Activity Set 1.2 CLASS PPTX Visual Algebra for Teachers

Chapter 1 INTEGERS AND INTEGER OPERATIONS Visual Algebra for Teachers

Activity Set 1.2 Adding and Subtracting Integers with Black and Red Tiles Visual Algebra for Teachers

PURPOSE To learn how to add and subtract integers using black and red tiles. To investigate the rules: “When adding a negative number to a positive number, you can just subtract” and “When subtracting a negative number you can just add.”

MATERIALS Black and red tiles Black and red tiles are black on one side and red on the other side. No calculators for this activity set

INTRODUCTION

Addition and Subtraction Terms = 5: In this addition sentence 2 and 3 are both Addends 5 is the Sum = 2: In this subtraction sentence 5 is the Minuend 3 is the Subtrahend 2 is the Difference Zero Pairs A Zero Pair is a pair with net value 0—one black and one red tile.

Sketching Tiles While sketching integer addition in this activity set, you may wish to denote black tiles by B and red tiles by R rather than sketching and coloring square tiles.

Sketching Addition When using sketches to show integer operations, label the steps and corresponding collections clearly so that another reader can follow your steps. Briefly explain your steps.

Sketching Take Away When sketching taking away black and red tiles, one nice technique is to circle the tiles you are removing and label the circle as “Take Away” as shown in this example reducing a collection with net value 2

a) Model +4 and model -6 with your black and red tiles. Explain how you would use your collections to show the sum in the addition question: = ? Sketch and label your work. TRY IT, then we’ll look at the solution Solution Model each addend Class Question #1a (coursepack)

Combine tiles and match net value zero pairs Determine net value of final collection = -2

Class Question #1b (coursepack) b) What observations can you make about finding the sum = ?, with black and red tiles? Question for class: Discuss and list your observations. Are there different collections of black and red tiles that can be used to model this sum? Question for class: Explain.

Class Question #2 (coursepack) For the following addition questions, model each addend and then model the sum of the two addends. Sketch and label your work. Discuss any observations and note them by your sketches. a = ? SHARE b = ? SHARE c = ? SHARE

Class Question #3 (coursepack) Using the black and red tile model and part c in the previous problem as a guide; explain why the rule “When adding a negative number to a positive number, you can just subtract” works

Class Question #4a (coursepack) a) Model +6 and model +4 with your black and red tiles. Explain how you would use your collections to show the difference in the subtraction question: = ? Sketch and label your work. TRY IT, then we’ll look at the solution Solution Model the subtrahend and minuend

Class Question #4a (coursepack) Take away 4 black tiles from the minuend, +6 The difference is the net value of the remaining tiles = +2

Class Question #4bc (coursepack) b.Explain how you would use tile collections +6 and +4 to show the difference in the subtraction question: = ? Sketch and label your work. Hint: The collection for +4 does not have to be only 4 black tiles. c.What observations can you make about finding the difference = ? with black and red tiles? Discuss and list your observations. Are there different collections of black and red tiles that can be used to model these subtraction questions? Explain.

Class Question #5a (coursepack) a) Model the minuend and the subtrahend and then model the difference. Sketch and label your work. Discuss any observations and note them by your sketches. Note: Don’t change subtracting an opposite to addition, actually carry out the subtraction = ? TRY IT (with tiles, no “rule”) & we’ll look at the solution Solution Model the subtrahend and minuend

Class Question #5a (coursepack) Notice we don’t have 6 black tiles to take away Change the minuend collection Take away 6 black tiles from the minuend, -4 The difference is the net value of the remaining tiles = -10

Class Question #5bcd (coursepack) For the following subtraction questions, model the minuend and the subtrahend and then model the difference. Sketch and label your work. Discuss any observations and note them by your sketches. Note: Don’t change subtracting an opposite to addition, actually carry out the subtraction. b = ? c = ? d.d = ? SHARE

Class Question #6 (coursepack) Using the black and red tile model, explain why the rule “When subtracting a negative number you can just add” works. You may wish to use = ? to think about the question, but give a general answer that works for every situation.

Homework Obtain algebra pieces (at least B/R tiles) and a coursepack (WOU Bookstore) Log on to 392 Moodle page Review class materials, see HW schedule HW Quiz (1.1 & 1.2) due before 2 p.m. next class. See Moodle for HW questions (to study) and quiz Prep PPTX/Quiz (1.3 & 1.4) due before 2 p.m. next class. See Moodle for posted PPTX (to read) and quiz Turn in HW (1.1 & 1.2) due 2 p.m. in one week: See HW schedule