G. Darlunio Rhifau

Aims
  • Linking mental operations on numbers with pencil and paper algorithms and with a visual model of the number system.
  • Resources Vocabulary
  • A4 paper
  • Picturing Numbers 1 and 2 – one of each per pair
  • method, system, strategy, advantages, disadvantages,positive, negative
    Organisation
  • Near ability pairs on mixed ability tables
  • Whole Class Preparation: (about 10 mins)
  • You are going to do some mental maths in your head and compare this to other methods on paper and using number lines.
  • Work out 27 + 16 in your head.
  • Get several students to explain how they worked it out.
  • Model the recording for a few different mental methods on the board. It is best not to use the ‘=’ sign. Record each stage of the solution on a separate line
  • Ask other children if the explanation makes sense. Is it different from the method you used or similar? What is similar? Breaking the number down into easier numbers, numbers with HTOs and 5s.
  • How could we model this calculation on a number line? Show movement up the vertical number line. Ask children to suggest several different ways of recording.
  • Try 55 - 37 in your heads.
  • What written method might we use to work out this calculation?
  • Invite a child to come up and model the standard algorithm on the board.
  • What about recording on a number line? What is similar between the number line and the standard written method?
  • Paired Work: (about 10 mins)
  • Give out Picturing Numbers 1 and 2.
  • Choose another pair of two-digit numbers with your partner.
  • Mentally add them and describe the method you used. Record it using a numbe line. Use a written method.
  • Mentally subtract them and describe the method you used. Record it using a number line. Use a written method.
  • Discuss the advantages and disadvantages of the three methods.
  • It is important to ensure that both of the pair discuss and agree methods.
  • Class Sharing: (about 10-15 mins)
  • Ask one or two pairs to share the numbers that they used and their three methods. Is anything about the methods the same?
  • How do we keep track of batches of 6 when we are repeatedly adding?
  • Ask some other children to explain the advantages and disadvantages of the three methods for multiplication.
  • How is what we did here similar to what we did with addition and subtraction?
  • If you do the optional extension, division, it is important to refer to ‘x’ and ‘÷’ as inverse operations with division as sharing or repeated subtraction. Note also, the importance of estimation.
  • License

    Gwersi PCAME a Dewch i Feddwl Mathemateg (9 i 11 oed) Copyright © by Ann Longfield, David Johnson, Jean Hindshaw, Linda Harvey, Jeremy Hodgen, Michael Shayer, Mundher Adhami, Rosemary Hafeez, Matt Davidson, Sally Dubben, Lynda Maple, and Sarah Seleznyov. All Rights Reserved.

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