Cognitively Guided Instruction

Problem Types

Informal Strategy Types

Children’s Informal Strategies Direct Modeling -- Children “act out” the problem. They are very literal. They model every number and work the problem in chronological order.

Children’s Informal Strategies Counting Strategy -- The child does not model every number in the problem. The child “stores” one number and counts up or back to solve the problem.

Children’s Informal Strategies Derived Fact -- The child uses a known number relationship to figure out the desired relationship.

Problem Types JoinJoin -- The action in these problems is a joining of two sets.

The unknown quantity can be either the result, the change, or the start.

JoinJoin -- The action in these problems is a joining of two sets.

Result Unknown: Jim had 8 marbles. Sue gave him 4 more. How many marbles does Jim have now? 8 + 4 = ?

Change Unknown: Jim had 8 marbles. Sue gave him some more. Now Jim has 12 marbles. How many marbles did Sue give Jim? 8 + ? = 12

Start Unknown: Jim had some marbles. Sue gave him 4 more. Now Jim has 12 marbles. How many marbles did Jim have to start with? ? + 4 = 12

Problem Types SeparateSeparate -- The action in these problems is taking a subset out of a set.

The unknown quantity can be either the result, the change, or the start.

SeparateSeparate -- The action in these problems is taking a subset out of a set.

Result Unknown: Jim had 12 cookies. He ate 4. How many cookies does Jim have now? 12 - 4 = ?

Change Unknown: Jim had 12 cookies. He ate some. Now Jim has 8 cookies. How many cookies did Jim eat? 12 - ? = 8

Start Unknown: Jim had some cookies. He ate 4. Now Jim has 8 cookies. How many cookies did Jim have to start with? ? - 4 = 8

Problem Types Part-Part-WholePart-Part-Whole -- There is no action. A set (whole) with defined subsets (parts) is described.

The unknown quantity can be either one of the parts or the whole.

Part-Part-WholePart-Part-Whole -- There is no action. A set (whole) with defined subsets (parts) is described.

Whole Unknown: Jim had 8 red marbles and 4 blue marbles. How many marbles does Jim have in all?

Part Unknown: Jim had 8 red marbles. The rest are blue. Jim has 12 marbles in all. How many are blue?

Problem Types ComparisonComparison -- There is no action. The size of two sets is compared.

The unknown quantity can be either the difference between the sets or one of the sets.

ComparisonComparison -- There is no action. The size of two sets is compared.

Difference Unknown: Jim had 8 marbles. Sue had 12 marbles. How many more marbles does Sue have than Jim?

Large Set Unknown: Jim has 8 marbles. Sue has 4 more than Jim. How many marbles does Sue have?

Small Set Unknown: Sue has 12 marbles. Jim has 4 fewer marbles than Sue. How many marbles does Jim have?