SECTION 1 1 EVALUATING EXPRESSIONS INTEGERS USING COUNTING

SECTION 1. 1 EVALUATING EXPRESSIONS INTEGERS USING COUNTING CHIPS © Copyright all rights reserved to Homework depot: www. BCMath. ca

I) COUNTING CHIPS Yellow Chips are Positive and represent one positive point Red Chips are Negative and represent one negative point One yellow chip and one red chip will cancel out to equal zero points © Copyright all rights reserved to Homework depot: www. BCMath. ca Counter Chip Online Manipulative

II) MULTIPLYING USING COUNTING CHIPS When multiplying integers, each number can represent either How many groups to “put in” (+) or “remove” (-) OR How many chips in each group There are two ways to illustrate this expression using counting chips Add Withthis number Many in of groups each group With this many Add this in each group number of groups Put in TWO group of 4 positive chips Put in FOUR groups of 2 positive chips © Copyright all rights reserved to Homework depot: www. BCMath. ca Counter Chip Online Manipulative

EX: ILLUSTRATE EACH OF THE EXPRESSION USING INTEGERS Counting Chips: Total Points Description: Put in ONE group of 3 positive chips Put in THREE groups of 1 positive chip Counting Chips: Total Points Description: Put in TWO group of 3 positive chips Put in THREE groups of 2 positive chips © Copyright all rights reserved to Homework depot: www. BCMath. ca Counter Chip Online Manipulative

PRACTICE: REPRESENT EACH OF THE FOLLOWING USING COUNTING CHIPS Counting Chips: Total Points Description: Put in TWO group of 4 positive chips Put in FOUR groups of 2 positive chips Counting Chips: Total Points Description: Put in FIVE group of 7 positive chips Put in SEVEN groups of 5 positive chips © Copyright all rights reserved to Homework depot: www. BCMath. ca Counter Chip Online Manipulative

III) ZERO PAIRS Zero pairs include one positive chip and one negative chip The sum of any zero pair is equal to zero You can add as many zero pairs into an equation because adding zeroes do not change the total value Purpose: Adding zero pairs allow you to take away values from an equation Useful when multiplying by negative integers © Copyright all rights reserved to Homework depot: www. BCMath. ca Counter Chip Online Manipulative

IV) NEGATIVE INTEGERS: When multiplying negative integers, each number can represent either How many groups to subtract (Take away) How negative points in each group When taking away groups, need to add enough zero pairs to have any chips to remove There are two ways to illustrate this expression using counting chips Remove this many groups This many points in each group This many How many points in groups to each group put in Put in. TWO group of 4 negative chips © Copyright all rights reserved to Homework depot: www. BCMath. ca First put in 4 groups of zero pairs with two pairs in each group Then remove FOUR groups of 2 positive chips Counter Chip Online Manipulative

V) NEGATIVE INTEGERS Counting Chips: Total Points Description: Put in four groups of Negative 1 chips Remove 1 group of 4 positive chips First put in 4 zero pairs Now take away a group of 4 positive chips Counting Chips: Total Points Description: Put in five groups of Negative 2 chips Put in 10 zero pairs Take away 2 groups of 5 positive chips © Copyright all rights reserved to Homework depot: www. BCMath. ca Remove 2 groups of 5 positive chips Counter Chip Online Manipulative

PRACTICE: REPRESENT EACH EXPRESSION SYMBOLICALLY USING COUNTING CHIPS Counting Chips: Total Points Put in 3 groups with 7 zero pairs Now take away 3 groups of 7 positive chips Description: Put in seven groups of Negative 3 chips Remove 3 groups of 7 positive chips Counting Chips: Total Points Description: Put in six groups of Negative 4 chips Put in 4 groups with 6 zero pairs Now take away 4 groups of 6 positive chips © Copyright all rights reserved to Homework depot: www. BCMath. ca Remove 4 groups Of positive 6 points Counter Chip Online Manipulative

VI) MULTIPLYING TWO NEGATIVE INTEGERS Common Rule: The product of two negative integers will be positive One integer will be how many groups to take away Other integer will be how many negative points in each group Always put in enough zero pairs to remove negative points When Negative points are removed then the result will be positive Put in FOUR groups of Zero pairs with 2 pairs in each group This manythis points Subtract in eachgroups group many Put in TWO groups of Zero pairs with 4 pairs in each group This many Take away this points in each many groups group Now remove 2 Groups of Negative 4 points Total Points © Copyright all rights reserved to Homework depot: www. BCMath. ca Now remove 4 Groups of Negative 2 points. Counter Chip Online Manipulative

PRACTICE: REPRESENT EACH EXPRESSION SYMBOLICALLY USING COUNTING CHIPS Counting Chips: Total Points Description: Remove five groups of Negative 4 chips Remove four groups of Negative 5 chips Counting Chips: Total Points Description: Remove seven groups of Negative 3 chips Remove three groups of Negative 7 chips © Copyright all rights reserved to Homework depot: www. BCMath. ca Counter Chip Online Manipulative

EVALUATE WITHOUT USING A CALCULATOR:

EX: JASON OWNS 5 CREDIT CARDS AND OWES $10 ON EACH CARD. WHICH OF THE FOLLOWING DIAGRAMS REPRESENTS HOW MUCH MONEY HE OWES? © Copyright all rights reserved to Homework depot: www. BCMath. ca Counter Chip Online Manipulative

CHALLENGE: REPRESENT THE FOLLOWING USING COUNTING CHIPS (IN ATLEAST 2 DIFFERENT WAYS) Multiply these Now Multiply these twotwo first Multiply these Now Multiply two first these two Take away 2 Groups Add two groups of of Negative points 6 positive 3 points Put in 2 Groups of Take away 2 groups Negative 3 points Of Negative 6 points Put in 2 groups With 6 zero pairs Now take away the two groups of Negative 6 points © Copyright all rights reserved to Homework depot: www. BCMath. ca Counter Chip Online Manipulative

HOMEWORK: Assignment 1. 1 © Copyright all rights reserved to Homework depot: www. BCMath. ca