mastery mathematics medium term planning year 5 phase 1 ... · mastery mathematics medium term...

Mastery Mathematics Medium Term Planning

Year 5 PHASE 1

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Year 5 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

Measures Time

Phase 2 Fractions

Geometry Shape, symmetry, position and direction

Fractions Decimals

Phase 3 Measures Converting measures

Measures Length

and perimeter Geometry Angles

Fractions Percentages

Measure Volume

Phase 4 (EoY)

Statistics Number Prime numbers

Ongoing throughout the year:


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Year 5 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

ns

Number and Place Value Read, write, order and compare numbers to at least 1000000 and determine the value of each digit. Count forwards or backwards in steps of powers of 10 for any given number up to 1000000. Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers including through zero. Round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000 Solve number problems and practical problems that involve all of the above. Read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Addition and subtraction Add and subtract numbers mentally with increasingly large numbers. Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy. Solve addition and subtraction multi-step problems in contexts deciding which operations and methods to use and why.

Multiplication and division Multiply and divide numbers mentally drawing upon known facts. Multiply and divide whole numbers by 10, 100 and 1000. Multiply numbers up to 4 digits by a one or two digit number using a formal written method, including long multiplication for 2 digit numbers. Divide numbers up to 4 digits by a one digit number using the formal written method of short division and interpret remainders appropriately for the context. Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers. Recognise and use square numbers and cube numbers and the notation for squared (2) and cubed (3) Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes. Solve problems involving addition and subtraction, multiplication and division and a combination of these, including understanding the use of the equals sign.

Measures: Time solve problems involving converting between units of time complete, read and interpret information in timetables


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S &

D S

ess

ion

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

Year 4 Fractions Objectives:

add and subtract fractions with the same denominator

recognise and show, using diagrams, families of common

equivalent fractions

count up and down in hundredths; recognise that hundredths

arise when dividing an object by one hundred and dividing tenths

by ten

solve problems involving increasingly harder fractions to calculate

quantities, and fractions to divide quantities, including non-unit

fractions where the answer is a whole number

Year 4 Fractions Objectives - Decimals find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths (use place value sliders) recognise and write decimal equivalents of any number of tenths or hundredths

recognise and write decimal equivalents to 1

4, 1

2, 3

4

round decimals with one decimal place to the

nearest whole number

compare numbers with the same number of decimal

places up to two decimal places

Year 5 Number and place value


Year 5 PHASE 1

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Year 5 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 to at least 1000000 and determine the value of each digit.


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Count forwards or backwards in steps of powers of 10 for any given number up to 1000000.


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Example tasks fluency Example tasks Reasoning Example tasks problem solving


Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers including through zero.


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Round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000



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Read

Roman

numerals to

1000 (M)

and

recognise

years

written in

Roman

numerals.


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




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Addition and subtraction

Add and subtract numbers mentally with increasingly large numbers.


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Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) .


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Use

rounding to

check

answers to

calculations

and

determine,

in the

context of a

problem,

levels of

accuracy


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

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?

http://www.thinkingblocks.com/


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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?

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

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?

https://www.youtube.com/watch?v=ykZjvbP2oGY

https://www.youtube.com/watch?v=T5nMU8gIFTo

https://www.youtube.com/watch?v=fD56R17q3Vk

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


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Multiply and divide numbers mentally drawing upon known facts.


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Multiply and divide whole numbers by 10, 100 and 1000.


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Multiply numbers up to 4 digits by a one or two digit number using a formal written method, including long multiplication for 2 digit numbers.

Multiplication Additional guidance:

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.

https://www.ncetm.org.uk/resources/40530

http://www.thinkingblocks.com/

http://scimathmn.org/stemtc/resources/mathematics-best-practices/modeling-word-problems


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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.

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?

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


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Divide numbers up to 4 digits by a one digit number using the formal written method of short division and interpret remainders appropriately for the context.

Division Additional guidance:

Division Video showing using place value counters for short division, in progression of no remainders and no exchange, remainders but no exchange, with exchange: 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

https://www.ncetm.org.uk/resources/43589

https://www.youtube.com/watch?v=LbxbDpnakoY

https://www.youtube.com/watch?v=8IXAqXGDMXw


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Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.


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Recognise and use square numbers and cube numbers and the notation for squared (2) and cubed (3)


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Measures: Time

Solve problems involving converting between units of time


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Measures: Time

Complete, read and interpret information in tables including timetables.


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