Algebra Tiles

1
Algebra Tiles Integer Operations
2
Objectives MSA now

• MA.600.60.10 Read, write, and represent integers
  (-100 to 100)
• MA.700.60.30 Add, subtract, multiply and divide
  integers using one operation and integers (-100
  to 100)
• MA.800.60.15 Add, subtract, multiply and divide
  integers using one operation (-1000 to 1000)

3
Objectives CCSS

• 6.NS.5 Understand that positive and negative
  numbers are used together to describe quantities
  having opposite directions or values (e.g.,
  temperature above/below zero, elevation
  above/below sea level, credits/debits,
  positive/negative electric charge) use positive
  and negative numbers to represent quantities in
  real-world contexts, explaining the meaning of 0
  in each situation.

4
Objectives CCSS

• 7.NS.1c Understand subtraction of rational
  numbers as adding the additive inverse, p q p
  (q). Show that the distance between two
  rational numbers on the number line is the
  absolute value of their difference, and apply
  this principle in real-world contexts.
• 7.NS.1d Apply properties of operations as
  strategies to add and subtract rational numbers.

5
Objectives CCSS

• 7. NS.2. Apply and extend previous understandings
  of multiplication and division and of fractions
  to multiply and divide rational numbers.
• a. Understand that multiplication is extended
  from fractions to rational numbers by requiring
  that operations continue to satisfy the
  properties of operations, particularly the
  distributive property, leading to products such
  as (1)(1) 1 and the rules for multiplying
  signed numbers. Interpret products of rational
  numbers by describing real-world contexts.
• b. Understand that integers can be divided,
  provided that the divisor is not zero, and every
  quotient of integers (with non-zero divisor) is a
  rational number. If p and q are integers, then
  (p/q) (p)/q p/(q). Interpret quotients of
  rational numbers by describing real world
  contexts.
• c. Apply properties of operations as strategies
  to multiply and divide rational numbers.
• 7.NS.3. Solve real-world and mathematical
  problems involving the four operations with
  rational numbers.

6
Algebra Tiles BASICS

• Algebra tiles can be used to model operations
  involving integers.
• Let the small yellow square represent 1 and the
  small red square (the flip-side) represent -1.

• The yellow and red squares are additive inverses
  of each other.

7
Algebra Tiles Modeling integers

• Using your Algebra tile mat, model each of the
  following integers
• A gain of 4 yards
• The temperature went down 3 degrees.
• A loss of 2 pounds
• The stock went up 6 points

8
Zero Pairs

• Called zero pairs because they are additive
  inverses of each other.
• When put together, they cancel each other out to
  model zero.

9
Addition of Integers
10
Addition of Integers

• Addition can be viewed as combining.
• Combining involves the forming and removing of
  all zero pairs.
• For each of the given examples, use algebra tiles
  to model the addition.
• Draw pictorial diagrams which show the modeling.

11
Addition of Integers

• (3) (1)
• (-2) (-1)

12
Addition of Integers

• (3) (-1)
• (4) (-4)

13
Addition of Integers

• (2) (-3)
• (4) (-2)
• After students have seen many examples of
  addition, have them formulate rules.

14
Game of one

• Each player has 11 tiles
• A player tosses the 11 tiles on the mat, records
  the result as an addition expression, and finds
  the sum on the chart.
• A game continues for 10 rounds.
• At the completion of the game, each player finds
  the sum of the 10 rounds.
• The player whose sum is closest to one wins.

Round Expression Sum
1
2
3
4
5
6
7
8
9
10
Total
15
Subtraction of Integers
16
Subtraction of Integers

• Subtraction can be interpreted as take-away.
• Subtraction can also be thought of as adding the
  opposite.
• For each of the given examples, use algebra tiles
  to model the subtraction.
• Draw pictorial diagrams which show the modeling
  process.

17
Subtraction of Integers

• (5) (2)
• (-4) (-3)

18
Subtracting Integers

• (3) (-5)
• (-4) (1)

19
Subtracting Integers

• (3) (-3)
• After students have seen many examples, have them
  formulate rules for integer subtraction.

20
Least is Best

• Each player starts with 3 yellow tiles on a work
  mat.
• A player spins the spinner and then subtracts the
  number from 3 and performs the operation using
  tiles if necessary.
• The player records the result as a subtraction
  expression, and writes the difference on the
  chart.
• The difference for Round 1 is the starting number
  for Round 2. This continues for 10 rounds.
• At the completion of the 10 rounds, each player
  finds the sum of the 10 rounds.
• The player with the lowest sum wins.

21
Least is Best
Round Expression Difference
1 3 -
2
3
4
5
6
7
8
9
10
Total
22
Multiplication of Integers
23
Multiplication of Integers

• Integer multiplication builds on whole number
  multiplication.
• Use concept that the multiplier serves as the
  counter of sets needed.
• For the given examples, use the algebra tiles to
  model the multiplication. Identify the
  multiplier or counter.
• Draw pictorial diagrams which model the
  multiplication process.

24
Multiplication of Integers

• The counter indicates how many rows to make. It
  has this meaning if it is positive.
• (2)(3)
• (3)(-4)

25
Multiplication of Integers

• If the counter is negative it will mean take the
  opposite of. (flip-over)
• (-2)(3)
• (-3)(-1)
• After students have seen many examples, have them
  formulate rules.

26
Division of Integers
27
Division of Integers

• Like multiplication, division relies on the
  concept of a counter.
• Divisor serves as counter since it indicates the
  number of rows to create.
• For the given examples, use algebra tiles to
  model the division. Identify the divisor or
  counter. Draw pictorial diagrams which model the
  process.

28
Division of Integers

• (6)/(2)
• (-8)/(2)

29
Division of Integers

• A negative divisor will mean take the opposite
  of. (flip-over)
• (10)/(-2)

30
Division of Integers

• (-12)/(-3)
• After students have seen many examples, have them
  formulate rules.

31
Algebra Tiles and Integers

• Questions?????