# UNIT ALIGNMENT

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```					                                                      APS MATH UNIT ALIGNMENT
INTEGRATED MATH 7        UNIT: Accentuate the Negative
CDE Benchmarks:
1.1 Demonstrate meaning for integers, rational numbers, percents, exponents, square roots, and pi () using physical materials and technology in problem-solving
situations.
1.1b Use models to represent integers
1.2 Read, write and order integers, rational numbers and common irrational numbers such as 2, 5, and pi ()
th
1.2a (8 ) Compare and order sets of integers and rational numbers that are expressed in a variety of ways
1.2b Locate positive rational numbers and integers on an number line
1.4c Develop, test and explain conjectures about properties of numbers (associative, commutative, identity, distributive, multiplicative property of
zero) for positive rational numbers and integers
1.5 Develop, test and explain conjectures about properties of integers and rational numbers
1.6 Use number sense to estimate and justify the reasonableness of solutions to problems involving integers, rational numbers, and common irrational numbers
such as 2, 5, and pi ()
1.6a Estimate, solve and justify the reasonableness of solutions to problems involving positive rational numbers or integers
2.1 Represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation
2.1a Represent, describe, and analyze numeric or geometric patterns involving common positive rational numbers or integers using tables, graphs,
rules, or symbols (2.1a)
2.2 Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.
2.5a Solve problems by representing and analyzing patterns involving positive rational numbers or integers using tables, graphs, or rules
4.4 Solve problems using coordinate geometry.
4.4a Construct a coordinate graph and plot ordered integer pairs in all four quadrants
5.3 Read and interpret various scales including those based on number lines, graphs, and maps.
5.3b Select the appropriate scale for a given problem (for example, using the appropriate scale when setting up a graph or intervals on a histogram)
(5.3b)
6.2 Construct, use and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers
6.2a Apply order of operations, (including exponents) with positive rational numbers.
6.2b Add, subtract, multiply, and divide positive rational numbers or integers
6.4 Select and use appropriate algorithms for computing with commonly used fractions and decimals, percents, and integers in problem-solving situations and
determining whether the results are reasonable
6.4b Solve problems involving positive rational numbers and/or integers
th
6.4b (8 ) Use and explain strategies to add, subtract, multiply and divide rational numbers, including integers

Big Ideas:
   Use models, including number lines, to represent, compare and order positive and negative numbers
   Develop and use algorithms for operations with positive and negative numbers
   Construct a coordinate graph and plot ordered integer pairs
   Use properties of numbers and operations (associative, commutative, identity, distributive) to simplify expressions
   Use order of operations (including use of exponents) fluently

Prior Learning Experiences:
Bits and Pieces II: Rational number relationships and operations (number line)
Integrated Math 7: Accentuate the Negative                                                                                                              July 2009
Comparing and Scaling: Rational number operations
Data About Us, Covering and Surrounding: First quadrant coordinate graphing; using models to develop understanding of mathematical concepts (number line)

PROBLEM NUMBER            BENCHMARK(S)                                    KEY LEARNING                                    NUMERACY                CONNECTIONS
AND TITLE                   BEING                                        QUESTION                                                                TO OTHER
DEVELOPED
and/or                                                                                                              STANDARDS
MAINTAINED
INVESTIGATION 1: Extending the Number Line
1.1 Playing MathMania       1.5a                          How do you compare integers? What situations do you          Signed number notation
6.4b                          use to think about integers?

Group Processes [note – most investigations in this book
recommend pair groupings] How well did you and your
partner work together? What positive contribution(s) did
each person make?
th
1.2 Winning the Game                   6.4b & 6.4b (8 )   What strategies can you use to find the differences          Inequality notation
between integers?
1.3 Measuring Temperature              1.1d               How do you find opposites? How do you use opposites          Modeling differences on      Median and range
th
1.2d & 1.2a (8 )   to find the distance between integers on a number line?      the number line.             (ACE 26)
6.4b                                                                            Opposites                    Extension: Use
positive and negative
decimals (ACE 27)
2.1 Adding on the Number    1.4c                          Without calculating the sum, how can you decide if the       Number line model
Line                        1.1d                          sum of two integers is positive, negative, or zero?          Commutative property
1.2d
th
2.2 Inventing a New Model   6.4b & 6.4b (8 )              How do you add any two integers? Do these strategies         Opposites                    Extension: make and
1.1d                          work for all rational numbers?                               Use fractions and decimals   test conjectures (ACE
31 – 37)
INVESTIGATION 3: Subtracting Integers
3.1 Subtracting on a Chip   1.1d                          What patterns can you use to help you subtract integers?     Absolute value
Board                       6.4b                          What does subtracting a negative integer mean?               Combinations to zero
improved? How will you further improve your partner          as inverse operations
work?
3.2 Subtracting on a Number            1.1d               Without calculating the difference, how can you decide if
Line                                   1.2d               the difference between two integers is positive, negative,
6.4b               or zero?
th
3.3 Exploring Patterns                 6.4b & 6.4b (8 )   How can using patterns help in subtracting integers?         Include fractions and
decimals in patterns

Integrated Math 7: Accentuate the Negative                                                                                                                      July 2009
th
3.4 “Undoing” with Addition &          6.4b & 6.4b (8 )   How are addition and subtraction of integers related?                               Distributive and
Subtraction                            6.4g               How do you write an addition sentence that is equivalent                            associative properties
6.5a               to a subtraction sentence?                                                          with negatives (ACE
39)
Extension:
equivalent
expressions (ACE
40)
INVESTIGATION 4: Multiplying and Dividing Integers
th
4.1 Rising and Falling      6.4b & 6.4b (8 )   How is multiplying integers like adding integers?                     Relationship between
multiplication
th
4.2 Studying Multiplication            6.4b & 6.4b (8 )   Without calculating, how can you tell if a product is      Decimals and fractions   Extension: Using
Patterns                               6.4g               positive, negative, or zero?                                                        negative numbers as
6.5a                                                                                                   exponents
Using rates (ACE 35
-38)
Transformations with
rule (Question Bank
10)
th
4.3 Playing the Integer Product        6.4b & 6.4b (8 )   What patterns did you notice when trying to find the       Factors and multiples
Game                                                      product of any two integers?
th
4.4 Dividing Integers                  6.4b & 6.4b (8 )   How are the operations of multiplication and division                               ACE 27 & 29: mean
6.4g               related? Does this same relationship work with all                                  ACE 28: distance,
integers?                                                                           rate, time
INVESTIGATION 5: Coordinate Grids
5.1 Extending the Coordinate 4.4a                         How can you tell which quadrant a point is in by looking                            Extension: Use slope
Grid                                                      at the signs of the coordinates?                                                    to prove parallel
Median and mean
(ACE 13a)
Extension: periodic
functions (ACE 13b)
5.2 Breaking Even                      2.5a               How does a graph show a break-even point?                  Rate of change (slope
6.5a                                                                          as ratio)
1.5a                                                                          Division: determining
4.4a                                                                          scale
5.3 Using a Calculator to              2.2a               What effect does a negative coefficient for x have on a
Explore Lines                                             graph? What effect does a negative starting point have?
5.4 Exploring Window Settings          5.6b               How do you determine the window settings for a graph       Scale
on a graphing calculator?                                  Range
5.5 Revisiting Jean’s Problem          1.5a               How do you set the scale and range to solve a break-       Scale
2.2a               even point problem on a graphing calculator?               Range
6.5a

Integrated Math 7: Accentuate the Negative                                                                                                                   July 2009

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