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Algeblocks Basic Mat
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One green block, , represents one unit or whole number.
Representing Integers
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2 blocks placed “up”represent 2
2 blocksplaced “down”represent -2
Finding the opposite of 3:
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Step 1. Place3 blocks on the toppart of the mat.
Step 2. Takethe opposite bymoving the 3blocks down
Step 3. Theopposite 0f 3 is -3
-3
3
Finding the opposite of -2 can be written --2
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Step 1. Place-2 on the mat.
Step 2. Finding the opposite of -2 canbe written --2
Step 3. The oppositeof -2 (written as - -2)is 2
2
Adding Integers: 5 + -8 = Step 1. Place 5 and -8 on the mat.
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Adding Integers: 5 + -8=Step 2. Make a zero if you can: 5 + -5 = 0. Remove the blocks that make the zero.
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Adding IntegersStep 3. Read the answer from the mat 5 + -8 = -3
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Subtracting IntegersWhat integer is represented on each mat?
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Example 1: -3 - -1
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Step 1. Place-3 on the mat.
Step 2. Addzeros, ifnecessary.
Step 3. Takeaway (remove) -1
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Step 4. Answer on Mat.-3 - -1 = -2
Example 2: 4 - -1
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Step 1. Place4 on the mat.
Step 2. Addzeros, ifnecessary.
Step 3. remove -1
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Step 4. Answer on Mat.4 - -1 = 5
Example 3: -2 - -3
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Step 1. Place-2 on the mat.
Step 2. Addzeros, ifnecessary.
Step 3. remove -3.
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Step 4. Answer on Mat.-2 - -3 = 1
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Algeblocks Quadrant Mat
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Step 1. Place 2in positive part of horizontal axis. Beginat right of center.
Step 2. Place 3 in the positive partof vertical axis. Beginat left of center
Step 3. Formrectangular areain quadrant boundedby cubes.
Step 4. Answeris number ofcubes with signof quadrants.2 x 3 = 6
Example 1: Find the product of 2 and 3.
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Step 1. Place 3in negative part of horizontal axis. Beginat left of center.
Step 2. Place 1 in the positive partof vertical axis. Beginat left of center
Step 3. Formrectangular areain quadrant boundedby cubes.
Step 4. Answeris number ofcubes with signof quadrants.-3 x 1 = -3
Example 2: Find the product of -3 and 1.
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Step 1. Place 3in negative part of horizontal axis. Beginat left of center.
Step 2. Place 1 in the negative partof vertical axis.
Step 3. Formrectangular areain quadrant boundedby cubes.
Step 4. Answeris number ofcubes with signof quadrants.-3 x -1 = 3
Example 3: Find the product of -3 and -1.
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Step 1. Place thedivisor (2) in the positive part of the horizontalaxis.
Step 2. Form a rectangle of 6 cubes in the negative quadrant (quadrant 4) bounded by the divisor. One side of the rectangle will be 2.
Step 3. Complete the other dimension of the rectangle. This is the answer by cubes.
Example 1: Dividing integers: division is the inverse of multiplication. That is, because (2)(-3) = -6, -6/2 = -3
Step 1
Step 3Step 2
In Summary:
Algeblocks Basic MatAddition of integersSubtraction of integers
Algeblocks quadrant matMultiplication of integersDivision of integers
Copyright © 2008 Texas Education AgencyCopyright © Notice. The materials are copyrighted © and trademarked ™ as the property of the Texas Education Agency (TEA) and may not be reproduced without the express written permission of TEA, except under the following conditions:•Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts’ and schools’ educational use without obtaining permission from TEA.•Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of TEA.•Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way.•No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged.Private entities or persons located in Texas that are not Texas public school districts, Texas Education Service Centers, or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from TEA and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty.For information contactRichard JarrellOffice of Copyrights, Trademarks, License Agreements, and RoyaltiesTexas Education Agency1701 N. Congress Ave.Austin, TX 78701-1494(512) 463-9270 or (512) 936-6060
Resources:
Johnston, Anita M., Algeblocks, South-Western Publishing Co., Cincinnati, Ohio 1994
ISBN 0-538-62493-0
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