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One Pathway for Teaching Percentages. Level three Number and Algebra Knowledge NA3-5 Know fractions and % in everyday use Strategies NA3-1 Use a range of additive and simple multiplicative strategies with whole numbers,fractions,decimals and %. Level four Number and Algebra Knowledge - PowerPoint PPT Presentation
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Where do Percentages sit in NZC?Level three Number and
AlgebraKnowledgeNA3-5• Know fractions and % in
everyday use
StrategiesNA3-1• Use a range of additive
and simple multiplicative strategies with whole numbers,fractions,decimals and %
Level four Number and Algebra
KnowledgeNA4-5• Know the equivalent
decimal and % for everyday fractions
Strategies• NA4-3Find
fractions,decimals and % of amounts expressed as whole numbers, simple fractions and decimals
Where do Percentages sit on the Number Framework?
KnowledgeStage 7• The student recalls
fraction,decimal,% conversions for halves,thirds,quarters,fifths and tenths.
Stage 8• The student recalls
fraction, decimal,% conversions for given fractions and decimals, eg 9/8 = 1.125 = 112.5%
StrategiesStage 7• The student can find simple
equivalent fractions and rename common fractions as decimals and %
Stage 8The student chooses from a
wide range of mental strategies to solve problems,
Eg 65% of 24 (50% = 12, + 10% = 2.4 ,+ 5%=
1.2) so the answer is 12 + 2.4+ 1.2 = 15.6)
partitioning %
Some starters
Put an amount on the board eg $40
Students make that amount by as many different % as possible
Eg• 100% of 40 = 40• 50% of 80 = 40• 25% of 160 = 40• 200% of $20 = 40
100%$250
10% 5% 15% 10 2 3
100%$60
50% 25% 75%
100%$2
25% 5% 30%
100% 10%5.5kg
5% 1%
100% 10% 5%9
2.5%
100%$250
1% 2%
20%$250
10% 15%
100%90kg
80%
30%24kg
10% 11%
Box trails
This is a simple versionStudents draw up a 3 x 3 grid and pick 9 of these
0.5 0.15 0.7 0.01 0.10.9 0.2 2.1 1.5 0.1251.3 0.175 0.03 0.25 0.40.6 0.75 0.3 0.37 0.8
Call out % or the decimal and students pick the %
0.5(50%) 0.15(15%) 0.7(70%) 0.01(1%)0.1(10%)
0.9(90%) 0.2(20%) 2.1(210%) 1.5(150%)0.125(12.50%)
1.3(130%) 0.175(17.50%) 0.03(3%) 0.25(25%)0.4(40%)
0.6(60%) 0.75(75%) 0.3(30%) 0.37(37%)0.8(80%)
• Knowledge is essential• Equipment very important at the start• Teach the strategy reasonably quickly and
then………• Application is crucial - students need lots of
opportunities to make the strategies work for them.
• Context• Revisit ideas frequently
Fraction, percentage conversion
Use the 100 square to find the percentage to match the fraction
1/10 10% 1/20
1/5 1/25
1/4 2/10
1/8 3/5
3/4 1/100
Percentage Strips Imagine that the 100% is a row of elastic that when stretched stretches evenly. The 50 row is just the first 50 beads on the elastic stretched evenly to be the same length as the 100.
10 out of 50 maps on to 20% 35 out of 50 maps on to 70%
Can you use this double number line to map as many values out of 60 as you can onto a percentage.
0 30 60 0% 50% 100% Work through Hot Shots Book 7 – Teaching fractions, decimals and percentages
What we going to look at to day?
• How to use double number lines to answer % problems
• Using the teaching model• What our students need to know to do this work?
• Resources for practising and sustainability
Teaching progression
Materials
Images
Knowledge
Start by:•Using materials, diagrams to illustrate and solve the problemProgress to:•Developing mental images to help solve the problemExtend to:•Working abstractly with the number property
PercentagesWhat type of problem do we expect to meet in years 9/10 ?
•Finding one number as a % of another•Finding a % of a quantity•Finding the total given a % of the total•Increase/decrease by a %•Finding the original after an increase/decrease•GST and other problems
0% 20% 100%
20% of 150 is
Question (in context)
The local dairy farmer is selling 20% of his herd of 150 cows. How many is he selling? Rewrite in
maths language
150
How do we use the lines to get the answer?
0% 20% 100%
150
20 x 5 = 100
150 divided by 5 = 30
0% 20% 100%
150
Find 10% : 150 divided by 10
So 10% = 15
So 20% =30
In a berry mix there are 30% strawberries and 20% raspberries and the rest are blackberries. In a 500gm punnet of berries what weight are the strawberries?
There are 30 students in 9CT and 40% are girls. How many girls are there in the class?
40% of 30 is
30% of 500gm is
Abigail is working on a set of 50 number problems and she has just finished question 28. What % of the questions has she finished.Mr Sharp spent the day at the races and his horses were placed in 8 out of 20 races. In what % of the races was he successful?
28 is % of 50
8 is % of 20
30% of the swimming team are girls. If there are 18 girls . How many are in the team altogether?
18 is 30% of
Activities to practice these skills
• Activity 1
• Activity 3 Note: these are not teaching activities
FIO’s• Fully grown Page 9• The Percentage Game page 14/1• Laser Blazer page 12/13
What do students need to be able to do before we use
this?
Have a sound knowledge of percentage
To know answers must be in context with correct
unitsCommon factors and lowest common
multiples
Recall of all multiplication and division facts
•AM/AP
Discounts, markups, inflation etc
Decreasing by a %Sarah went shopping for a new bike which cost $350 When she got to town there was a sale and she got 20% off the price, What did she pay?
Did she pay more or less?
How much less?
So instead of paying 100% she only paid?
Show all this on the number lines
0% 80% 100%
$350
Increasing by a percentage
The value of a $400 antique vase has been increased by 20%. What is its value now? What questions do we ask?
120% of 400 is
Or divide 400 by 10 (to get 10%) and multiply by 12.
X 4 X 40% 120%100%
$400
Moving to number properties20% of 150 is ?
Now is time to link what they know about % with decimal fractions.
How else can we write this?
What does 20% actually mean?
How could we do this without the number line?
For some students this stage will be a long time coming! For others they will tell you.
Now might be the time to bring in a calculator and some more “awkward” q’s
Finding the original amount after a % increase/decrease
Example: After an increase in his weekly wage of 20% Joe has $480.What was his wage before the increase?
Talk through and write the maths question
$480 is 120% of Complete a number line with this information
0% 100% 120%
$480