What could you write about the diagram below?
Is this always true:
How does calculating 42 x 47 help expand
What is bigger:
?
How could this be simplified?
What is 1002 – 992? What about 1002 – 982? What, then, for – ?
What would you do with – –
?
When is ? How many solutions can you find
What can you say about the terms:
Inquiry 1: Simplifying expressions
5 bar
8 bar
Don’t forget to record your answers! Is there a quicker way than drawing diagrams??
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Can you write ? in terms of w only
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Ready for some magic?
1. Choose a number and write it here
1. Choose a number and write it here
2. Work clockwise. Place consecutive numbers here
1. Choose a number and write it here
2. Work clockwise. Place consecutive numbers here
Fill in the circles by adding together each of the two corner numbers that each circle is connected to
1. Choose a number and write it here
2. Work clockwise. Place consecutive numbers here
Fill in the circles by adding together each of the two corner numbers that each circle is connected to
The middle square is calculated by summing the three circles
By giving me your first number, I will give you your middle number within seconds. How? 1. Choose a number and write it here
2. Work clockwise. Place consecutive numbers here.
3. Fill in the circles by adding together each of the two corner numbers that each circle is connected to
4. The middle square is calculated by summing the three circles.
What could you write about the diagram below?
Is this always true:
How does calculating 42 x 47 help expand
What is bigger:
?
How could this be simplified?
What is 1002 – 992? What about 1002 – 982? What, then, for – ?
What would you do with – –
?
When is ? How many solutions can you find
What can you say about the terms:
Inquiry 2: Substitution
Always, sometimes, never The next few slides will have mathematical expressions that are always true, sometimes true or never true. Before we begin, discuss in your groups and try to answer the following two questions. 1. Can you give examples from everyday life that are always true? Sometimes true? Never true? 2. Can you give mathematical examples that are always true? Sometimes true? Never true?
Always, sometimes, never 1)
6+2+4=4+2+6
Always, sometimes, never 2)
5–1=1–5
Always, sometimes, never 3)
2+3x4=5x4
Always, sometimes, never 4)
3÷½=3x2
Always, sometimes, never 5)
Always, sometimes, never 6)
Always, sometimes, never 7)
Always, sometimes, never 8)
Always, sometimes, never 9)
Always, sometimes, never 10)
What does this statement mean in words?
Is this ever true?
What does this statement mean in words?
Is this ever true?
Write values of x and y which prove that the statement is not always true.
Activity Each group has a set of cards on their desk, a large sheet of paper and a glue stick. You will need to divide your poster into three columns and head these with the words: ‘Always true’, ‘Sometimes true’, ‘Never true’. Take it in turns to pick up a card and decide whether the statement is ‘Always true’, ‘Sometimes true’, or ‘Never true’. When you have agreed , stick the card down and write examples around it to justify your choice. For example. If it is sometimes true, show the examples where it is true and also when it isn’t true.
What could you write about the diagram below?
Is this always true:
How does calculating 42 x 47 help expand
What is bigger:
?
How could this be simplified?
What is 1002 – 992? What about 1002 – 982? What, then, for – ?
What would you do with – –
?
When is ? How many solutions can you find
What can you say about the terms:
Inquiry 3: Brackets and factorising
Can you make new questions using different rods?
? ? ? ?
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How many different ways can you arrange these rods to leave an equal number of each colour?
Make up some of your own. Remember to sketch before and after drawings. Try and write your results using letters?
How many equivalent expressions?
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What could you write about the diagram below?
Is this always true:
How does calculating 42 x 47 help expand
What is bigger:
?
How could this be simplified?
What is 1002 – 992? What about 1002 – 982? What, then, for – ?
What would you do with – –
?
When is ? How many solutions can you find
What can you say about the terms:
What happens when: • you add 6 cubes to bag A? • You take 3 cubes from B?
What happens when you: • Double the cubes in A? • Halve the cubes in B?
On your desks you have two empty bags and some multilink cubes. Begin by placing a known number of cubes in a bag. This can be the same in each or different, mix it up!!. Now, answer the prompts. Write down what happens to your starting values. Try this 5 times, or until you feel confident.
Express yourself Challenge!! Only person A knows the number of cubes in each bag. Person B begins by representing the number of cubes in bag A with the letter and the number of cubes in bag B as . They then have to write expressions for each prompt. Person A checks their work. Then swap. Can you write new questions??
Have the same number of cubes in both bags. 6 cubes are to be taken away. How many different ways can this be achieved?
Begin with 5 green and 6 red cubes. Divide these in your bags. How did you do it? Is there another way? How could you record this?
Simplify the expressions for the perimeter of the shapes given.
Can you fill in the missing lengths?
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Every side has length &
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Perimeter ?
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Can you make up some of your own for others to calculate. How about using different shapes?
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Choose a number
Add 2
Add the number you first thought of
Add 8
Halve your current total
Take away the number you first thought of
Try these a number of times. Discuss everyone's results. Can you use algebra to show why?
Choose a Times number it by 3
subtract your original number
Add 4
Can you make one for the class?
Chains
Halve your total
What’s the longest chain you can make?
Choose a number Square it
Add your original number
Divide your total by your original number
Add 17
Take away 2
Subtract your original number
Divide your total by 3
( Which expressions have the same value when: % ( ?
Which expressions have the same value when: (?
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Matchings Explore what happens when * ( are: • •
all even all odd
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Order the expressions (smallest- largest) when: ( ( + ( #
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