Math Skills

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Math Skills
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• Solve each using the specified method.
• Partial sums addition 3581 2718
• Adding up 64 - 28
• Partial differences 578 319
• Partial products 18 27
• Lattice 24 67
• Alternative division wrestling 947 ?19

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Addition and Subtraction Models

• Problems that take action to join or separate.
• Problems that do not take action but compare.

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Join Problems

• Unknown result
• Kim had 5 dolls. She got 2 more for her
  birthday. How many dolls did she have then?
• Unknown change
• Kim had 5 dolls. She got some more for her
  birthday. Now she has 7 dolls. How many did she
  get for her birthday?
• Unknown start
• Kim had some dolls. She got 2 more for her
  birthday. Then she had 7 dolls. How many did
  she have before her birthday?

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Separate Problems

• Unknown result
• Kim had 5 dolls. She lost 2. How many dolls did
  she have then?
• Unknown change
• Kim had 5 dolls. She lost some. Now she has 2
  dolls. How many did she lose?
• Unknown start
• Kim had some dolls. She lost 4. Then she had 7
  dolls. How many did she have to start?

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With a partner

• Write a story problem for
• Join unknown result
• Join unknown change
• Join unknown start
• Separate unknown result
• Separate unknown change
• Separate unknown start

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Problem Styles

• Part part whole
• Whole unknown5 boys and 8 girls were eating
  lunch. How many children were eating lunch?
• Part unknown13 children were eating lunch. 5
  were boys. How many girls were eating lunch?
• Compare problems
• Difference unknownHillary has 5 goldfish. Matt
  has 8 goldfish. How many more goldfish does Matt
  have than Hillary?
• Compare set unknownHillary has 5 goldfish. Matt
  has 3 more goldfish than Hillary. How many
  goldfish does Matt have?

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Division Models

• Quotitive or grouping
• There is a predetermined number of items in each
  group, the solution is the number of groups there
  are
• Partitive or sharing
• There is predetermined number of groups, the
  solution is the number of items in each group

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Quotitive Grouping Examples

• A jar contains 12 quarters. There are 4 quarters
  in a dollar, how many dollars are there in the
  jar?
• Karen is having a party and invited 11 guests (12
  people including her). She wants to seat people
  at tables of four, how many tables does she need?
• Jesse is going on vacation and is packing 24
  shirts. If he can fit 12 shirts in each bag, how
  many bags will he need?

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Partitive Examples

• Jon has 30 baseball cards, they are split into 6
  groups. How many cards are in each group?
• Susie has 50 gumballs and is putting them into 10
  bags, how many are in each bag?
• Eddie made a batch of 10 large cookies. He put
  them in 20 separate baggies, how many cookies are
  in each baggie?

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With a partner

• Write a story problem that involves partitive
  division.
• Write a story problem that involves quotitive
  division.

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Representations for 3 4

• Additive
• Multiplicative

Array
Area
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Properties of Numbers

• Commutative
• a b b a
• Associative
• a ( b c) ( a b ) c
• Distributive
• a ( b c ) ab ac
• Identity
• a 0 a or a 1 a
• Inverse
• a - a 0

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Algorithms

• An algorithm is a procedure (set of directions)
  for doing a routine task.
• Being able to perform a procedure is not the same
  as understanding it relationally.

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With a partner

• Write algorithms for the following situations.
  Be sure to include directions for all situations.
• Adding two digit numbers
• Multiplying fractions

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What do you call the result of an operation?

• AdditionSum
• SubtractionDifference
• MultiplicationProduct
• DivisionQuotient

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• Turn homework in before you leave.