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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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.

https://cdn-goldreefcity.pressidium.com/wp-content/uploads/2020/10/grctp19_parkmap_01112019.pdf

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