Types of Addition and Subtraction Problems
Examples with whole numbers

Overview
  • Join problems
  • Separate problems
  • Part-part-whole problems
  • Compare or equalize problems
  • Samples to classfiy

Join Problems (start + change = sum or result)
(start + change = sum or result)

Missing Sum or Result Unknown
(start + change = ____________)

  1. Pete had 3 apples. Ann gave Pete 5 more apples, How many apples does Pete have now?
  2. Sandi had 7 dimes. Mike gave her 4 more. How many dimes does Sandi have altogether?

Missing Change Addend Unknown
(start + ____________ = sum or result)

  1. Kathy had 5 pencils. How many more pencils does she have to put with them so she has 7 pencils altogether?
  2. Sandi has 7 dimes. Mike gave her some more. Now Sandi has 11 dimes. How many did Mike give her?

Missing Start or Initial Addend Unknown
(____________ + change = sum or result)

  1. Bob got 2 cookies. Now he has 5 cookies. How many cookies did Bob have in the beginning?
  2. Sandi has some dimes. Mike gave her 4 more. Now Sandi has 11 dimes. How many dimes did Sandi have to begin with?

Separate Problems
(start - change = difference or sum or result)

Resulting Difference or Sum Unknown
(start + change = ____________)

  1. Sandi has 11 dimes. She gave 4 dimes to Mike. How many dimes does Sandi have now?
  2. Joe had 8 marbles. Then he gave 5 marbles to Tom. How many marbles does Joe have now?

Missing Change Addend/Subtrahend Unknown
(start + ____________ = difference or sum)

  1. Sandi had 11 dimes. She gave some to Mike. Now she has 7 dimes. How many did she give to Mike?
  2. Fred had 11 pieces of candy. He lost some of the pieces. Now he has 4 pieces of candy. How many pieces of candy did Fred lose?

Initial Addend/Minuend Unknown
(____________ + change = difference or sum)

  1. Sandi had some dimes. She gave 4 to Mike. Now Sandi has 7 dimes left. How many dimes did Sandi have to begin with?
  2. Karen had some word problems. She solved 2 of them. She still has 3 word problems. How many word problems did she have to start with?

Part - Part - Whole Problems
(part + part = whole)

Missing Whole or Sum Unknown
(part + part = ____________

  1. There are 6 boys and 8 girls on the volleyball team. How many children are on the team?
  2. Bobbi has 3 dimes and Azzie has 5. If they put them together how many do they have?
  3. Mike has 5 pennies and 10 dimes. How many coins does he have?
  4. Mike has 5 dimes and Sandi has 10 dimes. They put there dimes into a piggy bank. How many dimes did they put into the bank?
  5. Sara has 6 sugar donuts and 9 plain donuts. Then she puts them all on a plate. How many donuts are there on the plate?

Missing Part Unknown
(part + ____________ = whole) or
( ____________ + part = whole)

  1. Carlos had 8 quarters in his pocket. He reaches in and pulls out four. How many are still in his pocket?
  2. Brian has 14 flowers. Eight of them are red and the rest are yellow. How many yellow flowers does Brian have?
  3. Bobbi and Sandi put 12 dimes into a change purse. Sandi put in 8. How many did Bobbi put in? or Mike and Sandi put 11 dimes into a piggy bank. Mike put in 7 dimes. How many dimes did Sandi put in?
  4. Mike has 10 coins. 7 of his coins are dimes, and the rest are pennies. How many are pennies?
  5. Joe and Tom have 8 marbles when they put all their marbles together. Joe has 3 marbles. How many marbles does Tom have?

Compare or Equalize Problems
(one value + or - difference = second value)

Difference Unknown
(one value + or - difference = second value)
(one value - second value = difference)

  1. Joe has 3 balloons. His sister Connie has 5 balloons. How man more balloons does Connie have than Joe?
  2. Janice has 8 sticks of gum. Tom has 2 sticks of gum. Tom has how many sticks less than Janice?
  3. Mike has 11 dimes and Sandi has 5. How many more dimes does Mike have than Sandi?
  4. Mike has 11 dimes. Sandi has 5 dimes. How many fewer dimes does Sandi have than Mike?

Larger Unknown
(one value + difference = second value)
(second value - difference = first value)

  1. Luis has 6 goldfish. Carla has 2 more goldish than Luis. How many goldfish does Carla have?
  2. Dad bought 18 bottles of milk on Sunday and on Monday he brought 6 bottles less. How many bottles did he bring on Monday?
  3. Mike has 4 more dimes than Sandi. Sandi has 7 dimes. How many dimes does Mike have?
  4. Sandi has 4 fewer dimes than Mike. Sandi has 7 dimes. How many dimes does Mike have?
  5. Jane has 7 dolls. Ann has 3 dolls. How many dolls does Jane have to lose to have as many as Ann?
  6. Connie has 13 marbles. If Jim wins 5 marbles, he will have the same number of marbles as Connie. How many marbles does Jim have?

Smaller Unknown
(one value + difference = second value)
(second value - difference = first value)

  1. Maxine has 9 sweaters. She has 5 sweaters more than Sue. How many sweaters does Sue have?
  2. Jim has 5 marbles. He has 8 fewer marbles than Connie. How many marbles does Connie have?
  3. Sandi has 4 fewer dimes than Mike. Mike has 11 dimes. How many dimes does Sandi have?
  4. Mike has 4 more dimes than Sandi. Mike has 11 dimes. How many dimes does Sandi have? Susan has 8 marbles.
  5. Fred has 5 marbles. How many more marbles does Fred have to get to have as many marble s as Susan has?

Where would you put these?

  1. There were 6 boys on the soccer team. Two more boys joined the team. Now there is the same number of boys as girls on the team. How many girls are on the team?
  2. There were 11 glasses on the table. I put 4 of them away so there would be the same number of glasses as plates on the table. How many plates were on the table?
  3. There were some girls in the dancing group. Four of them sat down so each boy would have a partner. There are 7 boys in the dancing group. How many girls are in the dancing group?
  4. Jim has 7 quarters. Ann has 3 quarters. How many quarters does Jim have to spend to have as many as Ann?

Ideas originated from: Research on Whole Number Addition and Subtraction. Karen C. Fuson in Handbook of Research on Mathematics Teaching and Learning. Ed. Douglas A. Grouws. Macmillan Publishing Co. 1992.

Dr. Robert Sweetland's notes