Parent Numeracy Information Evening
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Parent Numeracy Information
Evening
Welcome and introduction
Visual Snapshot
What exactly do we teach and when, and the importance of
Place Value thinking
Basic Facts
IKANs
Gloss
Problem Solving Strategies
Break into groups – Problem Solving Activities / Questions
Come back together for any further questions and feedback
Parent Numeracy Information
Evening
Visual Snapshot
of Maths
throughout the
school
What exactly do we teach and when Year 1 Jess Year 2 Steph Year 3 Sue/Mary Year 4 Tracey Year 5 Lynley Year 6 Jillian/Lynne
How many? Counting sets
Year 2 What we teach and how: Screening to Imaging (Stage 3) To encourage children to move away from needing to see the objects to count we screen them (momentarily hide them: look, hide, think, answer, check by looking). Counting on and back (Stage 4) Finding the biggest number and putting it “in our head” then count on in ones to add, or count back to subtract.
Year 2 What we teach and how: Teaching tens and ones: Numbers 10-100. Tens in decades Unpacking and packing out numbers with materials. Bundling Teaching groupings 10 and (teen numbers) to 10 ( 7+3, 1+9 etc) to 20 (i.e. 18+2, 16+4)
In year 3 there is a big shift from counting on and back from a number when adding and subtracting, to using their knowledge of numbers in other ways. It can be a lengthy and difficult transition for some children to make.
Initially children are taught to split numbers into parts and then rejoin them: e.g. to work out 9+4=? We can take 1 from the four and add it to the 9 to make a ten. We have 3 left to add to the 10. 10+3=13 26 + 9 can be solved as 26 +10 =36 36 -1=35 We use the opposite for subtraction 26-9 is shown as 26-10=16 16+1=17
Children can use their knowledge of doubles to solve problems E.g. 5+6 is solved as 5+5=10 10+1=11 Or 6+6=12 12-1=11
Rapid recall of facts to 10 is important at this stage to split numbers into parts. e.g. 37+ 7 7 can be split into 5+2, 2+5, 6+1, 1+6, 3+4, 4+3 3+4 is selected to get to the nearest 10 37+3=40 40+4=44 In addition we go up to nearest ten and in subtraction we go back to the nearest ten. 43-7 43-3=40 40-4=36
Children are taught to solve problems using place value to count in tens from any number. e.g. 34+30 44, 54, 64 42-20 42,32,22
• To progress through this stage, children need to read any number to 1000, to sequence and order numbers, have an understanding of place value and know what the digits in numbers mean. They must know addition and subtraction facts to 10 and doubles and halves to 20. • In order to have a sound understanding of place value children need to know the groupings of tens in two and three digit numbers e.g. there are 32 tens in 320.
It is easier for children to solve problems if the context is relevant to their experiences.
Year Four
• In Year 4 we build on the knowledge and
strategies introduced in Year 3.
• Place value addition and subtraction with
larger numbers.
e.g., 33 + 16 as or 44 – 21 as
33 + 10 = 43 44 – 20 = 24
43 + 6 = 49 24 – 1 = 23• We also build on the strategy of ‘making tens’ –
or ‘tidy number’ (a ‘tidy’ number ends in a zero).
• Tidy number addition and subtraction with larger
numbers.
e.g., 29 + 18 as or 54 – 16 as
1 17 10 6
30 + 17 as 54 – 10 = 44
30 + 10 = 40 44 – 6
40 + 7 = 47
4 2
44 - 4 = 40 then 40 – 2 = 38Year Four continued…
• We also work on groupings to 100
the ones make a 10
E.g., 43 + 57 = 100
the tens make 90
• And rounding 3 digit numbers to the nearest
10 or 100 (swedish rounding system 1-4 down and 5-9 up)
E.g., 246 250 (10s) or 246 200 (100s)Year 5 What we teach and how. Level 2 - Level 3 Stage 5 – 6 Use place value knowledge to add 3 digit numbers • Compensation 365 + 199 = 365 + 200 – 1 565 – 1 = 564 • Tidy Numbers 436 + 247 = 433 + 250 433 + 250 = 683 • Standard Partitioning 354 + 467 = 300 + 50 + 4 + 400 + 60 + 7 300 + 400 = 700 50 + 60 – 110 4 + 7 = 11 700 + 110 + 11 = 821
Year 5 What we teach and how Level 2 - Level 3 Stage 5 – 6 Use place value knowledge to subtract 3 digit numbers • Compensation (take away) 365 – 199 = 365 – 200 + 1 165 + 1 = 166 • Standard Partitioning (take away) 453 – 236 = 453 – 200 – 30 – 6 253 – 30 – 6 = 223 – 6 223 – 6 = 217 • Tidy Numbers (difference) 468 – 253 = 465 – 250 465 – 250 = 215 Extend place value into larger numbers
Year 5 Addition and Subtraction using Place Value partitioning Addition 46 + 27 = 46 + 20 + 7 = 66 + 7 = 73 35 + 28 = 35 + 20 + 8 = 55 + 8 = 63 126 + 317 = 126 + 300 = 426 + 10 = 436 + 7 = 443 Subtraction 62 – 28 = 62 – 20 = 42 – 8 [2 + 6] = 42 – 2 = 40 – 6 = 34 73 – 29 = 73 – 20 = 53 – 9 [3 + 6] = 53 – 3 = 50 – 6 = 44 146 – 98 = 146 – 90 = 56 – 8[6 + 2] = 50 – 6 = 44 – 2 = 42
Year 6 Place value subtraction and addition change unknown to solve it. Farmer Brown had 147 cows. 63 cows were in the barn. The rest were in the paddock. How many cows were in the paddock?
Basic Math Facts
Basic Facts are a vital part
of Maths learning to help
children solve problems
more quickly and expand
their number sense.What is a Basic
Math Fact ?
An Addition or Subtraction Basic Math Fact is
a question such as 3 + 4 or 6 -2 that a child
should know quickly.
This also covers questions such as (start
unknown)?+3=10 and (change unknown)
7+?=10. If a child can say the answer within a
couple of seconds, this is usually considered
mastery of the fact.Basic Facts form the building blocks for higher-level Math concepts. Skills such as adding and subtracting larger numbers, telling time, counting money, measurement, long multiplication and division are just a few of the concepts that all children will encounter fairly early. If children have mastered basic facts, these concepts will be significantly easier and they will be better equipped to solve them more quickly.
By learning Math Facts, your child will also develop a keen number sense. This means that they will better understand the relationship between numbers. For example, it is important for your child to see that 6 - 2= 4 because 2 + 4 = 6. They should also develop an understanding of how far numbers are away from the nearest tens, which will aid in such skills as estimating and rounding.
It is important that children move from counting strategies to automaticity (rapid recall) of Basic Facts so they can use them as a tool to solve more difficult Math problems. If they must count to find the answer every time they need to add two numbers, it will take a much longer time to get to the final answer. They will forget the problem they are trying to solve.
If your child is struggling with
recalling Basic Facts each day, they
may lose confidence in their Math
abilities.
Sometimes, this can lead to a loss of
interest or effort in Maths.
They will struggle to achieve in higher
level Maths without knowing these.What about the calculator and computer
argument?
Yes, calculators and computers play an important
role in Math education today, but it is still
important for a child to know their Basic Facts to
be able to do mental computation.
They will not always have a computer nearby, and
once they know them, they will find that doing it
mentally is a lot faster.
Try practising a few every day and watch the
difference.IKANs These are the tests that the children are expected to sit to check that they have automatic recall of basic number knowledge. What is it? How is it administered? What does it tell us? How do we use it?
GLOSS What is it? How is it administered? What does it tell us? How do we use it?
Practical Problem Solving Strategies
Problem Solving
Problem Solving? What is a Problem? A question that motivates you to search for a solution. It is a problem because you don’t know straight away how to do it. What is Problem Solving? Mathematical problem solving is about finding solutions and not just answers to mathematical problems. method + answer = solution. At a basic level are four steps that you need to go through in solving most mathematical problems. These are: • understand and explore the problem • find a strategy • use the strategy to solve the problem • look back and reflect on the solution. By solving problems students get a much better feel for what mathematics is all about, what it can do and how it does it.
What makes a good problem?
1. Suitable and engaging context
2. Relevant maths content - challenging but not too difficult (a problem for
one person may not be a problem for someone else)
3. Generates higher order thinking skills through richer tasksWhy Teach Problem Solving There are many benefits to teaching problem solving. These include: • it bases students’ mathematical development on their current knowledge • it is an interesting and enjoyable way to learn mathematics • it is a way to learn new mathematics with greater understanding • it produces positive attitudes towards mathematics • it makes the student a junior mathematician • it teaches thinking, flexibility and creativity • it encourages co-operative skills • it is a useful way to practice mathematical skills learned by other means • it is similar to the approach used in other curriculum activities.
Act it out or
Guess, check
use equipment
and improve
Problem Solving
Tools (Strategies)
Draw a diagram
Make a list
or picture
or table
Think!
What do I already
know about this?Level one problem Measle Spots Poor Pam has measles. She has one spot on her chin, one spot on each leg, one spot on each arm and one spot on her tummy. How many measles spots does Pam have? The next morning, Pam wakes up with even more spots! Now she has two on her chin, two on each arm and each leg, and two on her tummy. How many spots does she have now?
A Giant Mystery
(Unit of Work on nzmaths)
If this is a handprint of
the giant - how tall is the
giant?“As tall as my uncle. He’s really tall!”
“How many hands tall am I?”
“The giant will be 10 giant hands tall”“We will need 2 more.”
“This is how tall the giant will be.”
Collaborative Problem Solving Activities and
Developing Class Norms for working in groups
Questions to discuss with
the students.
• Why is it useful to work
in groups?
• How will we work
together in groups at
maths time?Level 4 and 5 Problems Problem 4: Towers (Level 4) Tom likes to build towers. He has a collection of black cubes and white cubes. Putting different cubes on top of one another forms a tower. If the height of a tower is the number of cubes used in that tower, how many different towers can be made which are of height one? how many different towers can be made which are of height two? how many different towers can be made which are of height three? how many different towers can towers be built for any particular height? Problem 5: Tennis (Level 5) In a round robin tennis championship, 20 people are to play each other. How many games need to be played? The organisers decide that that's too many games and so instead they use a knock-out competition. How many games are played under this system?
A Rabbit Run You have 20 metres of fence to make a run for your pet rabbit. What shape will make the largest area for it to run around in and have the most grass to munch on? Materials available: •20 popsicle sticks •squared paper •blank paper and ruler
Practical Problem
Solving and
questionsWrap Up – Feedback - Questions
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