## Using Cognitively Guided Instruction:

I love to use a problem solving approach to teach math. When I use this approach I begin by introducing the problem. We read through the problem several times. I like to have a large copy of the problem so students can read along with me before they have their own copy of the problem. The length of time we spend discussing the problem depends on how skilled the students are with the problem type I'm using. I usually provide several sets of numbers for the students to use. This is how I differentiate the lessons. Some students will only be required to use 2 number sets. Sometimes I challenge advanced students to do every number set. Most often I tell the class to select their own numbers from the choices with the requirement that they do at least 4 sets.

Students glue the problem into their math notebook and begin to work. They have the freedom to use whatever strategy they would like (using manipulatives, drawing a picture, counting, derived facts, etc.)

Learn more about my teaching at my other website: http://not-very-fancy.blogspot.com

Students glue the problem into their math notebook and begin to work. They have the freedom to use whatever strategy they would like (using manipulatives, drawing a picture, counting, derived facts, etc.)

Learn more about my teaching at my other website: http://not-very-fancy.blogspot.com

## Examples of different CGI problem types:

**Example Set 1--part-part-whole:**

There were 12 boys and 14 girls in Mrs. Maxwell's class. How many students were there in

all?

There were 26 students in Mrs. Maxwell's class. Fourteen of them were girls. How many were

boys?

This is a part-part-whole problem because there was no change happening in the story, but the whole number is broken down into 2 parts.

**Example Set 2--Separate:**

Mrs. Maxwell had 25 boxes of tissues. The students used 10 boxes. How many boxes does she have left?

Mrs. Maxwell had 25 boxes of tissues. The students used some. Now she has 15 boxes. How many did the students use?

Mrs. Maxwell had some boxes of tissues. The students used 10 boxes. Now she had 15 left. How many did she have in the beginning?

These are called a "separate" problem because the action involves separating some

items from the total. Although this problem would have traditionally been called a subtraction problem, we refer to it as a separate problem because the problem might not be solved using subtraction.

**Example Set 3--join:**

Mrs Maxwell had 8 pencils. Mr. Lord gave her 10 more pencils. How many pencils does she have now?

Mrs. Maxwell had 8 pencils. Mr. Lord gave her some more. Now she has 18 pencils. How many did Mr. Lord give her?

Mrs. Maxwell had some pencils. Mr. Lord gave her 10 more pencils. Now she has 18 pencils. How many pencils did she have in the beginning?

These are called "join" problems. We use the term join rather than addition because although the story is about putting two groups together, addition might not be the most efficient strategy to use to solve the problems.

**Example Set 4--compare:**

Mrs Maxwell has 22 students in her class. Mrs. Leeper has 19 student in her class. How many more does Mrs. Maxwell have?

Mrs. Maxwell has 22 students in her class. Mrs. Leeper has 3 fewer students than Mrs. Maxwell. How many students does Mrs. Leeper have?

Mrs. Maxwell has 3 more students than Mrs. Leeper. Mrs. Leeper has 19 students. How many does Mrs. Maxwell have?

These are comparison problems. These are usually difficult for first graders.

**Example Set 5--multiplication and division:**

There are 5 first grade teachers. Mr. Lord gave them each 4 computers. How many computers do they have all together?

Mr. Lord bought 20 computers for first grade teachers to share. If each teacher got 4 computers, how many first grade teachers are there?

There are 5 first grade teachers. Mr. Lord bought 20 computers for them to share. How many computers will each teacher get?*

*This is the most difficult problem type for first graders because they often are not familiar

with the procedure of "dealing" out items. Try to play games with your child that will help them develop this important concept!

These problems are multiplication/division problems. At the first grade level, students are not

familiar with the symbols for these concepts, but they are able to solve these problems with pictures or manipulatives or by repeated adding or subtracting.