Year 8: Probability Dr J Frost ([email protected]) Last modified: 23 rd January 2013.
Year 7 Order of Operations Dr J Frost ([email protected]) Last modified: 13 th...
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Year 7 Order of Operations Dr J Frost ([email protected]) www.drfrostmaths.com Last modified: 13 th September 2015 Objectives: Appreciate that in maths we evaluate operations in a particular order (according to BIDMAS). Be able to use a calculator to evaluate more complicated expressions.
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Transcript of Year 7 Order of Operations Dr J Frost ([email protected]) Last modified: 13 th...
Year 7 Order of Operations
Dr J Frost ([email protected])www.drfrostmaths.com
Last modified: 13th September 2015
Objectives: Appreciate that in maths we evaluate operations in a particular order (according to BIDMAS). Be able to use a calculator to evaluate more complicated expressions.
Starter
(−3 )2−32
Type each of these into calculator and see what result you get.Why are they different. What is the calculator doing in each case?
There’s two operations in each case: negating (i.e. making something negative) and squaring. The two are ordered differently in each example. How do we determine the order?
BIDMAS
1+2× (3+4 )2
What is the precedence of the operators? (i.e. the order we do the operations in)
!
¿1+2×72Do what first ?
¿1+2×4 9Then ?
¿1+98Then ?
¿99Then ?
Brackets
Prec
eden
ce Indices
Division Multiplication
Addition Subtraction
Includes negation
You can remember this as“BI[DM][AS]”
BIDMAS
(−3 )2−32
Brackets
Prec
eden
ce Indices
Division Multiplication
Addition Subtraction
If we want to do “minus 3, squared”. Why do we need the brackets then?The brackets forces the negation to be done before the squaring, as otherwise (by BIDMAS) the power would be done first.
20−3+2Which is the correct answer?
19 15If with have multiple operations with the same precedence, we evaluate left-to-right.20 – 3 + 2
?
Quickfire Questions
Evaluate the following (and optionally also suggest a stupid answer!)
Brackets
Prec
eden
ce Indices
Division Multiplication
Addition Subtraction
1+1×2=𝟑 1− (4×2+3 )=−𝟏𝟎?
????
??
??
?
Test Your Understanding
1+2×3+10÷5=𝟗
[IMC 2010 Q1] What is the value of ?
i
ii
iii [JMO 2006 A1] What is the value of ?
?
?
?
Exercise 1Calculate the following using rules of BIDMAS:
What number is missing?
[JMC 2008 Q1] Which of these calculations produces a multiple of 5?A B C D E Solution: D
[JMC 2015 Q1] Which of the following calculations gives the largest answer? A B C D E Solution: A
[JMC 2000 Q4] Which of the following has the greatest value?A B C D E Solution: D
[JMO 2011 A1] What is the value of ?
Solution: 33
[JMO 2001 A2] Which number should replace the box to make a true statement?
Solution: 6
[IMC 2009 Q1] What is the value of ?
Solution: 29
[JMC 2006 Q9] Four of these calculations give the same answer. Which is the odd one out?A B C D E Solution: E
Calculate the following:
1ab
c
def
2ab
3
4
5
6
7
8
9
10
???
??
?
??
?
?
?
?
?
?
?
?
abcd
??
?
Using a Calculator
You should hopefully have a calculator resembling this.
Learning Objectives:- Use ANS key.- Write embedded
expressions.- Convert between
decimal/fractional form.- Modify expressions using
arrow and DEL keys.- Use and 3
Starter
Using your calculator, find the value of:
What is in decimal form?
You should have used the S<->D button (S stands for Surd (i.e. a root), D for Decimal)
Subtract your answer to B from 143.5
You should have typed in “143.5 – ANS” to use your previous answer.
A
B
C
?
?
?
Bro Tip: Since the outermost thing is a fraction, press the fraction key first.Use direction keys to move around.
Modifying Existing Expressions
Type in this again and press the = key:
Suppose we were actually supposed to square 5.8 instead of cube it. Can we fix this without retyping the whole expression?
Press the left arrow key. Then navigate to the 3 using the arrow keys until you’re just after it. Press DEL and type in the new number.
?
Have a Go…
Evaluate
I made an error and meant 3.4 instead of 3.5. Without rewriting the whole calculation, find the new value of the expression.
Find 10 divided by the square of this above value.
?
?
?
A
B
C
More on using the ANS key.
Start by calculating ¿𝟏𝟏 .𝟖𝟓𝟖
Square your answer. ¿𝟏𝟒𝟎 .𝟔𝟏𝟐𝟏𝟔𝟒
Subtract your answer from 1000. ¿𝟖𝟓𝟗 .𝟑𝟖𝟕𝟖…
Square root your answer. ¿𝟐𝟗 .𝟑𝟏𝟓𝟑𝟏…
?
?
?
?
Cube Root
You should be familiar with meaning ‘square root’, i.e. what number squared gives this value?
What do you think is? Can you verify it using your calculator?
(the cube root of 8 is 2 because )
Using your calculator, determine:?
??? (said ‘pi’) has the
value 3.141… We’ll use it when we learn about circles. Use the ‘shift’ button to get it.
RED ORANGE GREEN BLUE
Use your diary coloured cards to vote for the correct answer in each question.
(Use the front of your diary for blue)
4567
Find the 5th digit of:
6789
Find the 5th digit of:
6015
Find the 5th digit of:
9876
Find the 5th digit of:
2468
Find the 5th digit of:Remember you can use the arrow and
DEL keys to modify an existing calculation.
0123
Find the 5th digit of:
(Interesting Fact: This calculation will give you the ‘golden ratio’)
0123
Find the 5th digit of:
Exercise 2Use your calculator to calculate the following. Write all the digits on your display.
Follow the sequence of instructions, making use of your ANS key. Write only the final value.
a. Calculate b. Cube root your answer.c. Divide your answer by 7.d. Subtract your answer from 10.
Calculator Fun!
How to get a list of square numbers:a. Press MODE then select choose ‘TABLE’.b. Type in , using the ALPHA key followed by the
red X in order to get the X.c. For ‘Start’ leave as 1 and press =.d. For ‘End’ type in 10 and press =.e. For ‘Step’ leave as 1 and press =.f. Voila! Use the arrow keys to scroll, and press
MODE -> 1 to return your calculator to normal.Can you generate other interesting sequences of numbers?
1 2
a
b
c
de
f
g
?
????
?
?
?
