 18𝑥 + 80
The first part
Factorising Expressions - Double Brackets