Math Resources for Gifted Children

edward zaccaroEngaging gifted mathematicians in a regular classroom can be incredibly challenging without good resources. Finding these resources is always the challenge. It is one thing to have good resources, it is another thing to use them effectively. Starting math lessons with an engaging and challenging problem can be useful for all students, however, it can be captivating for gifted mathematicians. Two resources that have helped me enormously over the last two years are the Challenge Math Series by Edward Zaccaro and the NRICH website.

While teaching resources rarely meet teacher’s high standards, Zaccaro’s books come very close. Three books I would highly recommend are Becoming a Problem Solving Genius, Challenge Math, and Primary Grade Challenge Math.

The NRICH website is a collaboration between the Faculties of Education and Mathematics at The University of Cambridge. This website has a vast array of games and problems. This website can be frustrating to navigate at first, however, once you use it for a while you learn how to unlock a treasure trove of incredible resources.

Edward Zaccaro
nrich.maths.org

Prime Numbers

Prime NumbersPrime Numbers can be a puzzling concept for many children.  “Why is one not a prime number?”, “Why are they important?”, “How many are there?” are all common questions.  The study of prime numbers can open the door to  an incredibly rich and deep mathematical knowledge.  A great place to start when teaching prime numbers is a clear definition and then an ongoing investigation into prime numbers.

According to A Maths Dictionary for Kids a prime number has exactly two factors and a prime number can only be divided evenly by itself and one.  It also states that one is not a prime number because it has one factor (1), not two.  Investigating prime numbers can be a fun and engaging whole class activity.  I have uploaded two charts that may help your class with prime numbers.  One is a one hundred chart with the prime numbers highlighted and the other is a one hundred chart that has not been highlighted.  You can use the blank chart to have the children investigate prime numbers and then enlarge the highlighted chart as a wall display.

The Prime Numbers Game

Gather the blank or coloured 0-100 chart, dice and a counter starting on zero. Then ask the children to role the dice and move that number of spaces on the chart.  If they land on a prime number they get to jump to the next prime number.  The player who passes 100 wins.  You can modify the game to suit younger age groups by making the winner the first to pass twenty or fifty.

Prime Number Chart 0-100

Blank Chart 0-100

Teaching Problem Solving Strategies

A number of years ago I was introduced to the concept of teaching formalized problem solving strategies to elementary aged children. This mathematics program was a tremendous success and dramatically improved the mathematical reasoning and problem solving of the students I taught. Most importantly the students enjoyed it and looked forward to it each week. The problem solving strategies included:

Acting it Out or Using Concrete Materials
Create an Organized List
Creating a Tree Diagram
Drawing a Diagram
Drawing a Table
Guess and Check (Guess and Checking)
Look for a Pattern
Using Logical Reasoning (Logical Reasoning)
Using Simpler Numbers (Solve a Simpler Problem)
Work Backwards (Working Backwards)

Once I began to look, I found a  number of problem solving resources online and in book stores. However, not all of the resources were easy to find. The purpose of this post is to bring these resources together so you can introduce problem solving into your classroom or school or further develop your program if you have one in place.

The program we taught was based on books published in Australia by Blake Education called Solve that Problem by Sharon Shapiro. There are two books in the series Upper Primary and Middle Primary. These books are available in the UK via Badger Publishing. US residents are able to purchase these books via Amazon in the UK.

A good starting point is to use resources offered online.  A number of the strategies explored in Solve that Problem are available free in .pdf format via the Blake Education website under the Problem Solving heading. Samples of another great problem solving book, “Mathematics Problem Solving Coach” are also offered in .pdf format online.

There are a number of books and online resources available to help you teach problem solving including:

Online Resources

Bogazici University Faculty of Education
Figure This Challenges
MathStars Newsletter
Math Stories (paid subscription)
New Zealand Ministry of Education
Port Angeles School District
Thinkquest 1
Thinkquest 2
Thinkquest 3

Books

Mathematics Problem Solving Coach
Maths Problem Solving Series by Val Morey
Problem Solving Strategies by Steck Vaughn
Solve that Problem by Sharon Shapiro
Targeting Maths Problem Solving by Judy Tertini & Gloria Harris
Problem-Solver’s Math Journal by Teacher Created Materials

How do student layout the problems?

The students would paste a copy of the problem at the top of a page in their workbook and then set out the problem as following:

What? The students write a full sentence explaining what they are trying to find out.
Strategy: The students write the strategy they are going to use.
Working: The students set their work out as taught for each particular strategy.
Answer: The students write a full sentence answer.

Problem Solving Layout Example.pdf

Marking

To reduce the emphasis on just the final answer each problem is given a mark out of five.  This encourages the students to set their work out in a clear and systematic way and take care when planning and formulating their answers.

What? One mark for explaining what they are looking for.
Strategy: One mark for choosing the correct strategy to solve the problem.
Working: Two marks for demonstrating the working for the strategy they chose and setting the working out in a clearly.
Answer: One mark for finding the correct answer and explaining the answer in a full sentence.

Problem Solving Unit

I have created a unit of work containing 56 problems using problems from the invaluable Port Angeles School District WASL website. The unit contains eight questions and answers for each of the following strategies, Act it Out, Draw a Diagram, Guess and Check, Logical Reasoning, Look for a Pattern, Using Simpler Numbers and Work Backwards.  Please download, modify and use this unit to suit your needs.

Problem Solving Unit of Work.zip

Creating a Fraction in Microsoft Word 2003 and 2007

Since I started teaching I have been creating maths worksheets and assessments in Microsoft Word. One of the most frustrating aspects was creating fractions. The fractions never looked or behaved the way I wanted them to. I eventually found a webpage that had detailed how to create a fraction that worked. I created a screen recorded tutorial demonstrating how to create a fraction for the staff at my school and wanted to share it with you. I used Word 2003 for the demonstration, however, it works equally well for Word 2007.

NSW Mathematics Syllabus 1989

This syllabus is simply a classic. Although the document is nearly twenty years old it has an array of wonderful maths activities that are still as relevant today as they were when they were published. I find this pdf version of the syllabus priceless when I am programming.

NSW Mathematics Syllabus 1989.pdf

(To download file: right click and choose “Save Target As”)