PRE-ALGEBRA DEVELOPMENTAL COURSES

Executive Summary

These lessons are for a Pre Algebra class for Junior College Mathematics. This course is a developmental course where students need help with their basic skills.
The students were placed in this course as a result of their placement test. Their low score was caused by weak mathematical background in recent school mathematics or for some, being out of education for many years. Therefore this material, which is at the middle school level, should be a review or reminder for most students.

The main topics in this course are the study of Whole numbers, Integers, Fractions, decimals , percents, measurement, ratio and proportion and a little intro to Algebra.

These lessons will cover the first unit, Whole numbers and Integers . It will cover about 3 weeks. The class meets Monday, Wednesday, and Friday for 50 minutes. I have Office hours for 2 hours those days and 1 hour Tuesday and Thursdays.

Since most everyone in the class will have knowledge of the Algorithms for the operations of whole numbers, these lessons will concentrate on the number skills that will help them better understand how these Algorithms work. Most of the class time will be spent doing number sense investigations in groups. The students will have as signments to do outside of class from a traditional textbook on the basic skills. They will have group quizzes on these assignments and a unit test on them.

I will give this plan a try this fall in my two Pre Algebra classes.

Lesson 1
MN Standard addressed: The student should be able understand numbers, ways of representing numbers and number systems. And to understand the meaning of operations and how they relate to each other.

Topic – Understanding whole numbers and the concept of place value.
1. I will put them in groups of 2 or 3 and issue each group some Base 10 blocks of 100’s, 10’s and units. I will put on the board some 2 or 3 digit numbers and ask them to illustrate them with the blocks. Examples 352, 77, 439, 58,105,14,3

2. Next, we will have them illustrate with the blocks another way of showing 105 and 14 with the blocks.

3. We move to addition and have them try some problems with the blocks. 35 + 44 , 35 + 94, 35 + 178, 352 + 439

4. Next do some subtraction problems 44 -23, 44 -35, 178 -125,
405 – 137

Finally I will load on to the computer the place value game found on the National Library of Virtual Manipulitives – Utah State University for addition and subtraction. This has great visual demonstrations of how place value affects these operations. To get to this site
1. type in NLVM.com
2. select The Five Towns.com
3. follow to Welcome to the Four Towns Directory 4 Kids
4. Select National Library Virtual Manipulitives
5. A grid will show, select Numbers and Operations for 6-8
grade box.
6. Select either addition or subtraction operations, and sample
problems will appear in the Base 10 format. For addition
you must en circle groups of 10, and they will automatically
be put together as one block. Then you can move them to
the next place value. For subtraction, when borrowing you
must move a block from higher to lower and it will split
apart so you can do the subtraction. Have the students
come to the computer and try some operations.
7. Some number sense problems which show the ability to
make intelligent decisions based on mathematical
relationships and the context of these relationships.

Try the following problems and fit the numbers in the appropriate

1. 1801 3 1743 58 13
Thomas Jefferson was born in Virginia on _______ April _____. He was the author of the Declaration of Indepence. He was also an architect, a scientist, and a farmer. In ______, at the age of ____, Thomas Jefferson became the ______ d president of the United States.

2. 27 1 206 54 26
Did you know that each of your hands has _______ bones? That means that you have a total of _______hand bones. Your foot has ______fewer bones than your hand, or _____ bones. Your body has a total of _____bones.

3. 268 34 4200 50 84 10
A high school basketball court is _____ feet long and _____feet wide. Its length is ____ feet more than its width. The perimeter of the court is ____feet, and the area of the court is _____square feet. The rim of the basket is _____feet from the floor.

SUMMARY: Today I hope you learned how place value impacts addition and subtraction and that it helps you improve those skills.

Source: Carole Greenes, Linda Schulman, and Rika Spungin

Lesson 2

Continuing the same standards as in Lesson 1
For reviewing Multiplication we will start with the game
Tic Tac Time Game -- Product Game Investigation #1

Factors: 1 2 3 4 5 6 7 8 9

Game board

Instructions: The students will be in pairs and they will need one board and each will have different colored tokens. The object is to get 3 tokens in a row either vertically, horizontally or diagonally. One token each will be used as a factor marker and the remainder as game tokens.

Example: player one puts a token on the factor line on a number say 4, player two puts his on 6. The product of these two is 24 and player two puts one of his tokens on the game board 24. Factor tokens may be placed on the same factor, resulting in squared numbers. Now player one can move his token from the 4 on to any number that will result in a position he desires on the game board to help him get 3 in a row or block player 2 from doing the same. Making an in correct product will result in a penalty, where the opposing player can move both factor tokens anywhere he desires.

Source: Marilyn J Sweeney , Skyline Middle School, Wilmington,DE 19808

The next investigation #2 which helps with the understanding of place value in multiplication and helps with good number sense is solving the following for the missing letters.

You must think 4 x Some number W will give you S and so on until the number for STRAW and WARTS gives a true multiplication product.
Investigation #3 for the lesson is playing the Hangman Multiplication game.

___ ___
X ___ ___
______________
___ ___ ___
___ ___ ___ ___
___________________________
___ ___ ___ ___

One person creates a 2 digit by 2 digit multiplication problem works it out on a paper and the other person tries to guess where each digit goes. The person guessing has to pick a digit and tell what column it falls in. If he misses a part of the hangman is developed (before starting, design your hangman, and agree on how many steps there are to complete it). If he gets it correct, that number is put in the correct place or places if it occurs in more than once in that column.

Source: Greg Sarles Bemidji State U.

The last investigation for this is a take home optional problem. With extra points for high totals. If 12 people hand it in the highest will get 12 points, the second high 11 points, and so on down to 1.

The game is “HOW GRAND IS YOUR TOTAL”

Using the board you can only use each digit 4 times through out the board to create the largest total. See the next page for the game board.

SUMMARY: These investigations were meant to help you understand how place value plays an important role in multiplication of whole numbers.