Enrichment Units in Math

Book 2, Grades 4-6

Dianne Draze, Judy Leimbach

• Publisher: Routledge
• Year: 2021
• ISBN:
  9781000492774
• Edition: 1
• Topic: Education
• Subtopic: Teaching Mathematics

Go beyond the regular curriculum with these units to challenge your more able intermediate grade math students. With their ease of use, clear instruction, and motivating topics, these are the perfect enrichment activities for the regular math curriculum. This book contains four units that are structured so that students can easily develop an understanding of the topics on their own. The four topics are:

• permutations and combinations,
• tessellations,
• line drawings, and
• graphing.

Each unit provides sequential activities that allow students to work through these motivating topics, whether they are working by themselves, in a small group, or in a whole-class setting. The units lend themselves easily to a math center arrangement with each student having an individual folder and checklist to record his or her progress. While they were designed to provide added challenge for students who have mastered the regular curriculum, some of the units can be used as supplements for whole-class instruction. The emphasis in these units is on promoting thinking, developing perseverance, expanding students' view of mathematics, enjoying a challenge, and keeping math students actively involved and enthused about math. This book will help you provide students with opportunities to explore mathematical ideas in ways that promote their intellectual growth and expand their views of mathematics. This is one of a three-book series. The other books cover the following topics: Enrichment Units in Math Book 1 —attribute pattern blocks, tangrams, sets and Venn diagrams, and ancient Egyptian numbers; and Enrichment Units in Math Book 3 —probability, topology, magic squares, and number characteristics.For other math units to extend the math curriculum and provide opportunities to work independently, see Math Extension Units Book 1 and Book 2. Grades 4-6

Combinations and Permutations

DOI: 10.4324/9781003235026-4

Combinations and Permutations 1

Introduction to Combinations

Name__________________________

In math a combination is a way of selecting certain objects from a set of objects. When you select those smaller sets of objects, the order in which they are selected does not matter. For instance, if you had the set of letters (a, b, c) and you wanted to select the letters two at a time, you would have (a, b), (a, c), and (b, c). With combinations, the order of the elements does not matter. The sets (a, b) and (b, a) are considered the same.

Pretend you have three kittens (Fluff, Muff and Pepper) and you want to take pictures of them. You have lots of film, so you want every possible combination of pictures that feature one kitten, two kittens and all three kittens. You would have the following choices:

one kitten	two kittens	three kittens
Fluff	Fluff and Muff	Fluff, Muff and Pepper
Muff	Fluff and Pepper
Pepper	Muff and Pepper

Some times you do not want to consider ail the possible combinations, you just want to consider some combinations (like selecting only the pictures of two kittens in the problem above).

1. Four friends (Alan, Burt, Charlie, and Darren) want to ride on the Ferris wheel at the fair. Only two people can ride in a seat. What are all the different ways that the friends could be divided into groups of two?

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Combinations and Permutations 2

Combination Solution Techniques

Name__________________

Two techniques that are helpful in solving combination problems are to make a drawing and make an organized list. The drawing will often help you visualize the problem that is being presented. The listing lets you systematically keep track of each possible combination. Use these techniques to help you solve these two problems.

1. Jacob has three different ways to go to school (car, walk, bike) and two different ways to go to the mall after school (subway, bus). List the ways Jacob could go from home to school and then to the mall. How many different combinations are possible?

2. What are all the lines that can be drawn connecting these four points? (Note: AB is the same as BA.)

Combinations and Permutations 3

Combination Practice Problems 1

Name__________________________

1. Justin is making a sea life game. He has selected five different kinds of sea life that he will draw on playing tiles so that there are two different animals on each tile. Draw or write the different combinations on the tiles.

2. How many domino pieces are in a double six set? (Note: Combinations include 0-0, 1-1, 2-2, etc., and a 1-2 piece is the same as a 2-1 piece.)

Combinations and Permutations 4

Combination Practice Problems 2

Name___________________________

Make a chart to help you find the answers to these problems.

1. Chef Tasty is preparing a menu. He knows that he has only four kinds of fruits (strawberries, bananas, grapes and peaches). How many different kinds of salads can he make if he uses only one fruit in the salad, if he selects two fruits for the salad, if he uses three fruits in the salad, and if he uses all four kinds of fruits?

one fruit	two fruits	three fruits	four fruits
total	total	total	total

2. Brenda is having trouble deciding what to wear to school. She has five different pants and three different sweaters. What are all the possible combinations of outfits she can wear?

Combinations and Permutations 5

Combina...

Table of contents

• Cover
• Title Page
• Contents
• Copyright Page
• Instruction for Teachers
• Independent Study Contract
• Line Designs
• Combinations and Permutations
• Tessellations
• Graphing
• Answers