Year 5 Mental Calculation

1
Year 5Mental Calculation
2
Objectives

• Establishing end-of-year learning expectations
  and objectives, and the key aspects of
  mathematics that children need to learn to make
  progress in a particular aspect of mathematics.
• Identifying and tracking progression and
  reviewing the pre-requisite knowledge, skills and
  understanding children need to make secure
  progress
• Looking at the teaching and learning approaches
  that might be used to secure learning
• Planning classroom-based activity and assessment
  and teaching opportunities

3
Calculation
169 6 How did you do this? Explain to your
partner how you did it.
4
Knowledge, skills and understanding

• Know multiplication facts
• Be able to use multiplication facts to find other
  facts such as 20x6120 can be derived from 6x212
• Be able to partition numbers in different ways
  including examples such as 169 is 12049
• Know that division is equal grouping
• Recognise that division is the inverse of
  multiplication
• Check if the calculation can be carried out
  mentally

5
Learning Overview

• Counting and understanding number Children are
  building their counting skills such as counting
  in decimals to enable them to understand how to
  use a number line with decimals as a tool for
  thinking about calculation. They are building a
  sense of where numbers fit with one another.
• Knowing and using number facts They are deriving
  number facts they dont know from ones that they
  do know. In particular there is an emphasis on
  using whole number calculations in order to be
  able to work with decimals. They continue to
  build the facts that they can recall and
  strengthen the connection between multiplication
  and division.

6
Learning Overview

• Calculating They are using mental calculation as
  a first resource. Children use partitioning to
  multiply and divide whole numbers by a one-digit
  number.

7
Using and Applying

• TU times U
• TU divided by U
• TU plus TU (U.tenth add U.tenth) (HTU)
• TU subtract TU ( U.tenth take away U.tenth)

Use only the digits 1, 6, 3, 4,
Which number where
8
Arrays
ITP
9
Importance of Arrays

• What experiences is it important that children
  have prior to Year 5 to develop their
  understanding of an array?
• Children need to have experience of using smaller
  arrays and playing with different ways of cutting
  the array up
• Children need to see the effectiveness of adding
  a row to an array and how this changes the
  calculation
• Children need to see the effect of adding a
  column to an array and how this changes the
  calculation
• The array can be used to create a table with all
  the multiplication facts written in the
  appropriate place on the grid.

10
Using Known Facts

• Look at the learning overview for Year 5 and
  highlight where What they know helps children
  to do other calculations.
• How can you support children with making
  connections between calculations?

11
Feedback

• Children apply to decimals their knowledge of
  addition and subtraction facts involving one- and
  two-digit whole numbers. They know that 7  8 is
  15 and therefore that 0.7  0.8 is 1.5 and
  0.07  0.08 is 0.15. They work out half of 7.4 by
  halving 74 and dividing by 10 they double 0.75
  by doubling 75 and dividing by 100, taking care
  that the decimal point is in the right place in
  the answer 1.50 or 1.5.
• Children derive families of calculations such as
  8  3, 80  3, 800  3, 80  30, 80  300, They
  derive division facts such as 56  8 and apply
  this fact to calculations such as 560  8 and
  560  80.

12
If I know . , then ..
15 16 240
24 16 1.5
240 16 15
30 8 240
240 8 30
3 8 24
8 3 24
15 8 120
24 3 8
0.3 8 2.4
15 4 60
24 8 3
3 4 12
13
Key Messages

• We need to be aware of the prior learning that
  has occurred for children to access the learning
  in each year group
• Think about the all the mathematics learning that
  contributes to a particular outcome

14
Good mathematics teaching

• Carefully planned blend of approaches
• Children are challenged to think
• They like to be challenged and enjoy the
  opportunities to practice and apply their
  learning
• They are happy to share their ideas and to
  explain their reasoning and methods
• Broad repertoire of teaching and organisational
  approaches

15
ICT

• Number dials (ITP)

• Multiplication Grid (ITP)

16
Cubes Sheena loved to count. One day Ms Small
put some cubes on Sheenas table. Sheena began to
count the cubes. She reported the following to Ms
Small When I arrange the cubes in threes I
have one left over, when I arrange in fours I
have one left over and when I arrange in sevens I
have none left over. How can Ms Small work out
how many cubes Sheena has?
17
Questioning techniques

• Is there more than one answer? How do you know?
• What numbers have one left over when divided by
  three?
• What numbers have one left over when divided by
  four?
• What numbers have one left over when divided by
  both four and three?
• What numbers have one left over when divided by
  twelve?
• Does this work for other numbers?
• Are there times this doesnt work
• If there where two left over when I counted in
  threes would the answer be one more?

18
Games

• Games allow children to practice their mental
  calculation.
• Games will offer a motivational approach for some
  children and be a natural development of other
  aspects of play
• Games encourage children to be more autonomous in
  their decision making
• Games allow some discussion of mathematics
  although this can be improved by encouraging
  children to play in pairs
• Games can give an opportunity to apply reasoning

19
Good Mathematical Classrooms

• Children discuss their mathematical thinking
• Children listen carefully to both the teacher and
  other children and offer comments on what has
  been said
• Children support each other in understanding
• Children explain each others methods to each
  other

20
Good Mathematical Classrooms

• The teacher does not always act as sole arbiter
  for what is right or wrong..
• The teacher elicits alternative solutions and
  methods for one problem
• The teacher encourages elaboration.
• The teacher promotes collaborative problem
  solving