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Understanding Basic Arithmetic Operations: Addition, Subtraction, Multiplication, and Division

This resource provides an engaging approach to teaching fundamental arithmetic operations—addition, subtraction, multiplication, and division—using number lines and partitioning. It emphasizes starting with the larger number in addition, demonstrates subtraction through counting back, illustrates multiplication as repeated addition, and introduces division via the concept of chunking. The methods foster a deeper understanding of the formal written techniques and provide practical tools for both educators and parents to assist children in mastering math concepts.

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Understanding Basic Arithmetic Operations: Addition, Subtraction, Multiplication, and Division

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  1. Routes through Calculation Friday, 21 March 2014

  2. What you say counts.

  3. Addition: Number lines: Addition can be done in any order, but encourage pupils to begin with the largest number e.g. 5+8 is the same as 8+5 +1 +1 +1 +1 +1 8 9 10 11 12 13

  4. Addition: The number line can be extended to larger numbers, and used For counting on in GROUPS of tens and ones/units. PARTITIONING can now be into larger groups. e.g. 86+57 +50 +4 +3 86 136 140 143

  5. Addition: Partitioning can be used to build on the knowledge used from number lines 35+26 30+20=50 5+6=11 50+11=61

  6. Addition: This leads on to the informal and formal written method!

  7. Subtraction: The number line can be used for subtraction, but going the other way. e.g. 19-5 -1 -1 -1 -1 -1 14 15 16 17 18 19

  8. Subtraction: And with larger numbers too! e.g. 219-37 -7 -30 182 189 219

  9. Subtraction: By partitioning.

  10. Subtraction: This leads to a better understanding of the formal method! • 1 • 7 4 – • 7 • --------- • 4 7

  11. Multiplication Begins with simple dot arrays and groupings O O O O O O ooo Is either 3 lots of 2, or 2 lots of 3 ooo OOO OOO * * * * * * * * * * * * * * * 4 lots of 3 4 X 3 3+3+3+3 (Solve with a number line beginning at 0) Multiplication is simply repeated ADDITION!

  12. Multiplication: • Partitioning again. • 12 X 6 • (10+2) X 6 • 10 X 6 = 60 • X 6 = 12 • 60 +12 = 72

  13. Multiplication: The GRID method, using partitioning. E.g.9 X 46 40 6 9 360 54 360 + 54 = 414

  14. Multiplication: And larger numbers… 72 X38 70 2 30 2100 60 =2160 8 560 16 = 576 2160 + 576 = 2736

  15. Multiplication Leading to the expanded methods:

  16. Multiplication And finally the formal written methods:

  17. Division: Like multiplication, begins with dot arrays and groupings. O O O O O O ooo Is either 6 shared between 2, or 6 shared between 3 ooo OOO OOO * * * * * * * * * * * * * * * 12 ÷ 4 = 3

  18. Division: Division is simply repeated SUBTRACTION! Using a number line. E.g. 35 ÷ 7 -7 -7 -7 -7 -7 0 7 14 21 28 35 35 ÷ 7 = 5 There are 5 “jumps”

  19. Division: With remainders. E.g. 38 ÷ 7 -7 -7 -7 -7 -7 -1 -1 -1 3 10 17 24 31 38 38 ÷ 7 = 5 “jumps” – 3 38 ÷ 7 = 5 r 3

  20. Division: Chunking! Simple With remainders

  21. What have you got to help you and your child with maths? Conker Maths/ KIRFS http://www.conkermaths.org/cmweb.nsf/pages/kirfs.html RMEasimaths http://www.rmeasimaths.com/ Mathletics http://www.mathletics.co.uk/

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