Year 1 Learning overviews - Spring

Block A - Counting, partitioning and calculating: Unit 2

Learning Overview

In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils' Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children's learning, this accumulating evidence will help you to determine the level at which they are working.

To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum, as well as through the application of skills across the curriculum.

In this unit the illustrated assessment focuses are:

  • Ma1, Reasoning
  • Ma2, Solving numerical problems
  • Ma2, Operations and relationships between them

Children extend their counting and calculating skills. They estimate a number of objects that can be checked by counting, such as how many counters they can hold in one hand. Having counted how many of a particular object will fit into a box, they use this to estimate how many of a different object will fit into the box, explaining how they made the estimate. As their experience grows of using numbers to 20 and beyond, they begin to understand place value in two-digit numbers. For example, they count 17 art-straws, use an elastic band to group together a bundle of ten and identify that they have 1 bundle of ten and 7 single straws. They count out 34p using 10p and 1p coins. They relate these activities to the way that 17 and 34 are written.

Using the correct symbols and appropriate language, children read and write numerals to 20 and beyond, identifying for example where all the numbers that start with ‘twenty’ lie on a number line or 100-square. They use this pattern of numbers to locate given numbers and explain how to identify a hidden or missing number. They continue to compare and order numbers, saying which of two numbers is bigger and which is smaller using their knowledge of where numbers lie on a number line. For example, they give numbers smaller than 20, identify numbers bigger than 9, find numbers lying between 25 and 35, and know numbers which are beyond 50 but less than 100.

Children extend their understanding of addition and subtraction. They relate addition to counting on and to combining groups. They solve problems such as: There are eight pencils in a pot. Three more are added. How many are there altogether now? They use practical apparatus to model the problem or represent the problem in a drawing. Later, they count on using a number line, then count on mentally. They explain orally how they worked out the problem, and record the problem and answer using the + and = symbols. They understand and use an increasing range of vocabulary related to addition.

Assessment focus: Ma2, Solving numerical problems

Look for children who can interpret a range of oral language to understand the context of problems that involve either addition or subtraction. Look for children who recognise the relevant information and canrepresent the problem appropriately with objects, drawings or numbers. Look for children who are beginning to recognise the operation that is needed to solve a problem.

Children relate subtraction to taking away and to counting back. They solve problems such as: There are 15 toys in a box. Six toys are taken out. How many are in the box now? They use practical apparatus to model the problem or represent the problem in a drawing. Later, they count back using a number line, then count back mentally. They explain how they worked out the problem and record it using the – and = symbols.

Through a range of practical activities, children gain experience of ‘difference’. For example, they find out how many more beads are on a longer string than a shorter one, recognising that one way to answer such a question is to count the extra beads. They represent the problem on a number line, counting the ‘extra’ by counting up from the smaller to the larger number. They understand and use an increasing range of vocabulary related to subtraction.

Assessment focus: Ma2, Operations and relationships between them

Look for children who demonstrate an understanding of addition as both counting on and as combining two or more sets of objects. Look for evidence of children using objects to represent and solve problems such as, 'Three people are on the bus and five more get on. How many are on the bus now?', and notice whether they need to count out the two sets and then count all the objects or if they can remember the number in one set and count on the extra objects.

Look for evidence of children's understanding of subtraction and for the strategies they use to solve subtraction problems. Look for children using objects either to remove some from the set and then count the objects that remain or to compare two sets of objects to find 'how many more' in the larger set. Look for children who begin to choose a number track or line to take away by counting back or to locate two numbers and find 'how many more' by counting on.

Throughout the work children solve problems involving addition and subtraction, such as:

Break this rod of eight cubes into three pieces. How many cubes are in each piece? Can you do it in a different way?

Jane has six pencils. Tom has two pencils. How many pencils do Jane and Tom have altogether? How many more pencils has Jane than Tom?

Half of the ten apples in a bag have been eaten. How many apples are left in the bag?

Children describe how they solve problems and explain their reasoning.

Assessment focus: Ma1, Reasoning

Look for children who, with the support of probing questions, draw conclusions from their work. For example, if children find different ways of breaking a rod of eight cubes into three pieces, notice how they respond to questions about their results. Look for children who review their results and offer an example where the smallest piece broken from the rod was one cube. As results are collected from different children, look for children recognising results that represent the same three pieces, for example, 1, 2, 6 and 1, 6, 2. Look for children who persevere to find several of the five possible different outcomes.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2
Activities / Resources
Activity 3 - Pick a pair / Puzzles and problems for Years 1 and 2
Activity 4 - Snakes and ladders
Activity 5 - Bean-bag buckets
Intervention programmes
Springboard unit
None currently available
Supporting children with gaps in their mathematical understanding (Wave 3)
Diagnostic focus / Resource
Can only begin counting at one; inaccurately counts objects when rearranged; has no consistent recognition of small number of objects; lacks systematic approaches / 1 YR +/−
DCSF 1118-2005
Makes unequal groups and cannot compare the groups / 3 YR ×/÷
DCSF 1139-2005
Misunderstands one more and one less / 2 YR +/−
DCSF 1119-2005
Counts up unreliably, still counting the smaller number to get one too many in the answer / 3 Y2 +/−
DCSF 1124-2005

Block B – Securing number facts, understanding shapes: Unit 2

Learning Overview

In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils' Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children's learning, this accumulating evidence will help you to determine the level at which they are working.

To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum, as well as through the application of skills across the curriculum.

In this unit the illustrated assessment focuses are:

  • Ma1, Reasoning
  • Ma1, Communicating
  • Ma3, Properties of shape

Children continue to count in as many different contexts as possible. They count as far as they can towards one hundred. They count and record the number of children present each day. They count in a soft voice to ten, a loud voice to twenty, a soft voice to thirty, and a loud voice to forty, and so on. They continue the count after given a sequence such as twenty-four, twenty-five, twenty-six, … They count forwards and backwards in ones and in tens. They begin to count in twos, at first to ten and then to twenty. When shown a numeral such as 16, they count out that number of small cubes and show that they have ten and six cubes. They count on from one number to another, for example, from 25 to 30, counting twenty-six, twenty-seven, twenty-eight, twenty-nine, thirty, recording on their fingers that they have counted on five numbers. They count sounds such as chimes on a xylophone or beats on a drum, including groups of two beats. They continue to recognise a small number of objects without counting them and explain how they know. They estimate how many there are in a larger number of objects such as shells and check by counting.

Children use patterns and relationships to solve problems and puzzles. For example, they make simple patterns with numbers or shapes and refer to the resources to help them to describe the pattern. They explain how to continue the pattern using appropriate mathematical words.They use their developing calculation and problem-solving skills to identify whether a problem involves addition or subtraction, for example:

There are six pegs on the coat hanger. I clip on two more. How many pegs on the hanger now?

There are eight pegs on the coat hanger. Five are showing. How many are hidden under the cloth?

Assessment focus: Ma1, Reasoning

Look for evidence of children reasoning about patterns and relationships. When they copy and continue repeating patterns, look for children who can identify and describe the short sequence of numbers or shapes that is repeated and for children who can identify the number or shape that comes next. When they are solving addition and subtraction problems, look for children who can explain the numbers they used, the calculation they performed and the conclusion they reached.

Children derive and learn to recall pairs of numbers with a total of 10. They derive and then recall addition facts for totals up to at least 5 and the related subtraction facts. They extend their recall of doubles of numbers up to at least 5+5.

Children continue to identify the number that is one or ten more or less than a given number, extending to a wider range of numbers and contexts, including the 100-square. They use this to support their calculating skills for examples such as 12+1, 13–1, 30+10 and 60–10. Children continue to develop their understanding of how to represent number stories with number sentences. This supports their use of appropriate mathematical vocabulary and symbols.

Assessment focus: Ma1, Communicating

Look for the ways in which children choose to represent and record numbers. For example, they might hold up a number of fingers, use linking cubes or other objects, make marks or pictures on paper, or write numbers in numerals. Look out for how they record number stories when they have opportunities to choose their own way. They might use objects, pictures or diagrams, or choose to use symbols '+', '–' and '=' to record addition or subtraction sentences.

Children build models, pictures and patterns with 2-D shapes and 3-D solids. The experience helps them to name shapes and describe their features. They refine their everyday language to include appropriate mathematical terms. Children continue to develop mental images of these shapes by participating in activities such as:

Tell me where in the classroom you can see a circle, a square, a triangle, … What about a cube? Can you see a cone anywhere?

I've hidden an object/shape/wooden numeral in this cloth bag. Pass it round and tell me what you think it is. How do you know?

Imagine a big triangle painted on the floor. How many corners does it have? How many sides?

Imagine holding a tin of beans, and turning it round and round in your hands. How many circles can you see?

Shut your eyes. Listen while I describe a shape to you … Now open your eyes. Can you pick up the shape I was describing? Now describe a shape for someone else to guess.

Assessment focus: Ma3, Properties of shape

Look for the language children use to describe shapes. Look out for children who can use the mathematical names for common 2-D and 3-D shapes and for those who are beginning to use mathematical terms to describe the properties and features of shapes. Look for those children who, after practical experience of making models, pictures and patterns with shapes, can begin to form a mental image of the shapes and their properties.

Children sort numbers and shapes into groups and develop their information-processing skills. For example, they separate squares from rectangles and cubes from cuboids. They sort number cards to identify all the numbers that are even or all the numbers that they say when they count in fives. They identify capital letters made from only straight lines, distinguishing them from those with at least one curved line.

Children listen carefully to instructions, descriptions and explanations to pick out the key points such as the features of the shape that is being described. They take turns to speak, listen to others’ suggestions and talk about what they are going to do. Theydevelop their ability to work with others and become more familiar with taking an active part in paired or small-group work.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2
Activities / Resources
Activity 5 - Bean-bag buckets / Puzzles and problems for Years 1 and 2
Intervention programmes
Springboard unit
None currently available
Supporting children with gaps in their mathematical understanding (Wave 3)
Diagnostic focus / Resources
Has difficulty identifying doubles and adding a small number to itself / 2 YR ×/÷
Wave 3 (2 YR ×/÷) Teaching activities to help children identify and use doubles
Misunderstands one more and one less / 2 YR +/−
Wave 3 (2 YR +/-) Teaching activities to help children count one more and one less

Block C – Handling data and measures: Unit 2

Learning Overview

In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils' Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children's learning, this accumulating evidence will help you to determine the level at which they are working.

To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum, as well as through the application of skills across the curriculum.

In this unit the illustrated assessment focuses are:

  • Ma1, Problem solving
  • Ma2, Solving numerical problems
  • Ma4, Interpreting data

Children take greater responsibility forposing and answering questions. They begin to explore their own ways of solving problems and organising the information that they gather. They build on their experience of measuring by direct comparison. They useuniform non-standard units such as wooden bricks to balance an object, egg cups to fill a container and straws to fit along a line or their own steps to measure a longer distance. They solve problems such as:

Which is wider: the table or the doorway? How much wider is it?

How heavy is each of these objects?

How many cups does it take to fill this jug? Check your estimate.

Children begin to use standard units to measure and sort objects. For example they sort objects according to whether they are taller than 1metre or not. They make a collection of items that together weigh just over 1kilogram.