mastery mathematics medium term planning year 6 phase 1 ...€¦ · post sats project work ongoing...

Mastery Mathematics Medium Term Planning

Year 6 PHASE 1

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Year 6 Overview

Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11

Phase 1 Number and Place Value

Addition and Subtraction Multiplication and division

Fractions Geometry Pos & Dir

Phase 2 Fractions Decimals and percentages

Geometry Properties of shape

Measurement Area, perimeter, volume

Geometry and statistics

Phase 3 Fractions Ratio & proportion

Algebra SATs revision SATs week

Phase 4 (EoY)

Post SATs project work

Ongoing throughout the year:


Year 6 PHASE 1

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Year 6 Phase 1 Objectives Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11

Ma

in S

es

sio

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Number: place value Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit. Round any whole number to a required degree of accuracy. Use negative numbers in context, and calculate intervals across zero. Solve number and practical problems that involve all of the above

Addition, subtraction, multiplication and division Solve addition and subtraction multi step problems in contexts, deciding which operations and methods to use and why. Multiply multi-digit number up to 4 digits by a 2 digit number using the formal written method of long multiplication. Divide numbers up to 4 digits by a 2 digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions or by rounding as appropriate for the context. Divide numbers up to 4 digits by a 2 digit number using the formal written method of short division, interpreting remainders according to context. Perform mental calculations, including with mixed operations and large numbers. Identify common factors, common multiples and prime numbers. Use their knowledge of the order of operations to carry out calculations involving the four operations. Solve problems involving addition, subtraction, multiplication and division.

Fractions Use common factors to simplify fractions; use common multiples to express fractions in the same denomination. Compare and order fractions, including fractions > 1 Generate and describe linear number sequences (with fractions) Add and subtract fractions with different denominations and mixed numbers, using the concept of equivalent fractions. Multiply simple pairs of proper fractions, writing the

answer in its simplest form [for example ] Divide proper fractions by whole numbers [for example

] Associate a fraction with division and calculate decimal fraction equivalents [ for example, 0.375] for a simple

fraction [for example ] Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

Geometry: position and direction Describe positions on the full coordinate grid (all four quadrants). Draw and translate simple shapes on the coordinate plane, and reflect them in the axes.


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S &

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s Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11

Year 5 Fractions Objectives: Compare and order fractions whose denominators are multiples of the same number. Identify, name and write equivalent fractions of a given fraction, represented visually including tenths and hundredths. Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number

Add and subtract fractions with the same denominator and denominators that are multiples of the same number. Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams.

Read and write decimal numbers as fractions [ for example 0.71 = . Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

Year 6 Objectives – Addition, subtraction, multiplication and division


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Year 6 MTP – Phase 1

Domain NC Objectives

Example tasks fluency Example tasks reasoning Example tasks problem solving

Number and place value

Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit.


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Round any whole number to a required degree of accuracy.


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Example tasks fluency Example tasks Reasoning Example tasks problem solving


Use negative numbers in context, and calculate intervals across zero.

Additional Guidance:

Children should be able to place a variety of numbers onto a numberline accurately, or estimate their position on a blank numberline (this will help them to visualise rounding). Use arrow cards to secure place value understanding of large numbers. Available to print here:

http://www2.research.uky.edu/pimser/p12mso/pub/Forms/AllItems.aspx?RootFolder=%2Fpimser%2Fp12mso%2Fpub%2F2008-

http://www2.research.uky.edu/pimser/p12mso/pub/Forms/AllItems.aspx?RootFolder=%2Fpimser%2Fp12mso%2Fpub%2F2008-09%20Archives%2FHopkinsville%20Math%20Leadership%20Support%20Network%2008-09%2FAugust%2FPlace%20Value%20Arrow%20Cards&FolderCTID=&View=%7BB5C77598-8CC9-4CB1-B08B-0F73CC77E89F%7D


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09%20Archives%2FHopkinsville%20Math%20Leadership%20Support%20Network%2008-09%2FAugust%2FPlace%20Value%20Arrow%20Cards&FolderCTID=&View=%7BB5C77598-8CC9-4CB1-B08B-0F73CC77E89F%7D

http://www2.research.uky.edu/pimser/p12mso/pub/Forms/AllItems.aspx?RootFolder=%2Fpimser%2Fp12mso%2Fpub%2F2008-09%20Archives%2FHopkinsville%20Math%20Leadership%20Support%20Network%2008-09%2FAugust%2FPlace%20Value%20Arrow%20Cards&FolderCTID=&View=%7BB5C77598-8CC9-4CB1-B08B-0F73CC77E89F%7Dhttp://www2.research.uky.edu/pimser/p12mso/pub/Forms/AllItems.aspx?RootFolder=%2Fpimser%2Fp12mso%2Fpub%2F2008-09%20Archives%2FHopkinsville%20Math%20Leadership%20Support%20Network%2008-09%2FAugust%2FPlace%20Value%20Arrow%20Cards&FolderCTID=&View=%7BB5C77598-8CC9-4CB1-B08B-0F73CC77E89F%7D


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Addition, subtraction, multiplication and division

Solve addition and subtraction multi step problems in contexts, deciding which operations and methods to use and why.

Additional Guidance: Bar Model for understanding word problems An interactive teaching program for modelling word problems: http://www.thinkingblocks.com/ Part-Part-Whole Problems

http://www.thinkingblocks.com/


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Lily and her brother, Scotty, were collecting cans for the recycling drive. One weekend they collected 59 cans and the next weekend they collected 85 cans. How many cans were collected in all?

Cole had 238 blocks. 100 of them were yellow. If all Cole's blocks are either blue or yellow, how many were blue?

Join or Separate Problems Maria had $20. She got $11 more dollars for babysitting. How much money does she have now?

Maria had $31. She spent some of her money on a new CD. Maria now has $16 left

Comparison Problems Tameka rode on 26 county fair rides. Her friend, Jackson, rode on 19 rides. How many more rides did Tameka ride on than Jackson?

How many more rides did Tameka ride than Jackson?

How many fewer rides did Jackson go on than Tameka?

How many more rides would Jackson have had to ride to have ridden the same number of rides as Tameka?

How many fewer rides would Tameka have had to ride to have ridden the same number of rides as Jackson?


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26 - 19 = ? or 19 + ? = 26; the difference is 7 so Tameka rode 7 more rides. Place value counters for securing written methods (here is a video of using the counters or Dienes to model basic addition and subtraction as an example, follow this method to demonstrate the methods with larger numbers): Addition https://www.youtube.com/watch?v=ykZjvbP2oGY https://www.youtube.com/watch?v=T5nMU8gIFTo https://www.youtube.com/watch?v=fD56R17q3Vk

Subtraction https://www.youtube.com/watch?v=w0MJ5wc8Llc https://www.youtube.com/watch?v=iHPApVGn4K4 https://www.youtube.com/watch?v=0HEzlr7-wBg https://www.youtube.com/watch?v=8a78H6Za5Go

https://www.youtube.com/watch?v=ykZjvbP2oGYhttps://www.youtube.com/watch?v=T5nMU8gIFTohttps://www.youtube.com/watch?v=fD56R17q3Vkhttps://www.youtube.com/watch?v=w0MJ5wc8Llchttps://www.youtube.com/watch?v=iHPApVGn4K4https://www.youtube.com/watch?v=0HEzlr7-wBghttps://www.youtube.com/watch?v=8a78H6Za5Go


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Multiplication and division

Multiply

multi-digit

number up

to 4 digits by

a 2 digit

number

using the

formal

written

method of

long

multiplication


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Multiplication and division

Divide

numbers up

to 4 digits by

a 2 digit

whole

number using

the formal

written

method of

long division,

and interpret

remainders

as whole

number

remainders,

fractions or

by rounding

as

appropriate

for the

context.

Additional Guidance:

Children should arrive in Year 6 secure in the formal methods for addition, subtraction, short and long multiplication and short division with whole number remainders. If they are not, use the following progression to secure methods: Division Video showing using place value counters for short division, in progression of no remainders and no exchange, remainders but no exchange, with exchange:


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https://www.ncetm.org.uk/resources/43589 Video showing place value counters for long division a 3-digit divided by a one-digit, using a sharing model (using the vocabulary of sharing, quotient, dividend and divisor, please use the vocab of ‘ones’ instead of ‘units’), : https://www.youtube.com/watch?v=LbxbDpnakoY . Video showing using dienes to model long division as sharing https://www.youtube.com/watch?v=8IXAqXGDMXw Multiplication Using place value counters to model the grid method and moving from the grid method to the formal method https://www.ncetm.org.uk/resources/40530 Bar Model for understanding word problems An interactive teaching program for modelling word problems: http://www.thinkingblocks.com/ Examples of using the bar model: http://scimathmn.org/stemtc/resources/mathematics-best-practices/modeling-word-problems Alana had 6 packages of gum. Each package holds 12 pieces of gum. How many pieces of gum does Alana have in all? The following bar model uses a repeated addition view of multiplication to visualize the problem.

12 + 12 + 12 + 12 + 12 + 12 = 72 (or 6 x 12 = 72) so Alana has 72 pieces of gum.

As pupils move into multi-digit multipliers, they can use a model that incorporates an ellipsis to streamline the bar model. Sam runs 32 km a day during April to get ready for a race. If Sam runs every day of the month, how many total kilometers did he run in April?

. Juan has 36 CDs in his collection. This is 3 times the amount of CDs that his brother, Marcos, has. How many CDs does Marcos have? In this situation, students would construct a bar model, shown below on the left, with 3 parts. Students could divide the 36 into 3 equal groups to show the amount that is to be taken 3 times to create 3 times as many CDs for Juan.

30 x 32 km = 30 x 30 km + 30 x 2 km = 960 km Sam ran 960 km during the 30 days of April

https://www.ncetm.org.uk/resources/43589https://www.youtube.com/watch?v=LbxbDpnakoYhttps://www.youtube.com/watch?v=8IXAqXGDMXwhttps://www.ncetm.org.uk/resources/40530http://www.thinkingblocks.com/http://scimathmn.org/stemtc/resources/mathematics-best-practices/modeling-word-problems


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36 ¸ 3 = ? or 3 x ? = 36 12 + 12 + 12 = ? (or 3 x 12 = ?)

so Marcos has 12 CDs. so Juan has 36 CDs. A similar model can be used if the greater quantity is unknown, but the lesser quantity, and the multiplicative relationship are both known. If the problem was: Juan has some CDs. He has 3 times as many CDs as Marcos who has 12 CDs. How many CDs does Juan have?


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Perform

mental

calculations,

including with

mixed

operations

and large

numbers


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Identify

common

factors,

common

multiples

and prime

numbers.


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Use their knowledge of the order of operations to carry out calculations involving the four operations.


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Solve

problems

involving

addition,

subtraction,

multiplicatio

n and

division

Covered above Jessica is rowing along the coast to Sunshine Cove. Each day she rows less because she gets more tired. On the first day she covers 38 kilometres, on the second day 35 kilometres, on the third day 32 kilometres and on the fourth day 29 kilometres. How many days will is take her to cover the distance of 203 kilometres to Sunshine Cove? Covered

Covered above My way! Give a group of four a list of sums e.g. 19 x 24 198 + 997 Half of 57.6 3841 – 665.3 5.2 ÷ 4 101 x 16 x 4 Each child must work out the answers mentally but think about the strategies they are using. After, explain their strategy and discuss why you used it

Covered above Letter challenge Can you solve these calculations by using 0,1,2,3,4,5,6,7,8 & 9 E X F = HA I X H = D A X B = B J X D = IG C X C = EC You have been asked to bury some bags of money on an island. The money has been divided into nine separate bags containing these amounts: £21, £20, £19, £12, £11, £10, £3, £2, £1. You must bury the money in a three by three grid so that each row and column, horizontal, vertical and diagonal has £33.


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Use

estimation

to check

answers to

calculations

and

determine

in the

context of a

problem,

an

appropriate

degree of

accuracy.

345 + 452 ≈800 691 + 113 ≈800 368 + 482 ≈800

She has got a £5.00 note. As she goes round the shop she estimates how much she has spent to make sure she has enough money. Below is a list of what Hannah bought- estimate what she has spent- has she got enough? Chocolate bar- 79p Can of pop- 65p Magazine- £1.50 Crisps- 45p Puzzle book - £1.80 Would it be better for Hannah to overestimate or underestimate her answer? Explain why.

Do the following estimates sound about right? Explain your reasoning. 1. Last month the energy costs in my lab were £560. I estimate that my energy costs per year will be £7000. 2. Today I ate a 30g packet of crisps at morning break time, as I always do, so I estimate that I eat almost 11kg of crisps a year. 3. My round trip to work each day is about 22 miles, but I can claim mileage from work. I estimate that I can claim for 8000 miles each year.

Play a game in pairs. Use the addition grid, the aim is to make a total as close to 1000 as possible. Take turns to throw the dice and decide which of your cells to fill. This can be done in two ways: either fill in each cell as you throw the dice, or collect all your numbers and then decide where to place them. Whoever has the sum closest to 1000 wins.


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Fractions Use common factors to

simplify

fractions; use

common

multiples to

express

fractions in

the same

denomination

.


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Fractions Compare and order

fractions,

including

fractions > 1


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Fractions Generate and describe

linear

number

sequences

(with

fractions)


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Fractions Add and subtract

fractions with

different

denomination

s and mixed

numbers,

using the

concept of

equivalent

fractions.


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Fractions Multiply simple pairs

of proper

fractions,

writing the

answer in its

simplest form

[for example


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Fractions Divide proper fractions by

whole numbers

[for example


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Domain

NC Objectives


Fractions Associate a fraction with

division and

calculate

decimal fraction

equivalents [ for

example, 0.375]

for a simple

fraction [for

example 3/9]


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Domain

NC Objectives


Fractions Recall and use

equivalences

between

simple

fractions,

decimals and

percentages,

including in

different

contexts.


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Domain

NC Objectives


Geometry: position and direction

Describe

positions on

the full

coordinate

grid (all four

quadrants).


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Domain

NC Objectives Example tasks fluency Example tasks reasoning Example tasks problem solving

Geometry: position and direction

Draw and

translate

simple shapes

on the

coordinate

plane, and

reflect them in

the axes.


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mastery mathematics medium term planning year 6 phase 1 ...€¦ · post sats project work ongoing...

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