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Ma2 Number

Count in fours

Teacher's notes

  • Works with a partner to find how many buttons in the class collection.
  • Chooses to group buttons in fours to count them.
  • Records the total so far under the latest group.

Next steps

  • Work with partner to add their totals and find the number of buttons in the whole collection.
  • Regroup all of the buttons in tens and count them in tens to check the total.

Multiples

Handwritten note of the teacher on Daniel's understanding of numbers and number system dated 6-7 April 2008

Handwritten note of Daniel's attempt to determine multiples

Handwritten note of Daniel's attempt to determine multiples of 5

Teacher's notes

  • Groups linking cubes in twos to demonstrate that 10 is an even number.
  • Recognises larger even numbers.
  • Continues ascending and descending sequences of even numbers.
  • Also knows that odd numbers end with 1, 3, 5, 7 or 9.
  • Understands multiples as the numbers he says when counting in twos, fives, tens, etc.
  • Completes sequences of multiples and uses the same numbers to create descending sequences.

Next steps

  • Explore multiples in other contexts, e.g. sorting numbers of cubes that can be used to create four equal towers with none remaining.
  • Apply his knowledge of multiples to reading simple scales on measuring instruments or to interpreting a pictogram where one symbol represents two or more items.

Sorting and ordering numbers

Teacher's notes

  • Assembles a new classroom resource, which has a 10 by 10 arrangement of clear pockets to hold cards numbered from 1 to 100.
  • Chooses to find numbers 1 to 10 and position them in turn across the top row.
  • Adapts his approach to include positioning numbers in columns.
  • Uses the units digit to decide the column and the tens digit to decide the row.
  • Orders all of the numbers from 1 to 100.

Next steps

  • Talk about what would happen if:
    • the numbers started with zero
    • there were only five columns in the grid.
  • Pose his own questions, predict where numbers will be placed and test the prediction.

Ordering numbers

Handwritten note of teacher's comment on Daniel's ability to order numbers

Teacher's notes

  • Withdraws pairs of digit cards from a 1 to 9 pack and uses them to create two different two-digit numbers.
  • Says which of the numbers is greater.

Next steps

  • Record the pairs of two-digit numbers made, using the symbols '>' or '<' to show the relationship between them.
  • For each pair find out how much greater the greater number is, i.e. find the difference.
  • Record all of the differences on a 100-square, compare results with others and look for a pattern in the results.

Place value

Handwritten note of Daniel finding out totals of 67, 38, 49, 23, 95, 81, 71, and 22

Teacher's notes

  • Partitions two-digit numbers.
  • Begins to understand place value in numbers greater than twenty.
  • Is less secure with 'teens' numbers.

Next steps

  • Use a range of models and images for two-digit numbers:
    • base 10 materials
    • positions on a number line
    • arrow cards.
  • Match the number names that sound similar to the numbers in figures:
    • 'sixteen' and 'sixty' to 16 and 60
    • 'seventeen' and 'seventy' to 17 and 70…

Addition facts

Handwritten note of Daniel's attempt to find different possibilities to determine total of 1, 2 and 3
Handwritten note of Daniel's attempt to find different possibilities to determine total of 4 and 5
Handwritten note of Daniel's attempt to find different possibilities to determine total of 6
Handwritten note of Daniel's attempt to find different possibilities to determine total of 7
Handwritten note of Daniel's attempt to find different possibilities to determine total of 8

Teacher's notes

  • Chooses to list addition facts he knows for different numbers.
  • Works in an organised way finding pairs of numbers that add to 1, 2, 3…
  • Records addition sentences using symbols '+' and '='.
  • Understands addition can be done in any order.
  • Checks he has all addition pairs for each number.
  • Looks for pattern in results.
  • Notices that the number 1 has two facts, number 2 has three facts…
  • Predicts that for the number 9 there will be ten facts and for 10 eleven facts.

Next steps

  • Reorganise his calculations as a way of justifying his prediction, e.g.
    0 + 3 = 3
    1 + 2 = 3
    2 + 1 = 3
    3 + 0 = 3
  • Test the prediction by listing the addition facts for 9 and 10.
  • Find different pairs of numbers to make these subtraction sentences correct:

     

    ☐ - ☐ = 1,  ☐ - ☐ = 2
    	

     

  • Talk about why there are an infinite number of ways to complete the subtraction sentences.

Coins problem

Illustration of different coin denominations to find total of 28 pence, 36 pence, 45 pence, 56 pence and 72 pence

Teacher's notes

  • Shows how to pay for various items using as few coins as possible.
  • Works in an organised way selecting the largest coin values first.
  • Places coins next to items.
  • Records by tracing around the coins, accidentally moving a 1p coin into the wrong group.
  • Records coins that total 72 pence but not the fewest possible.

Next steps

  • Review and check his work.
  • Investigate a related situation:
    • find all the ways to pay exactly 10 pence and talk about how you know you have them all
    • find ways to pay each amount from 1p to 50p using as few coins as possible and talk about amounts that can be made with just one coin, with just two coins.

What the teacher knows about Daniel's attainment in Ma2, Number

Daniel groups objects in twos, fives or tens to count them efficiently. He knows the numbers he says in these counts as multiples of 2, 5 and 10. Daniel orders two-digit numbers and is beginning to use place value to do this. For example, when assembling a new resource for the classroom, he placed the numbers 1 to 100 into pockets on a 100-square. He used the units digit to decide the column and the tens digit to find the correct row for cards as he took them from the pile. Daniel also demonstrates his understanding of place value when he partitions two-digit numbers.

Daniel colours one-half and one-quarter of shapes. He also finds half of a number up to 20 using the doubling facts that he knows. Asked to find half of fourteen, for example, Daniel says, 'I know seven and seven equals fourteen so half of fourteen is seven.'

He understands addition as finding how many altogether and subtraction as 'taking away' to find how many are left. He knows that halving and doubling are related and uses doubling facts to halve even numbers. Daniel represents problems that involve multiplication as repeated addition.

Daniel knows addition facts for numbers up to 10. He is beginning to use these facts and place value to add examples such as 30 + 50, rather than counting on in tens. He knows doubles of numbers up to double 10 and some others such as the value of two 20p coins or two 50p coins. Daniel uses mental calculation and counting to solve problems including those that involve money. He solves shopping problems that involve finding the total cost of several items. He uses coins, counters or a number line to solve problems that involve calculating change, from 50 pence, for example. Daniel explains the calculations he does to solve word problems and records calculations using addition and subtraction sentences.

Summarising Daniel's attainment in Ma2, Number

His teacher judges that Daniel's attainment is best described as level 2 in most of the assessment focuses for number. Reading the complete level descriptions for levels 1 and 2 confirms the level 2 judgement.
Of the level 2 assessment criteria that Daniel meets, he does so consistently. There is a criterion in level 2 that Daniel does not yet meet and others that he has yet to demonstrate in a range of contexts. His teacher refines her judgement to secure level 2.

To make further progress in level 2 Daniel should develop his understanding of addition and subtraction as inverse operations. He needs to solve a wider range of problems that involve subtraction. He should begin to solve problems that involve sharing or grouping including, for example, sharing a set of objects between four and recognising that each has one-quarter of the set. He should also solve problems that involve measures and units such as kilograms, metres or centimetres.