Math Matters of San Joaquin County

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

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Fourth Grade Head Problems

Some hints:

Look at hints and samples for third grade for review ideas. (Use the "Back" button on your browser to return to this page.)

Remember that the "preview" lets you include one step that is more challenging than the others, even something students have not been exposed to before.

Writing your head problems, whether in a matrix, individually, or in some other form that works for you, will improve the quality of your head problems. If you just make them up on the spot, there is a tendency to repeat the same language and concepts.

Here is a problem from the third grade samples that would be a good review for fourth grade.

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?

Are there words in that head problem that your students might not know? Perhaps you would want to do other head problems that would get them familiar with those words before doing the one above.

Here are some samples of head problems from the math standards for fourth grade.

PREVIEW:

• Put 5 + __ = 9 on the board and ask for a quiet hand for the number that goes in the blank.

• Ask if instead of a blank, the 4 could be symbolized as a heart or a star or a box.

• Ask if it could be represented by a letter of the alphabet like x or n.

• Write 5 + __ = 9 using those different symbols (i.e., 5 + heart = 9; 5 + n = 9), then ask if an equation could be written with each symbol that says symbol = 4(i.e., heart = 4; n = 4).

HP:

Put on the board 5 + x = y and x = 2.

1. In your head, think of the number that y equals if x = 2. (7)

2. Multiply that by the fourth prime number. (49)

3. Round to the nearest tens (50)

4. On your fingers, show me the product of the digits. (0)

DEBRIEF:

As above.

PREVIEW:

• Draw a rectangle on the board and ask for someone to tell you what perimeter is. If no one knows, tell them what perimeter is. (Prefix peri- means around. Root meter means measurement.)

• Add the dimensions 1 and 2 to your rectangle and ask if someone can tell you what the perimeter of your rectangle is, while moving your f inger around the perimeter. -- Clarify what perimeter means if there is confusion.

• Change the dimensions on the rectangle to 2 and 3.

HP:

1. In your head, find the perimeter of this rectangle. (10)

2. Triple that number. (30)

3. Divide your answer by the number of sides on a hexagon. (5)

4. When I say go, show your neighbor your answer on your fingers.

DEBRIEF:

As above.

PREVIEW:

• Put the number 6 on the board and ask students for factors of 6. If there are no answers, put 2 x 3 = 6 on the board and explain that 2 and 3 are factors.

• Ask if they can think of any other factors of 6.

• Put 7 on the board and ask for factors of 7. Ask if there are any other factors of 7.

• Draw a rectangle that is labeled 3 x 2.

HP:

1. In your head, think of the largest factor of 5. Whisper that number to your neighbor. (5)

2. Add to it -2. (3)

3. Multiply your answer by the perimeter of this rectangle. (30)

4. I'll take a quiet hand for the answer.

DEBRIEF:

As above.

Geometric solids are a good source of numbers that lets students learn the vocabulary of three dimensional shapes.

PREVIEW:

• Hold up a cube and, brushing the faces, ask for students to show you on their fingers the number of faces on a cube.

• Then ask them for the number of vertices on the cube as you point to the vertices.

• Then ask for a quiet hand to tell you how many edges are on the cube, as you run you finger along one edge after another.

HP:

1. In your head, think of the number of faces on a cube. (6)

2. Multiply that number by the number of vertices on a cube. (48)

3. Round that number to the nearest tens. (50)

4. Show me one tenth of your answer on your fingers. (10)

DEBRIEF:

As above.

PREVIEW:

• On the board or overhead, draw a circle with a diameter line drawn. Label the diameter 10.

HP:

1. In your head, think of the radius of this circle (indicating half the diameter with your hands) if the diameter is 10. (5)

2.Multiply that number by 100. (500)

3. Add the number of cents in one quarter and one nickel and two pennies. (532)

4. Show me the sum of the digits on your fingers.

DEBRIEF:

As above.

PREVIEW:

• Have a number line posted or drawn that goes from -10 to +10.

• Put the number 321 on the board. Ask for the value and place of each digit. (What is the value of the 3 in this number? What place is it in? What is the value of the 2 ... etc.)

HP:

1. (Using the number 321) In your head, think of the value of the digit in the tens place of this number. (20)

2. Now think of one fourth of that number. (5)

3. Find that number on a number line and hop 7 numbers in a negative direction.(-2)

4. Raise a quiet hand if you'd like to write your answer on the board.

DEBRIEF:

As above.

In a later problem, or if your students are familiar with subtracting larger numbers from smaller numbers, step 3 (above) might read, "Subtract 7."

PREVIEW:

• Have a transparency with 4 equilateral triangles, 2 isosceles triangles and 6 scalene triangles. Save this transparency and use to introduce the other triangles as well.

• Ask students what the word equilateral might mean. (Prefix equi- means equal. Root lateral means side or sides.)

• Then ask students if they see any equilateral triangles on your transparency. Point at triangles and ask them to show you signals if they are or are not equilateral triangles.

• Also write the number 439 on the board.

HP:

1. In your head, think of the number of equilateral triangles on the overhead. (4)

2. Multiply that number by the number of sides on three triangles. (36)

3. Subtract from that number the value of the digit in the tens place in this number (the number 439 on the board). (6)

4. When I say go, write that number in the air.

DEBRIEF:

As above.

While it is useful to tie your head problem to your current math lesson, it is recommended to also include steps from other areas of math. A variety of math concepts can be combined so that there is review, check for understanding on current learning, and sometimes introduction all in the same head problem.

If head problems are taking more than 5 to 7 minutes, try doing fewer steps. Finding quick ways to preview material before the head problem will shorten the head problem by allowing more students to be successful. It might also help to use a Mode of Response with each step so students who have trouble following will be able to look around and check their own thinking with other students' responses.

As you find some head problems that work really well, you might offer to share them with other teachers at your grade level. Sharing head problems is a great way to a have larger collection to draw from and to get more ideas for writing your own.

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