10 Elementary School Math Teaching Tips

Posted by David Wetzel

Elementary Math Teaching Tips

Teaching math to elementary students is critical for establishing a foundation of success in mathematics.

There is a need for some basic memorization of facts, because students who do not memorize arithmetic functions struggle in upper grades.

However, math must be fun and interesting, along with making connections with real-world applications.

Math Teaching Tips

Problem solving, critical thinking, mental math, math games, technology, interactive websites, and more:

Asking Questions – write the word “ten” on the board. Now ask students if there is another way to express “ten.” A student may write “10,” now ask is there another way to express “10.” A second student may write “llllllllll,” now ask is there another way to express “llllllllll.” This can be continued until most possibilities are exhausted. Students are using critical problem solving skills and eagerly participate.

Collect Own Data – instead of using data for graphing from a text book or worksheet. Let them collect their own data. For example: measuring the lengths of various objects in the classroom or counting the number objects in a box placed on their desk.

Positive and Negative Integers Game – divide students in groups and give each group a deck of playing. Red numbers and face cards are negative. Black numbers and face cards are positive. Aces equal “1” and face cards are Jack “11,” Queen “12,” etc. Now then play a game similar to war by attempting to be the first in their group to reach 25. Read more…

Multiplication Challenge – have all students turn their seats to face the front of the room. Then have a student walk around the room and stand next to another student. Both students stand are asked a multiplication problem, whoever gets it correct first moves on to select another student.

Real World Geometry – take students outside and have them draw pictures of all the geometric shapes they see. Then have them share after reentering the classroom.

Weekly Word Problems – once a week begin math class with a word problem students must answer related to current concepts being studied. This is a key step in learning how to develop problem solving skills.

Interactive Math Websites – use computer learning centers for students to study math concepts using these interactive math websites, such as: Illuminations or National Library of Virtual Manipulatives .

Math WebQuests – develop your own or find some already prepared and have students work in groups to solve math problems or develop a better understanding of math concepts.

Use Math Tradebooks – use tradebooks in connection with concept being studied, such as: Anno’s Magic Seeds, Very Hungry Caterpillar, Sir Cumference, Grapes of Math, and more.

GeoBoards – use geoboards for students to design their own shapes and describe them to each other using correct geometric terminology.

Elimination of Misconceptions in Math

The math teaching tips above, when used effectively can help eliminate many misconceptions in mathematics by elementary students.

Eliminating math misconceptions is difficult and merely repeating a lesson or extra practice will not help.

Telling students were they are mistaken will not work either. Recognizing student misconceptions and immediately focusing a discussion on the misconception is important.

Providing guiding questions and hands-on approaches are the best approach. One Example is:

Geometric Shapes are not Recognized Unless Held Upright

This is typically an inadvertent misconception passed on by teachers. If geometric shapes, such as triangles or rectangles, are held in one direction all the time students will not recognize it when viewed in a different direction.

• Students can only find a diamond shape if pointed in the right direction. In reality there is no such thing as a diamond shape, it is either a square or a rhombus.

• The best ways to eliminate this misconception is to allow students to draw geometric shapes in any direction, provide examples of shapes in a variety of directions, and rearrange displays of geometric shapes to point in different directions regularly.

More examples….

It is important for students be placed in situations in which they must apply what they are learning to personal experiences and situations. This helps reinforce math concepts and moves them to a level of true understanding of mathematics.

Geometric Problem Solving with Snap Cubes

Posted by David Wetzel

Geometric Problem Solving

Problem solving in mathematics is critical to understanding geometric concepts and also making connections with other mathematics concepts.

The following activities cause students to use critical thinking and problem solving skills - often referred to as inquiry-based teaching and learning.

Inquiry Math Activity

Materials – 27 one inch snap cubes for each student

Procedures – Part 1

Give each student 27 snap cubes

Ask them to determine how many different ways can they can join three cubes face-to-face? (These are called “tri-cubes”)

Tell them that if a tri-cube can be flipped or repositioned (reflected, rotated) in such a way that it is exactly like a tri-cube already made, it is not different from the other one.

Notes

There are only two different tri-cubes – rectangular and non-rectangular.

Have students retain the non-rectangular tri-cube.

Procedures – Part 2

Ask students to find all possible non-rectangular tetra-cubes (4 unit cubes joined face-to-face).

Note

There are only six different tetra cubes – see picture (the picture also contains the one non-rectangular tri-cube).

Tetra-Cubes

Discussion

Ask the following questions:

Are any of the pieces reflections of each other? (If you put a mirror next to one piece, will you see the other in the mirror?)

Which pieces can be placed so that they are only one unit high?

Which pieces must occupy space that is 2 units high?

Which pieces have a line of symmetry on a given face?

Procedures – Part 3

Ask students to find the surface area and volume of each of the six tetra-cubes and the non-rectangular tri-cube – recording their data in a data table.

Discussion

Ask the following questions:

Did the pieces with the same volume have the same surface area?

Did the pieces with the same surface area have the same volume?

Procedures – Part 4

Ask to make a SOMA Cube by connecting their non-rectangular tri-cube and 6 tetra-cubes into a 3 by 3 cube without altering the shape of the tri-cube or tetra-cubes.

Ask students to record and share how they created a SOMA Cube with the class.

Note

There are 214 different ways.

Extension

Ask students to create other shapes using the non-rectangular tri-cube and 6 tetra-cubes without altering the shape of the tri-cube or tetra-cubes. (See picture for examples)

Soma Cube Shapes

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Pythagorean Theorem - Real World Application

Pythagorean Theorem - Real World Application

Posted by David Wetzel

Pythagorean Theorem

The Pythagorean Theorem is used any time you have a right triangle in which you know the length of two sides and want to find the third side.

The formula is: a² + b² = c²

There are many strategies for getting students to learn how to solve a problem related to this theorem. Many of these problems are boring, procedural driven, and lacking in connection to real world applications.

In the view of many this is often necessary because they do not have the time to teach it any other way. Curriculum, testing, and No Child Left Behind pressures cause these views.

However, there are other strategies to teach the same concept and yet make it more interesting for students. The critical aspect of this strategy is to make connections to their world.

Students always ask:

• When will I every use the Pythagorean Theorem?
• Why do need to learn this? It is boring!

The answer is, in any kind of job that deals with triangles. For example, carpenters, engineers, architects, construction workers, those who measure and mark land, artists, and designers of many sorts need to know it.

Problem Solving Application

The following are problem is more interesting and designed to find the length of a² and b², when only c² is known.

Shopping for a New TV

Jacob and Denise, brother and sister, are trying to get their parents to buy them a new TV. Their parents have agreed; however, they are limited to a size 32 inch TV.

Now they must go shopping to find the one they want. At their local electronics store, they discover that 42 inch TVs come in a lot shapes and sizes.

This does not seem to make since, until the salesman tells that 42 inches is diagonal measurement that is the normal way of sizing TVs.

They decide to compare the difference between a 32 inch standard TV and 32 inch flat screen HDTV. Jacob and Denise both agreed that they should buy the TV with greatest viewing area.

After looking a both TV types, they predicted that the flat screen HD TV had the greatest viewing area.

How would you determine which TV has the greatest viewing area?

Answer

TV Problem: the key to this problem is the aspect ratio of the TVs. The Standard TV has an aspect ratio of 4:3, while the Flat Screen HDTV has an aspect ratio of 21:9.

First they must find out what each unit equals (for example in the Standard TV is 4 units wide and 3 units high - aspect ration 4:3) in the aspect ratio for each TV by using the Pythagorean Theorem.

Next they must find the area of each TV using A = w x h.

Standard TV Area = 491.56 in²

Flat Screen HD TV Area = 370.44 in²

Jacob and Denise now must decide which TV they really want, because their prediction was wrong.

——

This problem not only makes connections to something that students are actually interested in, they also make connections to other math concepts. Pythagorean Theorem now has a real world application to students and they will see its value.

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