Making Math Easier for KidsBy Besnik Keja

www.angelfire.com/dragon3/besnik

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Introduction to Geometry

• Picture things in your mind

• Draw them with your hand and with computer tools

• Describe pictures and drawings with appropriate language

• This is a good start to the year

Habits of Minds

• Visualizing

• Experimenting

• Describing with formal and informal language

• Making and using definitions– Students develop skills with computer tools

1. Can the shadow of a square on a flat floor or wall ever be non-square? Can it ever be non-rectangular?

2. Which of these shadows could be cast by a square and which could not?

3. What kinds of shadows will an equilateral triangle cast?

12

3

4

56

7

8

Connected Geometry

• The goal of a math teacher is to make mathematics compelling and attractive to students.

• All mathematics is fair game for connected geometry.

• Encourage students not only to learn math content,but also to use and value math habits of mind.

Connected Geometry• Students first explore open ended problems.• Students refine these processes into formal algorithms.• Students learn about concept of area, area formulas and the

Pythagorean Theorem.• Any triangle may be cut into a rectangle.

Spreadsheets and Graphs

Graphs introduce relationships among decimals, fractions and percentages.

Spreadsheets are a good way to reinforce math concepts.

Mean and Formula

• Introduce concepts of mean and using formula.

• Don’t teach students shortcuts to the computer commands first.

• Students need to understand formulas.

Prepare Students for Testing

• Use power point to show students what they need to do to prepare themselves for testing

• How and when to use mental math problem solving

• How to use the vocabulary of mathematics in their written solutions.

• How to read open-ended tasks, select necessary information, devise a method of solution, perform appropriate calculations, and explain in writing the procedure used.

How teachers can help students perform successfully

• Familiarize themselves with students’ results.

• Analyze those results to determine a pattern of strengths and weaknesses.

• Identify strategies to help students improve their performance.

• Translate those strategies into instructional and practices.

How teachers can help students perform successfully

• Show logical and mathematical evidence as a verification for right answers

• Mathematical reasoning and memorization procedures.

• Connecting mathematics, its ideas, and its applications and away from treating mathematics as isolated concepts and procedures.

Using technology in cooperative learning

• Students engage in cooperative learning• Work as a group to solve problems• The website I suggested to students is Word

Problem for kids : http://www.mathstories.com• The stairway is made of cubes. How many cubes

would be needed to make h? 1) Look for a pattern         Steps   Cubes   Sum (Top -> Bottom)       

      2       3        1 + 2          3       6        1 + 2 + 3

Find a pattern.

Making Math Fun

• The following website is a unit designed for elementary students. http://www.math.nmsu.edu/breakingaway/Lessons/polygonanimal/cutout1.html

• This unit emphasizes skills in drawing equilateral triangles, squares, and regular pentagons and hexagons.

• It also involves precision cutting, and putting together geometric shapes to form "puzzles" that look like stylized animals or other objects.

Making a fox from a triangle Using compass and ruler, draw an equilateral triangle approximately three inches on a side, using the two-colored posterboard. Before cutting it out, set your compass radius at one half the length of a side. Put the point of the compass on a vertex of the triangle, and swing an arc of 60 degrees. Move the compass to another vertex, and draw a second arc of 60 degrees. You should have a shape like this:

Making a fox from a triangle cont.

Carefully cut out the triangle, and cut along the arcs to make three pieces. Reverse the two part circles, and you have a stylized fox

Making a fish from a square Using compass and ruler, or protractor or index card, draw a square approximately three inches on a side, using the two-colored posterboard. Before cutting it out, set your compass radius at one half the length of a side. Put the point of the compass on three different vertices of the square, and swing three arcs of 90 degrees. You should have a shape like this:

Making a fish from a square cont. Carefully cut out the square and cut along the arcs, getting four pieces. Reassemble them to look like a fish:

Need some ideas? Take a look at these three creations by a student: