Transcript Let`s Do Algebra Tiles

Algebra Tiles &
Integer Operations
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) *
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Objectives – CCSS
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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.
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.
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Objectives – CCSS
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7. NS.2. Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
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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.
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 flipside) represent -1.
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The yellow and red squares are
additive inverses of each other.
Algebra Tiles: Modeling integers
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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
Zero Pairs
Called zero pairs because they are
additive inverses of each other.
 When put together, they cancel each
other out to model zero.
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Addition of Integers
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.
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Addition of Integers
(+3) + (+1) =
(-2) + (-1) =
Addition of Integers
(+3) + (-1) =
(+4) + (-4) =
Addition of Integers
(+2) + (-3) =
(+4) + (-2) =
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After students have seen many examples of
addition, have them formulate rules.
Game of one
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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
1
2
3
4
5
6
7
8
9
10
Total
Expression
Sum
Subtraction of
Integers
Subtraction of Integers
Subtraction can be interpreted as “takeaway.”
 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.
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Subtraction of Integers
(+5) – (+2) =
(-4) – (-3) =
Subtracting Integers
(+3) – (-5)
(-4) – (+1)
Subtracting Integers
(+3) – (-3)
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After students have seen many
examples, have them formulate rules
for integer subtraction.
Least is Best
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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.
Least is Best
Round
1
2
3
4
5
6
7
8
9
10
Total
Expression
3-
Difference
Multiplication of
Integers
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.
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Multiplication of Integers
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The counter indicates how many rows
to make. It has this meaning if it is
positive.
(+2)(+3) =
(+3)(-4) =
Multiplication of Integers
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If the counter is negative it will mean
“take the opposite of.” (flip-over)
(-2)(+3)
(-3)(-1)
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After students have seen many
examples, have them formulate rules.
Division of Integers
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.
Division of Integers
(+6)/(+2) =
(-8)/(+2) =
Division of Integers
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A negative divisor will mean “take the
opposite of.” (flip-over)
(+10)/(-2) =
Division of Integers
(-12)/(-3) =
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After students have seen many
examples, have them formulate rules.
Algebra Tiles and
Integers
Questions?????