This is a collection of work. Click through the chapters to see the full collection or download the attached standards file.
Adding three-digit numbers
Teacher's notes
- Understands 789 as 700 + 80 + 9.
- Uses partitioning to add three-digit numbers.
Fractions of a number
Teacher's notes
- In oral work considers unit fractions.
- Relates fractions to sharing (division).
-
Understands that
of a number is less than
of that number.
Coins problem
Teacher's notes
- Represents 'seven 5p coins – how much is that?' as a multiplication.
- Understands multiplication as repeated addition.
- Represents the addition as jumps of a regular size on a number line.
Arrays
Teacher's notes
- Selects an appropriate array to represent a multiplication.
- Writes own 'multiplication story' in real-life context to match a given array.
Ways to add 9
Teacher's notes
- In oral work, suggests different methods to add 9.
- Uses +10 and then -1 to add 9.
- Draws a number line on his mini-whiteboard to demonstrate.
- Suggests 53 + 7 + 2 as an alternative method using 60 as a 'landmark' on the number line.
Sharing with your friends
Teacher's notes
- Uses doubling with halving as the inverse.
- In discussion with the teacher, responds to a suggested real-life context for the calculation.
Apples problem
Teacher's notes
- Derives multiplication facts from knowledge of ×2 table and doubling.
- Interprets the problem as 'How many fours make 34?' and records 8 and a half.
- Through discussion, concludes that Mrs Bond needs to buy 9 packs of four apples.
What the teacher knows about Daniel's attainment in Ma2
Daniel understands place value in three-digit numbers and is beginning to work with four digits. He rounds numbers to the nearest 10 and knows that 349 is closer to 300 than 400. He places two-digit numbers reasonably accurately on a number line he has drawn, initially showing 0, 50 and 100 as 'landmarks'. He has experienced negative numbers, 'minus 1', minus 2', etc., in the context of temperatures that are below zero.
Daniel finds one-half and one-quarter of a number of objects. He is beginning to relate fractions to division. He calculates one-third of numbers such as 12 as well as finding other unit fractions of larger numbers practically, by partitioning sets of cubes into an appropriate number of groups. He is beginning to understand the relative size of different unit fractions. For example, he understands that
of a set of sweets is more than
of the set.
Daniel understands subtraction as the inverse of addition. He uses this to complete calculations with missing numbers or, for example, to generate the related subtraction sentences, given an addition. He understands multiplication as repeated addition and represents examples as jumps of a constant size on a number line. He knows how an array of counters can be used to represent a multiplication. He uses his knowledge of 'doubles facts' to halve numbers. When solving division problems he interprets the remainder, sometimes with the support of probing questions, to decide whether to round up or down.
He uses an empty number line to support mental addition of two two-digit numbers. He uses addition facts to 10 and the strategy of 'jumping' to the next multiple of 10 on the number line when he adds or finds a difference. He also uses this knowledge when subtracting to check the accuracy of his answer. Daniel knows multiplication facts for ×2, ×5 and ×10. He uses the addition and multiplication facts that he knows to derive others. For example, he uses 6 + 4 = 10 to derive 60 + 40 = 100. He uses partitioning to add three-digit numbers and number line methods to add and subtract. When multiplying and dividing he is beginning to use known multiplication facts for 2, 5 and 10 to multiply larger numbers.
Daniel solves word problems where he needs to add and subtract money and measures, including those that involve bridging tens. He writes time problems for others to solve with solutions, for example 'The film starts at quarter to 9 and ends two and a half hours later. What time does it end? Quarter past 11.'
Summarising Daniel's attainment in Ma2
Daniel's attainment in Ma2 is best described as working at the lower end of level 3. He shows understanding of place value when he partitions a three-digit number into its hundreds, tens and units parts. Given a two-digit or three-digit number he can round to the nearest ten or say which hundred is nearest. He uses decimal notation for £p including recording the total of two £1 and five 1p coins as £2.05 and knows that negative numbers are used in temperature. Daniel recalls addition facts to 10 and 20. He adds two two-digit numbers mentally and uses mental and number line methods to subtract. He is beginning to use a written method of partitioning and recombining to add three-digit numbers. Daniel uses his knowledge of the ×2, ×5 and ×10 tables to derive other multiplication and division facts. He solves problems involving multiplication and division and is beginning to interpret remainders. He uses
unit fractions and is beginning to use fractions that are several parts of the whole, for example
in the context of time.
To make further progress within Ma2 level 3, Daniel needs to work with negative numbers in contexts such as counting backwards past 0 or using a calculator to explore whether order matters in subtraction. He also needs to develop his understanding of fractions that are several parts of a whole and simple equivalent fractions. He needs to develop his written methods for adding three-digit numbers and to extend his knowledge of times tables to support division and his multiplication of larger numbers.
