Addition: Counting all and counting on to 20 Dot images Rekenreks Double Ten-Frames Counting all Counting on One-to-one correspondence Subitizing Addition: Doubles/Near Doubles When using the rekenrek ask pupils ‘How many beads do you see? How do you see them? When using double ask pupils ‘How many dots do you see? How do you see them? Rekenreks i.e. 3 on top, 3 on bottom; 4 on top, 3 on bottom; 3 on top, 2 on bottom Double Ten-Frames i.e. Subitizing Counting all Counting on Fluency Concept of place value PROGRESSION FRAMEWORK FOR TALKING ABOUT NUMBER TERM 3 – Revise concepts from Terms 1 and 2 and introduce number sentences which should always be written horizontally. Please refer to “Number Talks: Helping Children Build Mental Math and Computation Strategies” by Sherry Parrish, Chapter 4, pages 106 to 118 What are we learning? How are we doing it? What skills are pupils learning? Addition: Making tens When using the rekenrek ask pupils ‘How many beads do you see? How do you see them?’ When using ten frames and ask pupils questions such as ‘How many did you see? How do you see seven?’ Move on to asking ‘How many more to make ten?’ Also ask ‘How many are left after removing three?’ Rekenreks Ten-frames with missing dots Double ten frames Complete ten frames and covers Subitising Fluency Subitising Concept of place value Computation – applying mathematical calculations Addition: Counting all and counting on to 10 If pupils are ready extend number sentences to 14 Number Sentences – start within 10 and build up to within 14 i.e. 3 + 6 4 + 6 9 + 1 3 + 7 7 + 4 9 + 3 3 + 8 4 + 8 9 + 5 4 + 9 Computation – applying mathematical calculations Pupils should be applying strategies from previous learning
Addition: Doubles/Near Doubles to 10 If pupils are ready extend number sentences to 14 Number sentences – start within 10 and build up to within 20 i.e. 2 + 2 3 + 4 5 + 5 2 + 3 4 + 3 5 + 6 3 + 2 4 + 4 6 + 6 3 + 3 4 + 5 6 + 7 Computation – applying mathematical calculations Pupils should be applying strategies from previous learning PROGRESSION FRAMEWORK FOR TALKING ABOUT NUMBER TERM 4 – Revise concepts from Terms 1, 2 and 3 Please refer to “Number Talks: Helping Children Build Mental Math and Computation Strategies” by Sherry Parrish, Chapter 4, pages 97 to 118, focusing on sections labelled Number Sentences. What are we learning? How are we doing it? What skills are pupils learning? Addition to 20: Making Tens When using double ask pupils ‘How many dots do you see? How do you see them? Double ten-frames: using two ten frames with different combinations of dots in each Subitising Fluency Concept of place value Addition to 20: Making Tens Can pupils recognise that 9 + 1 is 10 and then they add on 3? Are they still using counting all strategy or are they now using counting on? Number sentences i.e. 9 + 1 5 + 5 9 + 3 + 1 5 + 5 + 4 9 + 5 + 1 5 + 3 + 5 Computation – applying mathematical calculations Pupils should be applying strategies from previous learning Addition: Counting all and counting on to 20 If pupils are ready extend number sentences to 24 Number Sentences – start within 20 and build up to within 24 i.e. 6 + 4 7 + 3 9 + 11 6 + 6 7 + 7 9 + 13 6 + 8 7 + 9 9 + 15 6 + 9 7 + 5 Computation – applying mathematical calculations Pupils should be applying strategies from previous learning Addition: Doubles/Near Doubles to 20 If pupils are ready extend number sentences to 24 Number sentences – start within 20 and build up to within 24 i.e. 7 + 7 8 + 8 10 + 10 7 + 6 8 + 9 10 + 11 7 + 8 9 + 9 11 + 11 Computation – applying mathematical calculations Pupils should be applying strategies from previous learning
Teaching the Emergent Child – See Chapter 5 of “Teaching Number: Advancing children’s skills and strategies”: Wright et al, 2002 WORKING WITHIN 20 Concepts being taught Forward and Backward Number Word Sequences Numerals and numeral sequences in the range of 1 – 10 Counting visible items Subitising Finger patterns Temporal patterns and sequences Resources required N/A Numeral flashcards Numeral track Double-sided counters Domino, pairs and random array cards Hands and fingers Hands for clapping and chopping Top tips Don’t always start at 1 when counting – vary your starting point regularly. Also, when counting backwards stop at different numbers each time. Ask pupils to copy you and also to say alternate words i.e. I will say two, then you say three, then I will say four then you say five and so on. This should lead to them saying the next number. Do this for both Forwards and Backwards sequences. Best for whole class activities Start by placing out numeral sequences in order and asking pupils to count them forward and backward. Move on to numerals being randomly arranged and asking pupils to identify them. Also, use a numeral track with numerals covered and uncovered. Good for group activities Start with pupils counting small amounts of counters in one colour, before moving on to groups of counters of two colours. Also encourage pupils to count them both forwards and backwards. Lay out large amounts of counters (around 30) and ask pupils to give you x amount out of the group (up to 20). Good for group activities As discussed during the talking about number section – use different types of flashcards and ask the class ‘What do you see?’ and also ‘How do you see them?’ Good for whole class activities Encourage pupils to use their fingers to make patterns for the number sequences – start with sequential patterns for 1 to 5, raising one finger at a time. Move on to pupils doing this with their hands held above their heads (bunny ears). Move on to doing this up to 10. Good for whole class activities Encourage pupils to copy and count different hand movements, both clapping and chopping motions. Alternate with different speeds: deliberate chopping motions; clapping rhythmically; clapping slowly; clapping irregularly. Good for whole class activities
Concrete Materials Concrete materials should be used at all times within the class, both to support the introduction of new concepts and to enhance pupils’ understanding of, and confidence in, numeracy. It is now widely recognised that the use of manipulatives, or concrete materials, is a vital tool in the teaching toolkit and that the concrete-pictorial-abstract cycle should underpin the learning and teaching of numeracy. However, various studies have highlighted that whilst teachers are aware of the need to use manipulatives they are confused about which manipulatives to use in specific contexts. Also, a certain manipulative may be used to teach a given concept and then disappear, never to be used again. This serves to make learners associate this manipulative with one specific numerical task, rather than seeing it as a vehicle with which they can solve a wide range of problems. As Mike Askew states: While there is general agreement about the importance of ‘models and images’ in helping children learn mathematics, there is less clarity about why they are important and how to work with them. It is not the models of images themselves that are important, but the way that these support children’s mathematical activity. Models and images have to be worked with, not simply presented to the children. “Transforming Primary Mathematics”: M. Askew, 2016 There should be planned, purposeful and appropriate use of concrete materials throughout numeracy and mathematics lessons. Remember to use manipulatives and concrete materials for multiple purposes. For example Cuisenaire rods can be used to support number development, measurement concepts and graphing models. In this way pupils won’t associate a concept with only one manipulative. Also, these manipulatives should be available to pupils at all times so that there is no stigma attached to the need to use these to understand a mathematical concept. The use of concrete materials allows practitioners to develop a wide variety of activities for their pupils to develop a particular concept and to repeat and revisit this numerous times so that they can become proficient and strategic with the concept being taught. For example activities can be created for pupils around creating different combinations of 6 with a wide variety of materials: Blank ten frames that can be filled with a variety of resources i.e. leaves, acorns, stones, shells, gems; Double-sided counters; Numicon shapes; Pegs; Cuisenaire rods; Lego; Rekenreks.
Addition and Subtraction Hinge Questions for pupil Comments C O U N T I N G O N Counting On Chapter 8: Nurturing Facile Number Sequences to 20 ( Facile Number Sequences to 20 – non count-by-one strategies to 20) Can use understanding of number structures to develop and explain a range of strategies to solve tasks within 20 such as: compensation, using a known results, adding to ten, partitioning using 5 and 10 as a base commutativity, subtraction as the inverse of addition, awareness of the ‘ten’ in a teen number, using doubles and near doubles Compensation Using a known result Look for this throughout. Add to ten Subtract from ten 7 + _ = 10 10 - _ = 6 Partitioning using 5 and 10 Adding/ subtracting through 10 7 + 5 9 + 4 8 + 6 13 – 5 14 – 6 15 – 7 Commutativity 2 + 9 4 + 8 Subtraction as the inverse of addition 6 + 9 = So what is 15 – 6? Awareness of ten in the teen number 10 + 6 18 – 8 Using doubles and near doubles 6 + 6 7 + 6 9 + 9 18 – 9