Year Four NCETM Ready to Progress Supporting Resources
Supporting the ready to progress criteria.
Welcome to our Ready to Progress Hub! We know how important pupil’s progress is for all teachers and educators so we have provided resources aligned with the Ready to Progress Criteria in order to make assessments without having to search around for particular objectives. We have them all ready to go in order to save you time!
What are the Ready-to Progress Criteria?
The NCETM (National Centre for Excellence in the Teaching of Mathematics) have identified key objectives that children should meet by the end of the year.
The criteria is selected parts of the curriculum that have been identified as priority. If a child is taught the objectives from this criteria and the objectives are met, pupils will be able to more easily access many of the elements of the curriculum that are not covered by this guidance.
We are excited to be able to provide resources to help the children in your class make progress and have the confidence to access all parts of the maths curriculum.
Using the Ready to Progress Criteria to help children Master the Maths Curriculum:
The Rady to Progress criteria worksheets can be used in many ways. The resources can be used
- As part of a ‘catch up curriculum’
- Small groups who may need additional help
- SEND groups
- To inform your planning and assessments
When using the resources at the beginning of the year, it is advised to use material from the previous year group.
Year Four NCETM Resources
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Mastering Mathematics and Problem Solving
The role of mastery in nurturing young mathematicians.
Building relational understanding with the Core Competencies and NCETM’s Big Ideas
What do the Maths — No Problem! Core Competencies and NCETM’s Big Ideas have in common? They’re both important maths mastery principles that work together to build relational understanding.
The NCETM’s Five Big Ideas are lesson design principles for teaching maths for mastery and the Five Core Competencies are attributes that help learners develop deeper thinking.
Seems fairly straightforward. But how do the Big Ideas and the Core Competencies align? Do they serve different purposes? What are the implications for teaching?
To save yourself hours of digging through the internet, keep reading.
What are the NCETM’s Five Big Ideas?
Let’s start by looking at the Five Big Ideas in a bit more detail.
The NCETM Five Big Ideas were created to enhance teaching for mastery. These research-based principles frame the lesson studies, professional dialogue and lesson design process within Teacher Research Groups (TRGs).
Mastery specialists from regional maths hubs have helped spread the Five Big Ideas through TRGs.
So, what are the Five Big Ideas?
- Representation and structure: representations used in lessons expose the mathematical structure so that students can do the maths without needing the representation.
- Mathematical thinking: if taught ideas are to be understood deeply, they musn’t be passively received but must be worked on by the student: thought about, reasoned with and discussed with others.
- Fluency: quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics.
- Variation: Variation is twofold. It is firstly about how the teacher represents the concept, often in more than one way, to draw attention to critical aspects, and to develop deep and holistic understanding. It is also about the sequencing of the episodes, activities and exercises used within a lesson and follow-up practice, paying attention to what stays the same and what changes, to connect the mathematics and draw attention to mathematical relationships and structure.
- Coherence: breaking lessons down into small connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply the concept to a range of contexts.
What are the Maths — No Problem! Five Core Competencies?
Now, let’s take a look at what MNP brings to the table. The Maths — No Problem! Five Core Competencies are the attributes you want to see in your learners as you teach for mastery.
Learners who show these core competencies are set up for maths success.
The Five Core Competencies are:
- Visualisation: ask learners to show ‘how they know’ at every stage of solving the problem.
- Generalisation: challenge learners to dig deeper by finding proof.
- Communication: encourage learners to answer in full sentences. Try asking learners to talk about the work they’re doing or use structured tasks centred around a class discussion.
- Number sense: a learner’s ability to work fluidly and flexibly with numbers .
- Metacognition: teach learners to think about how they are thinking. This helps learners solve multi-step tasks and promotes the ability to keep complex information in mind.
How the Big Ideas and Core Competencies work together to build relational understanding
The last couple of Big Ideas don’t match up quite as neatly with the Core Competencies. But the ones that do align like this:
|
|
|---|---|
1. Representation and structure | 1. Visualisation |
2. Mathematical thinking | 2. Generalisation |
3. Communication | |
3. Fluency | 4. Number sense |
4. Variation | |
5. Coherence | |
5. Metacognition |
When you apply the lesson design principles from Big Ideas to develop the Core Competencies, you help learners build relational understanding.
Relational understanding focuses on not just knowing a rule, but understanding why it works and establishing connections.
So, how do the Ideas and Competencies work together to develop relational understanding?
‘Visualisation’ and ‘Representation and structure’
Relational understanding is all about visualising and understanding the underlying structure behind problems. To build relational understanding, try using Ban Har-style questioning like:
“Can you see?” “Can you imagine?”
It’s essential to allow learners space for visualisation before offering explanations. Also, try to avoid too much pencil on paper.
Using manipulatives helps learners to visualise and allows teachers to expose the structure of the mathematics at hand. But it’s vital to use manipulatives as tools — not toys.
How should you get started? I often build in time to allow learners to just play at first, especially if the resource is completely new to them. Manipulatives are a good way of promoting flexible thinking by asking those learners quick to arrive at an abstract solution to prove their thinking in a different way.
It’s worth noting that the Education Endowment Fund recommends removing manipulatives once understanding is secure to avoid over-reliance or procedural use of one particular model.
A critical component of scaffolding is making sure you carefully consider which representation to use. This helps provide access for all learners. When designing lessons, consider what to record on the board — even down to how colour-coding may aid understanding.
‘Generalisation’, and ‘Communication’
All three principles are about making connections, spotting links, noticing patterns and reasoning — which all help to build a connected body of knowledge.
Supporting learners’ generalisation skills can include getting them to explore whether statements are always, sometimes, or never true (or false — using the idea of negative variation).
Another good strategy is using peer discussion. Here, learners establish consensus around rules, examples and counterexamples (or non-examples). Encourage them to explain, describe and justify their methods and results, and reflect on their conclusions.
‘Fluency’ and ‘Number sense’
Fluency and number sense are closely related: partitioning facts, times tables facts and using connected facts like equivalent fractions. When learners are fluent, they can use the known to work out the unknown — an important component of relational understanding.
For me, number sense and fluency are all about noticing patterns, checking to see whether an answer is reasonable, and selecting efficient and appropriate methods of calculation. Sound number sense avoids emphasising procedural recall and rehearsal.
Developing relational understanding relies on lessons that encourage learners to make connections and delve deeper. Teaching relational understanding is demanding, but it’s worth it! By building a connected body of knowledge and skills, your learners can become true mathematical thinkers.
Joe Jackson-Taylor
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Year 4 - Mastery, problem solving - Counting in tenths and hundredths
Subject: Mathematics
Age range: 7-11
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Last updated
30 June 2024
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Multiplication and Division
Spine 2 of the Primary Mastery Professional Development Materials
Introduction
The Multiplication and Division spine is divided into 30 segments. For each of these segments we have produced a detailed teacher guide, including text and images.
The images are also presented as animated PowerPoint slides, which further enhance teacher knowledge and can be used in the classroom (for best results, please view these in ‘Slideshow’ view; for some slides, supporting notes are provided in the ‘Notes’ section).
These materials are not, in any way, lesson plans, but they can be used in conjunction with a high-quality mastery textbook to support planning.
The following PDF offers an overview of the complete Multiplication and Division spine, including a synopsis of each segment.
Spine 2 Overview
Counting, unitising and coins
Spine 2: Multiplication and Division – Topic 2.1
Structures: multiplication representing equal groups
Spine 2: Multiplication and Division – Topic 2.2
Times tables: groups of 2 and commutativity (part 1)
Spine 2: Multiplication and Division – Topic 2.3
Times tables: groups of 10 and of 5, and factors of 0 and 1
Spine 2: Multiplication and Division – Topic 2.4
Commutativity (part 2), doubling and halving
Spine 2: Multiplication and Division – Topic 2.5
Structures: quotitive and partitive division
Spine 2: Multiplication and Division – Topic 2.6
Times tables: 2, 4 and 8, and the relationship between them
Spine 2: Multiplication and Division – Topic 2.7
Times tables: 3, 6 and 9, and the relationship between them
Spine 2: Multiplication and Division – Topic 2.8
Times tables: 7 and patterns within/across times tables
Spine 2: Multiplication and Division – Topic 2.9
Connecting multiplication and division, and the distributive law
Spine 2: Multiplication and Division – Topic 2.10
Times tables: 11 and 12
Spine 2: Multiplication and Division – Topic 2.11
Division with remainders
Spine 2: Multiplication and Division – Topic 2.12
Calculation: multiplying and dividing by 10 or 100
Spine 2: Multiplication and Division – Topic 2.13
Multiplication: partitioning leading to short multiplication
Spine 2: Multiplication and Division – Topic 2.14
Division: partitioning leading to short division
Spine 2: Multiplication and Division – Topic 2.15
Multiplicative contexts: area and perimeter 1
Spine 2: Multiplication and Division – Topic 2.16
Structures: using measures and comparison to understand scaling
Spine 2: Multiplication and Division – Topic 2.17
Using equivalence to calculate
Spine 2: Multiplication and Division – Topic 2.18
Calculation: ×/÷ decimal fractions by whole numbers
Spine 2: Multiplication and Division – Topic 2.19
Multiplication with three factors and volume
Spine 2: Multiplication and Division – Topic 2.20
Factors, multiples, prime numbers and composite numbers
Spine 2: Multiplication and Division – Topic 2.21
Combining multiplication with addition and subtraction
Spine 2: Multiplication and Division – Topic 2.22
Multiplication strategies for larger numbers and long multiplication
Spine 2: Multiplication and Division – Topic 2.23
Division: dividing by two-digit divisors
Spine 2: Multiplication and Division – Topic 2.24
Using compensation to calculate
Spine 2: Multiplication and Division – Topic 2.25
Mean average and equal shares
Spine 2: Multiplication and Division – Topic 2.26
Scale factors, ratio and proportional reasoning
Spine 2: Multiplication and Division – Topic 2.27
Combining division with addition and subtraction
Spine 2: Multiplication and Division – Topic 2.28
Decimal place-value knowledge, multiplication and division
Spine 2: Multiplication and Division – Topic 2.29
Multiplicative contexts: area and perimeter 2
Spine 2: Multiplication and Division – Topic 2.30
Acknowledgements
The NCETM and Maths Hubs would like to thank the following for their contribution to the materials:
- Primary mathematics specialists : Joanna Caisová, Adrian Cannell, Clare Christie, Katie Crozier, Jonathan East, Claire Gerrard, Rebecca Holland, Alison Hopper, Elizabeth Lambert, Conor Loughney, Suzanne Mathews, Debbie Morgan, Sally O'Brien, Alexandra Parry, Georgia Ryan, Cat Stone, Debbie Weible, Andrew Whitehead
- Educational consultant : Dr Alf Coles, University of Bristol
- Editorial and production : Liam Benson, Design and Define; Nicholas Bromley; Charlotte Christensen; Tracey Cowell, Passion for Publishing; Rachel Houghton; Jalita Jacobsen; Bill Mantovani; David Mantovani; Sam Radford; Rosie Stewart, Swales & Willis; Cheryl Stirr; Yvette Sturdy, DiGiV8 Ltd; Rachel Trolove, Trolove Engineering Solutions Ltd; Andrew Young
- Illustrations : Steve Evans; Alphablocks Ltd
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COMMENTS
Imagining the position of numbers on a horizontal number line helps us to order them: the number to the right on a number line is the larger number. So 5 is greater than 4, as 5 is to the right of 4. But -4 is greater than -5 as -4 is to the right of -5. Rounding numbers in context may mean rounding up or down.
The whole of Year 4, split into units. The graphic above shows the year mapped into different areas of the curriculum, to give an idea of the time that should be spent on each unit. Spare weeks are included in each term to allow for variation across schools and classes. Click on the image to download a more detailed PDF version.
The aims of the National Curriculum are to develop fluency and the ability to reason mathematically and solve problems. Reasoning is not only important in its own right but impacts on the other two aims. Reasoning about what is already known in order to work out what is unknown will improve fluency; for example if I know what 12 × 12 is, I can ...
Developing Excellence in Problem Solving with Young Learners. Age 5 to 11. Becoming confident and competent as a problem solver is a complex process that requires a range of skills and experience. In this article, Jennie suggests that we can support this process in three principal ways. Using NRICH Tasks to Develop Key Problem-solving Skills.
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time? Age 7 to 14. Challenge Level. We have found 51 NRICH Mathematical resources connected to NC Yr 4, you may find related items under NC.
Greater Depth Finding missing numbers to decide which statement is correct adding two or more fractions with the same denominator where answers are > 1. Using some fractions with denominators that are double or halve of the previous fraction. Answers expressed as improper fractions and mixed numbers. More Year 4 Fraction resources.
The National Centre for Excellence in Mathematics (NCETM) aims to raise levels of achievement in maths across all schools and colleges in England. Our primar...
rs' Notes - Year 4RATIONALEBackgroundThis book has been written taking into account the principles out. ned in the current Mathematics curriculum. It focuses on a mastery approach to teaching mathematics, as outlined by NCETM's director, Charlie Stripp, in the short paper entitled 'Mastery approaches to mat.
This unit of work is based off of the NCETM lesson spines and is aimed at Year 4. Some tasks have been taken from White Rose to meet the learning objectives from the NCETM. There are two parts to this planning unit. ... Problem-solving, Reasoning' sheet to show clear progression. These lessons are provided with a 'next step' to move ...
Reasoning and Problem Solving - Multiply by 10 - Teaching Information. 1a.Three children pick numbers out of a hat. Use the clues below to match the children to their number. Marco's number is 10 lots of 3. Florence's number is 10 times greater than Marco's. Marco's number is 10 times bigger than Noah's. 1b.
This page, and all sections of the National Curriculum Resource Tool, will be removed in summer 2024. Find out more. National Curriculum Resource Tool. Selected Results. Year 4: Number and Place Value. count in multiples of 6, 7, 9, 25 and 1000. find 1000 more or less than a given number. count backwards through zero to include negative numbers.
Reasoning and Problem Solving - Estimate Answers - Year 4 Expected. 7a. out. six thousand, eight hundred and seventy-one add one thousand, five hundred and ninety-three. six thousand, three hundred and twenty-nine add two thousand, one hundred and thirty-three. four thousand, nine hundred and forty-two add three-thousand five hundred and ...
Divide 1,000 into 2, 4, 5 and 10 equal parts, and read scales/number lines marked in multiples of 1,000 with 2, 4, 5 and 10 equal parts. Number Facts Recall multiplication and division facts up to 12 x 12 , and recognise products in multiplication tables as multiples of the corresponding number
Reasoning and Problem Solving Divide by 100 Reasoning and Problem Solving Divide by 100 Developing 1a. Sara is incorrect. 200 ÷ 100 = 2. Her friends will have 2 lollies each. 2a. Various answers, for example: 300; 600; 900 3a. Mutya is correct. 8 x 100 = 800 Expected 4a. Sasha is incorrect. 1,600 ÷ 100 = 16 She will have 16 spools. 5a.
Year 4 Term by Term Objectives National Curriculum Statement All students Fluency Reasoning Problem Solving Fractions Count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten. Use the number line to count from 0.05 to 0.12. How many steps did you take?
We envisage working with other stakeholders, building on the existing problem solving materials (DfE, 2013; NCETM, 2014b; NCETM, 2015) to address each of the five aspects required to nurture young mathematicians. It is important that such resources should include a focus on developing a productive disposition towards mathematics, especially ...
The learning objectives of the lessons included in the unit of work are: 1: Identify the multiplier and multiplicand. 2: Count in and multiply by 3. 3: Count in and multiply by 6. 4: find the relationship between 3 and 6 times tables. 5: count in and multiply by 9. 6: Find links between the 3, 6 and 9 times table.
1.4 Simplifying and manipulating expressions, equations and formulae. Core concept 1.4 concerns the generalisation of number structures, the use of algebraic symbols, and techniques for their manipulation. The rearranging of formulae is also explored. KS3 Secondary. Mastery PD Materials.
This is a unit of work that is inspired by the planning from NCETM Year 4 Unit 5. The learning outcomes that the NCETM state are covered in this unit if planning are. ... Worksheets provided follow the structure of: Fluency, Problem-solving and Reasoning to ensure progression. 3 of these lessons are not intended to be in books and do not come ...
The Five Core Competencies are: Visualisation: ask learners to show 'how they know' at every stage of solving the problem. Generalisation: challenge learners to dig deeper by finding proof. Communication: encourage learners to answer in full sentences. Try asking learners to talk about the work they're doing or use structured tasks ...
National curriculum statutory requirements (p28) Pupils should be taught to: read, write and convert time between analogue and digital 12- and 24-hour clocks. solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days. When planning this unit, build on current understanding of time on an ...
A sport's journey from the streets of New York all the way to the Paris Games.
Age range: 7-11. Resource type: Worksheet/Activity. File previews. pdf, 121.72 KB. A set of four differentiated mazes for student to colour a path through, counting on in tenths or hundredths (or just ones for SEN). Plus a blank grid for students to design their own mazes. Year 4 Learning Objectives: count up and down in tenths and hundredths.
Introduction. The Multiplication and Division spine is divided into 30 segments. For each of these segments we have produced a detailed teacher guide, including text and images. The images are also presented as animated PowerPoint slides, which further enhance teacher knowledge and can be used in the classroom (for best results, please view these in 'Slideshow' view; for some slides ...