Transcript P3 and 4 Numeracy and Mathematics

Skills Framework:
Number and number
processes
I can use addition,
subtraction,
multiplication and
division when solving
problems, making
best use of the
mental strategies
and written skills I
have developed.
MNU 1-03a
Expressions and
equations
I can compare,
describe and show
number
relationships,
using appropriate
vocabulary and the
symbols for equals,
not equal to, less
than and greater
than.
MTH 1-15a
When a picture or
symbol is used to
replace a number
in a number
statement, I can
find its value using
my knowledge of
number facts and
explain my thinking
to others.
MTH 1-15b
Refer to cluster common
language and
methodology.
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Add and subtract to 15 or
beyond, using concrete
material.
Link addition and
subtraction number bonds
to 15:
e.g. 7 + 4 = 11, 4 + 7 =
11, 11 – 4 = 7, 11 – 7 = 4
Identify the missing
number in a calculation:
3 +  = 4, 11 -  = 6, 2 +
=5+1
Recognise that the equals
sign signifies balance in a
number sentence.
Understand that the
adding or subtracting zero
does not change the
answer.
Understand and use
mathematical language:
digit, add, sum of, plus,
total, more than,
altogether, subtract, take
away, minus, less than,
difference between, how
many more than and
equals.
Understand that
calculations can be set out
both horizontally and
vertically.
Solve oral problems with
an emphasis on a range of
mental strategies e.g. put
the larger number first in
order to count on,
arranging 3 + 9 as 9 + 3
Solve word problems
identifying the appropriate
calculation.
Interactive Mental Maths:
This part of the lesson can be used to:
• Consolidate previous work
• Establish knowledge of an attainment target (e.g. Express
two-digit numbers to the nearest ten)
• Focus on skills needed in the main part of the lesson
• Practise mental calculations and rapid recall of number
facts in a variety of ways
• Establish new facts from known facts and explain the
strategies used
• Develop a particular strategy
Develop a particular strategy
Focus on discussing these, e.g.
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Put the larger number first in order to count on
•
Add or subtract 9 by rounding to ten
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Find a small difference between a pair of numbers by “counting on”
•
Use factors to multiply
(15 x 6 = (15 x 2) x 3 = 30 x 3 = 90)
•
Use factors to divide
(90 ÷ 6 = (90 ÷3) ÷ 2 = 30 ÷ 2 = 15)
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Multiply a 2 digit number by a single digit, multiplying the tens first.
Mental Calculation
38 + 47
• count on in tens from 40, 50, 60, 70, add 8 to get 78
and then 7 to get 85;
• first add 38 and 40 to get 78, then add on 7 to get 85;
• add 30 and 40 to get 70. Add 8 and 7 to get 15. Add
70 and 15 to get 85;
• add 38 and 2 (from the 47) to get 40, add 40 and 40 to
get 80 and the 5 left to get 85;
• add 40 and 50 to get 90, take away 2 (for the 38) to
get 88 and take away 3 (for the 47) to get 85.
Mathematics 5-14 National Guidelines SOED 1991 p82
What?
A balance of activities, e.g.
•interactive games (Show Me, What’s My Number?, Catch
the Calculation, Bingo, Flip Flaps, Follow Me)
•individual/ collaborative games (Snap, Numeracy Power
Towers, Human Number Line, Loops)
•computer based games (Education City, Hit The Button,
Table Trees,
http://www.wmnet.org.uk/wmnet/14.cfm?p=125,index&
zz=20060605123751308)
•written challenge once a week (‘keep the plates spinning’)
Show Me
Fan Cards
• show me 2/3 digits which total 8, 10..
• show me a 2 digit number which is odd
• show me a 2 digit number between 50 and 75
• show me a 3 digit number between 250 and 500
• show me a 2/3 digit number divisible by 4
• show me a 2 digit prime number
• I’m thinking of a number….
The Answer is…
What is the Question?
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whiteboards
whole class
exchange facts
homework
9 o’clock challenge/
challenge of the day, etc
5 + 15
16 + 4
- 40 + 60
4x5
2 x 10
0·2 x 100
30 - 10
100 - 80
1081·5 - 1061·5
40 ÷ 2
100 ÷ 5
400 ÷ 20
Challenge
Pass Back: start with 120
Step 1: Add 279
Step 2: Multiply by 3
Step 3: Multiply by 5
Step 4: Subtract 1392
Step 5: Multiply by 2
9186
Pick a Challenge
½ of 124
163 - 85
5 x 19
36  4
Around the World
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Question master and judge picked
Pupil who starts stands behind chair
Question asked and fastest ‘travels’
See how far you can travel!
•Heightened mental agility helps raise attainment in
Mathematics and Numeracy across the board.
•Makes learning and teaching more effective:
differentiating tasks means teachers have time to
support/ challenge pupils/ groups as appropriate
while others are actively engaged in purposeful
learning activities.
•Makes learners want to learn!
What Comes Next?
•Main body of lessonlooking at Learning Intentions/ Success Criteria and how
these are shared- linked to National Curriculum and local
guidance
Learning Intention: add two-digit numbers with and without carrying.
Success Criteria: I have answered my calculations by adding in columns, showing where I have carried a ten.
differentiation- balanced time for each group
assessment- balance of summative and formative
•Plenary- post it notes, exit questions, plenary cubes, learning logs,
self assessment comments- learners reflect upon own learners and
discuss next steps
P3/ 4 Learning. . .
Addition and Subtraction
Place Value: THTU
Decomposition
TU
26
+1 4
TU
34
-16
Multiplication
 2, 3, 4, 5 and 10 times tables
Rote Learning (e.g. chanting)
Scottish Method
(2 x 0 = 0, 2 x 1 = 2)
Multiplying tens and units- place value
Division
Sharing equally using concrete materials
Using table facts (2 x 6 = 12
so 12 2 = 6)
Dividing tens and units- place value
Remainders
Children consolidate learning through recording
into jotters
Problem Solving
Focus on developing the strategies:
•Act out the situation
•Look for a pattern
•Draw a picture or diagram or make a
model
•Guess, check and improve a solution
•Try a simpler case
•Produce an organised list or table
Problem Solving Skills
•Identify one or more strategies
to solve problems.
•Apply one or more strategies
to solve problems.
•Evaluate solutions to problems.
•Report on solutions
to problems.
•Apply known problem
solving strategies
across learning.
Problem Solving Example:
Today we are going to draw a picture or
diagram to help us to solve the problems.
STRATEGY
Sam and Jill put up a rope to mark the starting line for the sack race. The rope was 10 meters (m) long. They
put a post at each end of the rope and at every 2m. How many posts did they use? (Hint: Finish drawing the
picture to help you)
Understanding the Problem
· How long was the rope?
· How far apart were the posts?
Planning a Solution and Finding the Answer
Answer:
· Imagine now that they placed the posts only at the end of the rope. How many posts would there be?
Discuss with your shoulder partner and draw a picture on your whiteboard.
Answer:
· If they used 3 posts and each post was 2 m from another post, how long would the rope be?
Discuss and draw on your whiteboard.
· Try 4 posts. Draw a picture to see how long the rope would be.
Draw a Picture
Problem Extension
Mr. Brown put a square fence around his vegetable garden to keep the deer from eating his corn. Each side was 10 m. If
the posts were placed 2 m apart, how many posts did he use?
Helping at Home
Number bonds (adding, subtracting, multiplication facts,
division facts)
Paying for items, working out change, weighing and measuring
Challenge your child to work problems through themselves