maths literacy term 2 content and teaching ideas
TRANSCRIPT
Maths Literacy Term 2 Content and teaching ideas
Brought to you by Sharp and SMD Technologies
Agenda
• Sharpies
• Basics
• Topics• Finance
• Measurement
• Maps, plans and other representations
• Probability
• Data Handling
Sharpies
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• Earn points for attending this webinar.
• Exchange your points for gifts.
• Sign up – link
• Tell all your friends - link
Free Downloads and Resources
• Download the simulator• Link
• Download Geogebra• Link
• Worksheets• www.mathsatsharp.co.za• www.e-classroom.co.za• www.math-drills.com• https://www.mathx.net/• https://www.worksheetworks.com/ (one of my favourites for younger grades
and fully customisable)• https://www.mathwarehouse.com/sheets/ (FET mostly)
• ATP documents (link)
Calculator Introduction
• 640 Functions
• Upgraded for the CAPS and AP maths curriculum
• Amazing new functions include a multiplicand function, highest common factor, lowest common multiple and many more!
• Download the simulator from www.mathsatsharp.co.za
Calculator Basics
• Turn the calculator on
• 2nd Function – used to activate orange functions
• Turn the calculator off by pressing 2nd F and ON
• ALPHA – used to activate teal functions
• Mode – change to different modes
• BS – backspace – to delete something.
• Change – change between mixed, improper and decimal answers.
• Equals – to find an answer or used as enter.
Modes
• Press
• 0: Normal• Fractions, integers, probability,
trigonometry and much more
• 1: Stat• Single data, linear regression and more
• 2: Table• Functions but can also be used for
teaching finance and factorising
• 3: Complex• For doing complex number calculations
• 4: Equation• Solving various equations – linear,
quadratic and cubic.
Finance
Finance - Budgets
• A financial plan for your expected income and expenses
• Fixed expenses – those monthly costs that are the same every month.
• Flexible costs – those monthly costs that change from month to month, depending on how much you use.
• Income – how much money you are earning per month.
• Template
Till Slip
• Where purchased from
• Date and time
• Payment method
• How many litres
• Total cost
• Loyalty program
Online Receipt/Tax Invoice
• Date
• Items purchased
• Tax/ Vat amount
• Total due before vat
• After vat
• Amount paid
Tariff Systems
• Pay attention to the story details.
• Read your tables very carefully.
Chocolate Vanilla
Less than 100 R6 each R5 each
More than 100 R5.50 each R4.50 each
Simple Interest
• 𝐴 = 𝑃(1 + 𝑖 × 𝑛)
• Press
• E.g. A = 1000 (1+ 5% x n)
• Press
• Press
Hire Purchase
• The purchase of a “big ticket” (more expensive) item that is paid off through a deposit and simple interest.
• Steps:• Work out how much the deposit is. • Work out how much is left to pay
(this is your P value)• Work out your final amount to pay
(over the time given)• Divide this by the number of
months (or whatever period is given) to work out the monthly payment.
Example:
• Mandisa decides to purchase a lounge suite from House and Home. Here is a picture of the advert:
• a) If Mandisa pays a 15% deposit, how much will she have to take out a hire purchase loan for?
• b) House and Home charges her 22% interest per year, with the loan payable over 3 years. What is the total amount Mandisawill have to pay back?
• c) If she also pays a monthly insurance of R29 and administration fee of R13, how much will Mandisa have to pay a month.
• d) How much more is Mandisa spending because she bought the lounge suite on hire purchase, than paying the cash price.
a)
• If Mandisa pays a 15% deposit, how much will she have to take out a hire purchase loan for?
• Total amount = R 14 999
• Deposit = R14 999 x 15%
• On the calculator press
• Now we say R14 999 – R2 249.85
Bonus shortcut ☺
• Press
b)
• House and Home charges her 22% interest per year, with the loan payable over 3 years. What is the total amount Mandisa will have to pay back?
• So what do we have?
• A = ?
• P = R12 749.15
• i = 22%
• n = 3 years
• Formula: 𝐴 = 𝑃 1 + 𝑖 × 𝑛
• Substitute: 𝐴 = 12 749.15 1 +22
100× 3
• On the calculator:
• Press
c)
• If she also pays a monthly insurance of R29 and administration fee of R13, how much will Mandisa have to pay a month.
• First, we find how many months Mandisawill have to pay for the lounge suite:
• 3 x 12 = 36 months
• Next we divide the total found in b) by 36:• 21 163.589 ÷ 36
• = 587.88
• Press
• Now we add the monthly total calculated to the insurance and admin fee:
• = R587,88 + R13,00 + R29,00
• = R629,88
d)
• How much more is Mandisaspending because she bought the lounge suite on hire purchase, than paying the cash price?
• She pays over 36 months• = R629,88 x 36
• = R22 675,59
• How much more means subtract the original from the end total (don’t forget the original deposit)
• = R22 675,59 + R2 249,85 – R14 999
• = R9 926,44
Inflation Rate
• The inflation rate is the average percentage increase in a price basket over a certain period.
• We use the percentage increase formula:
• 𝑖𝑛. 𝑟𝑎𝑡𝑒 =𝑛𝑒𝑤 𝑝𝑟𝑖𝑐𝑒 −𝑜𝑙𝑑 𝑝𝑟𝑖𝑐𝑒
𝑜𝑙𝑑 𝑝𝑟𝑖𝑐𝑒× 100
• E.g. 𝑖𝑛. 𝑟𝑎𝑡𝑒 =15.88 −13.79
13.79× 100
• Is….
Fuel Price Date
R 13.79 02-01-2019
R 13.86 06-02-2019
R 14.60 06-03-2019
R 15.94 03-04-2019
R 16.48 01-05-2019
R 16.57 05-06-2019
R 15.61 03-07-2019
R 15.72 07-08-2019
R 15.83 04-09-2019
R 15.79 02-10-2019
R 15.66 06-11-2019
R 15.88 04-12-2019
Exchange Rates
• Pay attention to the “direction” of the exchange.
• E.g. $1 = R14.52• Small to big
• If we have $10, how many Rands do we have?
• Small to big so we multiply
• If we have R1000, how many Dollars can we buy?
• Big to small so we divide
• Exchange rate = R1 = $0,069• Big to small
• If we have R10 how many Dollar do we have?
• Big to small, so we multiply
• If we have $100, how many Rands do we have?
• Small to big so we divide.
• Note: going in the same direction means multiply, going in the opposite direction means divide.
Measurement
ConversionsE.g. Ounces to grams• 23 ounces:
• Press 23
•
• Press until you find oz → g
• Press
• There are 44 different conversions.
DMS / Time Functions
• Changing minutes to hours
• E.g. How many hours are 470 minutes?
• Press to clear any chain calculations
• Press
• Press to change it into fraction or decimal format (remember to use your button).
29
DMS/ Time Functions
• Finding time in a speed-distance-time calculation.
• E.g. How long does it take to travel 450km at an average speed of 117km/h?
• Press
• Press
• Press
• The answer is 3 hours, 50 minutes and 46.154 seconds.
30
DMS / Time Functions
• Adding / Subtracting Time
• E.g. find the length of time spent on a bus if the bus left at 9.45 and arrived at 12.32.
• Press
• The answer is 2 hours and 47 minutes
• To change back to a fraction notation press
31
Calculating BMI• BMI = Body Mass
Index• It measures your level of weight
health.
• BMI = 𝑤𝑒𝑖𝑔ℎ𝑡
ℎ𝑒𝑖𝑔ℎ𝑡2
• Weight in kg
• Height in m
• E.g. Tony weighs 120kg and is 1.85m tall. What is his BMI?
Calculating Surface Area
• Formula for cube: 6𝑙2
• Formula for rectangular prism = 2ℎ𝑙 + 2𝑏ℎ + 2 𝑙𝑏
• E.g. find the surface area of a tissue box that measures 12cm across, 10cm high and 20cm wide.
• 𝑆𝐴 = 2 10 20 +2 12 10 + 2 12 20
• 𝑆𝐴 = 1 120 𝑐𝑚2
Maps, Plans and Other Representations
Scale
• A ratio calculation.
• E.g. map scale 1cm = 2km.
• If you measure 6cm on the map, what is the measurement in real life?
• If a park measures 3km by 4km what will its area be on the map?
Giving Directions
• Make it fun ☺
• This ties into language and life skills so its important that students can do this.
• Also – taking directions is an important skill.
Probability
Probability
• Press
• The random function:
• Press• 0: Random
• Random decimals between 0 and 1 to 3 decimal places
• 1: R.Dice• Random numbers between 1 and 6
• 2: R.Coin• Heads and Tails displayed as 0 or 1
• R.Int(• Random whole number between
any two numbers given
Theory
• Theoretical probability• The expected outcome based
on the information we have• E.g. rolling a 1 on a 6-sided
dice has a 1
6chance.
• Rolling a 7 on a 6-sided dice has 0 chance because 7 is not on the die.
• Relative frequency• The actual results based on the
number of “experiments” performed.
Die Roll Tally Total
1
2
3
4
5
6
Tree Diagrams
• Give a visual representation of the possible probabilities
• With replacement
• Means that the probabilities stay the same across the branches.
• Without replacement
• Means that the probabilities change based on what happened in the previous round.
• A spinner with five equal parts (numbered 1 to 5) is spun and another spinner with three equal parts (with the colours red, blue and yellow) is spun afterwards.
Two-Way Tables
• Show us the relationship between 2 categorical variables
• Two ways to read probabilities from the table:
• Big picture (one criterion)• E.g. What is the chance of
selecting a man from the group interviewed?
• Details. (2 criterion)• E.g. What is the chance of
selecting a woman who is studying maths from the group interviewed?
Men Women Totals
Maths 46 25 71
Math Lit 28 49 77
Totals 74 74 148
Some random things to do
• Create tally tables
• Create a poll on zoom
• Play snap in break away rooms
• Use it to test multiples, finding factors and so on.
• My favourite is the lottery• Which you could do through the
chat function so no cheating happens ☺
Data Handling
Collecting Data
• Keep an eye out for biased data.
• Sample vs population
• Size of sample, vs size of population
• How does your choice of sample affect your outcome?
Displaying Data: Pie Chart
• To calculate the angle of one slice of pie:
• 𝑠𝑙𝑖𝑐𝑒 =𝑐𝑜𝑙𝑜𝑢𝑟
𝑡𝑜𝑡𝑎𝑙× 360
• 𝑅𝑒𝑑 =31
190× 360
• = 59°
• To calculate the percentage of one slice of pie:
• 𝑠𝑙𝑖𝑐𝑒 =𝑐𝑜𝑙𝑜𝑢𝑟
𝑡𝑜𝑡𝑎𝑙× 100
• 𝑅𝑒𝑑 =31
190× 100
• = 16.32%
Colour Frequency
Red 31
Blue 33
Orange 42
Green 40
Pink 44
Total 190
Box and Whisker Plots
• First we need to find our 5-number summary:
• Minimum
• Quartile 1
• Median
• Quartile 3
• Maximum
• Then we draw our box and whisker plot
This Photo by Unknown Author is licensed under CC BY-SA
Example
• 52 53 71 75 75 76 79 82 96
• So:• Minimum = 52
• Quartile 1 = 62
• Median = 75
• Quartile 3 = 80.5
• Maximum = 96
On the calculator
• Press
• Type in the data:
• Clear the table by pressing
• To find the 5-number summary:
• Use your down arrow key to get to the 5-number summary:
Example• Given below is the box and whisker plot of the data for Danielle’s scores (out of 50) she received for
the 20 different dance routines she did over the last 6 months.
• a) Give the range of scores Danielle receives.
• b) How many scores did Danielle get between 24 and 41?
• c) How many scores did Danielle get between 17 and 41?
• d) What can you say about the spread of Danielle’s scores?
• e) If Danielle’s top 25% of scores occurred in the last two months, what can we say about Danielle’s dancing?
• f) In order to go through to the next round, you need to score more than 40. In how many competitions did Danielle go through to the next round?
Summarising Data
• Mean – the average
• Mode – appears the most
• Median – in the middle
• Range – highest result minus the lowest result.
Comments
• EL-W506T is the perfect calculator for AP and IEB maths curriculum
• Can be ordered in bulk from SMD directly at better than retail pricing.
• Available at Takealot, PNA, Loot, Makro and more!
Junior Calculator
• EL-W535SA – cheaper and 422 functions
• Ideal for grade 7 – 9 students
• 500 000 calculators given to No-Fee school students in Gauteng by the department of education
• With a 40% improvement between the pre- and post-tests after training.
Thank you for your valuable time!
Free worksheets and simulator:
www.mathsatsharp.co.za