Math Matters of San Joaquin County

Lincoln Unified School District - Lodi Unified School District - Stockton Unified School District

Third Grade Head Problems

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Some Hints:

By third grade, students have accumulated a fairly large body of mathematical knowledge. Head problems provide an enjoyable and quick way to review ideas from previous years and to keep current those being taught as the year progresses.

Head problems can also help build oral mathematical language, functioning as a stage in the development of math writing.

A great deal can be done with head problems that can help your students be more comfortable with standardized tests.

The math word wall, started early in the year and drawing vocabulary from Daily Head Problems, Daily Two Problem Approaches and your regular math lessons, give students a reference they will use every day.

Here are some sample head problems that might give you ideas for more of your own.

Regarding the third grade standard in Measurement and Geometry: while the standard does not specifically ask students to know the number of degrees in a right angle, it does require them to know what a right angle is in order to identify it as a property of shapes.

PREVIEW:

• Ask students to make a right angle with their arms.

• Ask for a quiet hand to tell you how many degrees there are in a right angle (90).

HP:

1. In your head, find the product of 3 and 6. (18)

2. On your fingers, show me the difference of the digits. (7)

3. Write on your mini boards what you get if you add the number of degrees in a right angle to the number you showed me on your fingers. (90+7=97).

DEBRIEF:

1. I'll take a quiet hand for the first thing I asked in the head problem.

2. Signals for what ___ said.

3. Now a quiet hand for what that number is.

4. And I see agreement for that.

5. I'll take a quiet hand for the next step in the head problem.

6. Signals?

7. And everyone, when I say go, tell me what number we have now.

8. And with a quiet hand who would like to say what we did next.

9. Signals for that?

From the third grade standard for Measurement and Geometry, 1.2:

PREVIEW:

• Hold up a 2x2x2 cube and ask for a quiet hand to tell you the volume of the cube.

• If no one knows, ask how many small cubes it took to make the larger cube and identify that as volume. (You might take the cube apart, put it together in layers, etc.)

HP:

1. In your head, think of the volume of this cube. (8)

2. Multiply that by the number of faces on this cube. (8x6=48)

3. On your fingers, show me the difference between the digits of your answer. (8-4=4)

DEBRIEF:

As above.

PREVIEW:

• Hold up a 2x2x2 cube and ask for a quiet hand to tell you the surface area of the cube.

•If no one knows, ask what the area of one face is. And how many on this face? Now how many do we have? Continue until students have figured out the surface area of 24.

HP:

1. In your head, think of the surface area of this cube. (24)

2. Now think of how many groups of 8 are in that number. (3)

3. When I say go, write your answer in the air. (3)

DEBRIEF:

As above.

From the third grade standard for Algebra and Functions, 2.0, 2.1, 2.2.

PREVIEW:

• Write a 3 digit number on the board and ask for a quiet hand to tell you how many digits there are and what digit is in each place. (review of the word "digit")

HP:

1. In your head, think of how many cents 3 pencils would cost if one pencil cost one nickel. (15)

2. Add those digits together. (1+5=6)

3. Show me one third of your answer on your fingers. (2)

DEBRIEF:

As above.

PREVIEW:

• Draw a pentagon on the board, and ask for a quiet hand to tell the class the number of sides on a pentagon.

HP:

1. In your head, think of the number of sides on four pentagons. (20)

2. Add to that the product of 5 and 6. (20+30=50)

3. I'll take a quiet hand if you would like to write your answer on the board. (Take 3 answers, then debrief.) (50)

DEBRIEF:

As above.

Multiplication facts can be practiced as above by asking for a product of two numbers for one step. It might also be practiced in the following ways.

PREVIEW:

• Write the following equation on the board: 3x__=27

HP:

1. In your head, think of the number that goes in the blank. (9)

2. Now think of how many groups of 3 are in that number. (3)

3. Show me what you get if you double your answer. (6)

DEBRIEF:

As above.

PREVIEW:

• Put the following pattern on the board: 7, __, 21, 28, 35

HP:

1. In your head, think of the number that goes in the blank. (14)

2. Double that number. (28)

3. Add those digits together and show me your answer on your fingers. (10)

DEBRIEF:

As above.

In general, it is more desirable to add complexity to a 2 or 3 step problem, than to add more steps. As you can see, the standards offer a rich resource for elements for your Daily Head Problems.

Remember if head problems are fun for you, they will be fun for your students too!

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