If I had a pound for all the times I’ve been told a child knows his numbers up to 10, I would be considerably richer than I am. Being able to say a word when you see a written numeral (or recite numbers in sequence) and actually having a concept of what it all means are two very different things. Then you get to the problem of not being sure if 3 things are always 3 things even if they are moved around. So every child has to learn about how many things will be in a ‘group of 3’ (or any other number) and that it doesn’t matter if the group is rearranged. Nor does it matter if it’s 3 apples or 3 elephants – 3 is 3! Besides the actual numerals and what they stand for, we have a huge list of words and phrases which relate to a quantity, which may vary depending on the situation. For example: if there are two groups and one has 4 objects and one has 5, then the 5-group will have more. But if the groups have 4 objects and 3 objects, then the 4-group has more. The trouble is: when you know, it’s hard to imagine not knowing!
Sometimes children get it wrong because they might have got the numbers bit, but they haven’t got the language. This problem often continues up the school so ‘sums in words’ (mental maths or in written form) pose a real problem even when ‘normal’ sums are manageable. It is helpful to use maths words at home in practical situations where the meaning is usually clear. Look! There are no more chocolate biscuits in the tin is demonstrable.
The Numicon website has some great free videos and articles about number. Numicon sell tools to help with maths: Numicon plates and Cuisenaire rods. Well-established things like an abacus or counting beads are also useful. Here are links to some of my free resources on TES about number and counting.
NUMBER CONSERVATION number and counting 1 The bricks are to be built to match the pictures and knocked down by a naughty toy. Work on hand-eye coordination and number conservation. Notes on the reverse of some of the booklets give background rationale.
SHARE, SEQUENCE, COUNT, GRID number and counting 2 A set of activities using purchased toys which are often available in school. Featured are sorting toys (vehicles), 2D shapes, 3D solid shape beads, threading fruit, colours, numbers 1-4. Suggestions for all activities included. Build skill in sorting, following symbol instructions, sequencing and recall, counting out fruit and checking with a Numicon layout on the reverse of the cards. Print single-sided except for the number cards which must be double-sided.
GRID SORT 1-4 number and counting 3 A simple grid layout for 1-4 objects to be placed correctly. If you can print on A3 card the pieces will be more manageable but okay on A4.
CHRISTMAS COUNT number and counting 4 Print 2-up on A4 card. CHRISTMAS 1-5 (dice layout). Cut out cards to make a pack. Ideas included for sorting to numeral or dice, finding, labelling, making a grid. COUNT 1-8 (Numicon layout). Cut to A5 and use for ordering 1-8. Could be used for Christmas vocabulary with young EAL learners.
ILLUSTRATED MATHS WORDS: the language of early maths number and counting 5 These pages show some of the words that underpin talking about quantity, position, comparing, placing, arranging and so on. They all need to be practised with many different objects to ensure generalisation. Beware of using too many of these key or information carrying words (ICWs) in the same instruction. Remember to stress that first in a row is always on the left. This is critical to the understanding of instructions in maths and other areas. (First in the queue, however, depends on which way the queue is going. It’s hard talking maths words!) Now in the same size so you can build up a collection and make Pairs games etc. Not in developmental order – just pick and choose to suit your current target. But try to check early concepts are secure before building on them. Index now in sheet order and alphabetical order. (See new worksheets based on this resource at number and counting 20 )
BONDS TO 5 number and counting 6 Bonds to 5 (and subtract from 5). Three similar stories and worksheets. Print the three stories 2-up on A4 paper. Print the worksheets on A4 paper. Suggestions on the worksheet pages use a very visual ‘take-away’ method first (by destroying the correct number of images). Then, the child has to say how many are needed to replace them to get back to 5 before the next sum, and cut the correct number of images for the replacement. Sums are also presented in written form.
COMPARE AMOUNTS number and counting 7 Tasks requiring attention to detail and logical thinking. Useful for children who can read but tend to rush and not take account of all the important words. One introductory page to create sentences with – you could write some down as they are created as the words used to compare amounts of uncountable nouns (such as hair, sugar and paper) can be hard to get right. Plus two sets of cards with lots of comprehension tasks for each. Moving the pictures to suit the descriptions means it is easy to change things if a rethink is necessary. Could also be used for EAL youngsters with reasonable skills.
1-10 NUMERALS, TEXT, AND +1 SUMS number and counting 8 Graded steps to encourage learning.
100 in 10s NUMERALS, TEXT, AND TIMES SUMS number and counting 9 Graded steps for solid learning.
WORKING IN UNITS number and counting 10 COUNTING ON shows a way to present sums using number and dot dice – includes layout and suggestions. ADD 1p, 2p or 5p. Money sums: aim is to predict the answer and get it confirmed immediately. Very immediate way of presenting written sums, illustrated with realistic money symbols. DOLLS HOUSE SHOPPING: add up units. Cut sheet into cards to make lots of different sums. Use tactile aids like an abacus, Unifix or Numicon.
COIN CARDS number and counting 11 Card games consisting of priced items and coin cards with realistically sized coins.
NUMBER WORK 10s number and counting 12 SORT OUT -TEEN AND -TY NUMBERS is a card game of Pairs for practising the sums/layout/pronunciation of these numbers. DEDUCTION FROM 50p/£1 (eight sums for each amount) is an outline for a worksheet (teacher to enter prices). CHANGE FROM 20p (4 pp of six sums) can be printed on paper for worksheets, or on card and cut up for combining items. Illustrated with items to be purchased. 10×10 TABLES GRID GAME is for quick searching for numbers to place a counter on. Using times tables is better than just looking. Aim is to strengthen knowledge of the reversibility of sums e.g. 3×4=4×3.
NUMICON-SHAPED PRICE TAGS number and counting 13 Basically these price tags are for (a) making it clear whether the price has been covered by the ‘money’ tendered and (b) whether any change is owing. The concept of ‘difference’ in sums in words or shopping is often a real stumbling block for many children.
PLUS, MINUS AND DOUBLING – FISHING number and counting 14 Fish, rubbish and gold might be caught in the canal. Keep your score using resources like Numicon, Cuisenaire rods or buttons.
NUMBER BONDS TO 10 (AND SUBTRACTION) number and counting 15 Extension (with permission) of another resource called The Witch’s Brew. Fun way to present bonds to 10 using a leg count! Things with no legs included as distractors. Subtraction from 10 as well. Illustrated with PCS or Widgit symbols. Already visual in presentation but can be supported with abacus, Numicon, Cuisenaire rods etc.
NUMBER BONDS TO 5p AND 10p (AND SUBTRACTION) number and counting 16 Follow-on resource to the witch’s brew resources.
NUMBER WORK: COUNTING ON FROM 10p, 20p & 50p number and counting 17 Another item related to the witch’s brew resources. This set of cards allow for counting on with one silver coin and one or more 1p coins and comparing the answer with the written version.
FRACTIONS – PIZZA PARTIES number and counting 18 A story about having guests and sharing. Illustrated with Widgit symbols. Text has some symbol-support. Gaps to complete. A text to talk about.
TIMES TABLES (3-9) ILLUSTRATED number and counting 19 An attempt to make the numbers more visual in their sets plus some ‘facts’ to talk about. Cuisenaire rods and a track or a long cm ruler are extra aids to show e.g. 4×7 with 4 of 7-rods – where do they reach to? Sets and facts illustrated with PCS or Widgit symbols.
MATHS CONCEPT WORDS AND PHRASES – WORKSHEETS number and counting 20 See illus. maths concept words and phrases number and counting 5. 2: all, some, none, pair, first, last. 3: bigger, smaller, lots, a few, too many, not enough. 4: equal. 5: all, some, only one. 6: all except one, both, the other one. 7: whole, half, quarter. 8: position in row. 10: some, more, the most, less. 11: 1st,2nd,3rd. Illustrated with PCS or Widgit symbols.
WORD SUMS: 2 GAMES (ADDITION AND SUBTRACTION ONLY) number and counting 21 Designed for children who can read and do simple calculations but who struggle to make sense of word sums and need to learn to spot the key words which help.
WORD SUM WORKBOOK (1) (ADD & SUBTRACT ONLY) number and counting 22 For children with number skills and reasonable reading skills who have difficulty sorting out what the word sum means they have to do. 8 pages of questions about a situation, working towards 2-step problems. Illustrated with PCS or Widgit symbols in Numicon layout.
WORD SUM WORKBOOK (2) (ADD & MULTIPLY ONLY) number and counting 23 For children with number skills and reasonable reading skills who have difficulty sorting out what the word sum means they have to do. 8 pages of questions about a situation, including a few 2-step problems. Illustrated with PCS or Widgit symbols in Numicon layout. Building on workbook 1 (add and subtract) to improve recognition of some of the key words that identify which of the operations that result in a bigger number is needed.
WORD SUM WORKBOOK (3) (MULTIPLY OR DIVIDE) number and counting 24 For children with number skills and reasonable reading skills who have difficulty sorting out what the word sum means they have to do. 6 pages of questions about a situation. Illustrated with PCS or Widgit symbols. Building on workbooks 1 & 2 to improve recognition of some of the key words that identify multiplication or division.
MAKING A PIZZA number and counting 25 If two people are taking turns to make requests, it will give added opportunities to explain there are no more mushrooms but you can have sausage etc. Gives practice in making four quarters equal a whole. You can also talk about two halves, no …, all … and so on.