Year 2 Block B - Securing Number Facts, Understanding Shape Unit 1

Yr 1 Learning Overviews - Autumn

Year 1 Block A - Counting, partitioning and calculating Unit 1

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, Numbers and the number system
Ma2, Operations and relationships between them

Children recite number names in order from 0 to 20 or more, forwards and backwards, using objects, number tracks and number lines. They use the sequence of number names to count a small set of objects reliably by touching or moving each object in turn, recognising that the number of objects does not change if the set is rearranged. Children identify which of two sets contains more objects, by matching the objects and counting the number in each set. They compare the numbers using their positions on a number track or number line.

Assessment focus: Ma2, Numbers and the number system

As children count objects, look for evidence of them saying one number name for each object and understanding that the last number they say is the number in the set. Look for children using strategies such as moving objects as they count them so that each object is counted just once. Look out for children who, given a small number, count that number of objects from a larger set and know when to stop. Notice the numbers of objects that children recognise without counting, for example, dots in domino patterns or a randomly arranged group of counters.

Using appropriate language and symbols in context, children read and write numerals from 0 to 10, then to 20. They understand that, for example, the number 12 is written with two digits. They know that as they count from zero along a number track each number is one more and the numbers get bigger. As they count back, each number is one less and the numbers get smaller. They find missing or covered numbers on a number track.

As they develop their understanding of addition and subtraction, children find the number that is one more or one less than a given number practically by adding another object or removing one object from a set then counting the new number. They use their knowledge of the counting sequence and number tracks to predict what number is one more or one less than a given number before checking using practical equipment. They relate addition to counting on and use the vocabulary of addition in practical activities. For example, they respond to instructions such as:

Put three more pencils on the table.
Add three spots to the ladybird.

When children use a number track to find the number that is one more than 7, they describe it as '7 add 1 is 8' or '7 plus 1 is 8' and record it in a number sentence as 7+1=8.

Children relate subtraction to taking away objects from a set and to counting back. They use the vocabulary of subtraction in practical activities; for example, they respond to instructions such as: Take away three spots. When they use a number track to find, say, the number that is one less than 8, they describe this as '8 take away 1 is 7' or '8 minus 1 is 7' and record it as 8−1=7.

Assessment focus: Ma2, Operations and relationships between them

Look for evidence of children's early understanding of addition and subtraction. Look out for children relating a range of practical problems to the operation of adding or counting on. For example, they might begin to make links between combining two sets, adding more to a set, and standing on a start number and moving a number of steps forward on a number track. In a similar way, look out for children who are beginning to make links between situations such as taking away from a set, standing on a start number and stepping back along a number track, and counting back.

Throughout the unit, children solve problems involving counting. For example: they work out whether there are enough pairs of scissors for everyone on the table to have a pair; they predict then check which of two containers will hold more pine cones; they make a collection of their ten favourite items for a display. Children describe how they solved the problem to the class. They listen to and ask questions about other children's descriptions.

Assessment focus: Ma1, Problem solving

Look out for children engaging with practical mathematical activities. For example, look for children who, given appropriate support to understand the activity, can sort objects, compare sets and count to solve problems. Look for children who are beginning to choose the materials that will help them to solve problems.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2
Activities / Resources
Activity 1 - Four-pin bowling / Puzzles and problems for Years 1 and 2
Activity 7 - Gold bars
Activity 4 - Snakes and Ladders
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 +/−
Wave 3 (1 YR +/-) Teaching activities to help children count more accurately
Makes unequal groups and cannot compare the groups / 3 YR ×/÷
Wave 3 (3 YR ×/÷) Teaching activities to help children make and compare equal groups
Misunderstands one more and one less / 2 YR +/−
Wave 3 (2 YR +/-) Teaching activities to help children count one more and one less

Year 1 Block B - Securing number facts, understanding shape Unit 1

Learning overview

In this unit the illustrated assessment focuses are:

Ma1, Reasoning
Ma2, Mental calculation
Ma3, Properties of shape

Children count in as many different contexts as possible. They count aloud in ones as a whole class, and continue the count after being given a sequence such as four, five, six, ... They count forwards and backwards. They say number rhymes and sing number songs. They count the number of claps that they hear. They count sets of objects in the classroom: books on the shelf, toys in a toy box, knives and forks, the children in a group. When shown a numeral, they count out that number of small toys or crayons. They recognise a small number of objects without counting them and explain how they know.

Children begin to use patterns and relationships to solve problems and puzzles involving numbers and shapes. For example, they continue a simple pattern of dominoes or put the domino doubles in order. They learn to identify problems and re-state them for themselves. They think about the methods they could use to reach a solution.

They locate numbers on a number track and begin to identify that the number before is one less and the next number is one more. They respond to questions such as:

What number comes after 6? Two after 6?
What number comes before 9? Two before 9?

They use this information to support addition and subtraction calculations. They explore calculation patterns in pairs of numbers with a total of 10, using their fingers in support. They continue their counting strategies, which underpin much of their work. They count on and back in steps of 5 to 30, and steps of 10 to 50. They make estimates of a number of objects based on their experience of visual patterns and arrays of objects.

Assessment focus: Ma2, Mental calculation

Look for the strategies children use to answer addition calculations. For example, when they are told the number of objects in an opaque bag and given one or two more objects, look for children who need to count all of the objects to find how many there are altogether and for those children who are able to count on.

Children use 2-D shapes and 3-D solids to build models, pictures and patterns. They learn to name shapes and describe their features. In describing the features they refine their everyday language to include appropriate mathematical terms. The children use flat '2-D shapes' made from card or thin plastic to support the early development of visualisation and mental imagery of shapes. They take part in activities such as:

I spy something that will roll, ... has a curved face, ... has two holes in it, ... has lots of points, ...
Put your hands into this big box. Can you find something soft? An object with corners? Something round? Something spiky?
Look at this collection of objects or shapes. Shut your eyes while I pick one up and hide it. Open your eyes. Tell me which object or shape I have hidden.

Assessment focus: Ma3, Properties of shape

Look for the criteria children choose and use to sort 2-D and 3-D shapes and for the everyday language they use to say how they have selected their shapes, for example, large, small, flat or tall. Look for evidence of children naming the shapes and beginning to refer to features such as corners and sides or edges in describing their shapes.

Children listen carefully to instructions, descriptions and explanations and pick out the key points. For example, they listen carefully to a description of a shape so that they can select the shape that matches the description from a collection. They talk about patterns they have made, describe the way they have solved a problem and respond to questions about what they have done, which helps them to clarify their mathematical thinking and understanding.

Assessment focus: Ma1, Reasoning

Throughout the unit look for children explaining how they worked out their solutions to problems. For example, when they are shown a string of ten beads with some beads hidden by a hand and others on view, look for children who explain how to work out the number of beads that are hidden or how they know their answer is right. Look for children reasoning about the properties of shapes. As a hidden shape is partly revealed they might respond to questions about what it could or could not be, giving their reasons.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2
Activities
Activity 3 - Pick a pair / Puzzles and problems for Years 1 and 2
Activity 14 - Card sharp
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 +/−
Wave 3 (1 YR +/-) Teaching activities to help children count more accurately
Does not relate combining groups of objects to + and/or does not interpret the counting of all of the objects as an answer to the question 'How many are there altogether?' / 3 YR +/−
Wave 3 (3 YR +/-) Teaching activities to help combine and count groups of objects
Misunderstands one more and one less / 2 YR +/−
Wave 3 (2 YR +/-) Teaching activities to help children count one more and one less

Year 1 Block C - Handling data and measures Unit 1

Learning overview

In this unit the illustrated assessment focuses are:

Ma1, Communicating
Ma3, Measures
Ma4, Processing and representing data
Ma4, Interpreting data

Children pose a question, gather information, order and interpret the information in group or whole-class enquiries. They solve problems such as:

Which of these things is heavier than the bag of sand?
Find four things in the classroom that are wider than your hand-span and four that are not.
Put the pencils into order from shortest to longest.
Which of the three bears would want which container? Put the containers into order, starting with the one that holds most.

Assessment focus: Ma1, Communicating

Look for evidence of children who can represent their solution to a problem practically, using objects. Look out for children who also recognise that they can make a pictorial record of information as they solve problems and who begin to use their recording to communicate with others about how the problem was solved.

Children measure by making direct comparisons. To compare the weight of one object with the weight of the bag of sand, for example, children hold one of the items in each hand and feel the difference, and they use a balance. They compare heights by placing objects together and the capacity of containers by pouring rice, sand or water from one container to the other. By comparing pairs of objects they build up the information they need to order more than two objects.

Assessment focus: Ma3, Measures

As they measure by direct comparison, look out for children responding to the language of comparison, for example, finding which of two objects is 'taller' or 'shorter', or 'heavier' or 'lighter'. As they pour material from one container to another, look for children who respond to or use language such as holds more, holds less or does not hold as much. Look for evidence of children using their comparisons of pairs of objects to begin to put three objects in order of weight or three containers in order of capacity.

Children place the objects on large diagrams prepared for the task to show what they have found out.

Children collect numerical information and record it in tables and block graphs. For example, to find out how many cubes different children in the group can pick up with one hand they might draw a table to show their names and record the numbers of cubes. Alternatively, each child might fix the cubes into a column and display the labelled columns as a block graph.

Assessment focus: Ma4, Processing and representing data

Look for children who, with the support of discussion to clarify the enquiry, make a list or use a given table or large diagram to assemble information. For example, look for children collecting names and numbers in tables and lists or placing objects on the appropriate part of a diagram.

Name / Cubes
Mary / 8
James / 7
Lisa / 5
Mark / 6

Children use the table or block graph to answer questions such as:

Who picked up the largest number of cubes?
How many cubes did Mark pick up?
Who do you think has the smallest hand? Why?
Who picked up one more cube than Lisa?

Children solve other problems. They collect information about likes and dislikes by placing a brick or cube on the tower of their choice. They use the completed towers and labels to find, for example, their favourite ice-cream flavour.

Assessment focus: Ma4, Interpreting data