Download Montclair Public Schools CCSS Math 7th Grade Unit: Marshall A.b

Montclair Public Schools
CCSS Math 7th Grade Unit: Marshall A.b
10
Subject
Mathematics
Grade
7
Unit #
1
Pacing
weeks
Unit Name
Number Sense, Algebra and Equations
Overview
Understand the magnitude of a variety of numbers (rational, whole and integers) and how to convert fluently between different forms of these
numbers. Use this knowledge to solve equations and inequalities, both mathematical and real world problems.
MC,
SC,
or
SLO
Standard #
Standard
AC
#
Student Learning Objectives
DOK
Apply and extend previous understandings of
addition and subtraction to add and subtract
Add and subtract rational numbers and show this in a
7.NS.A.1
rational numbers; represent addition and
MC
1
3
number line.
subtraction on a horizontal or vertical number
line diagram.
7.NS.A.1.A
7.NS.A.1.B
7.NS.A.1.C
2013-2014
Describe situations in which opposite quantities
combine to make 0.
Understand p + q as the number located a
distance |q| from p, in the positive or negative
direction depending on whether q is positive or
negative. Show that a number and its opposite
have a sum of 0 (are additive inverses). Interpret
sums of rational numbers by describing realworld contexts
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.
MC
MC
MC
2
Describe problems when numbers and their opposites add
to make zero.
3
3
Analyze and solve both math and real world problems
using absolute value. Understand that adding a number
and its opposite equals zero.
3
4
Re write subtraction of integers as addition of the opposite
and solve these problems in both mathematical and real
world contexts.
3
7.NS.A.1.D
7.NS.A.2
7.NS.A.2.a
7.NS.A.2.B
7.NS.A.2.c
7.NS.A.2.d
7.NS.A.3
2013-2014
Apply properties of operations as strategies to
add and subtract rational numbers.
Apply and extend previous understandings of
multiplication and division and of fractions to
multiply and divide rational numbers.
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.
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.
Apply properties of operations as strategies to
multiply and divide rational numbers.
Convert a rational number to a decimal using
long division; know that the decimal form of a
rational number terminates in 0s or eventually
repeats.
Solve real-world and mathematical problems
involving the four operations with rational
numbers.
MC
5
Add and subtract rational numbers.
2
MC
6
Multiply and divide rational numbers.
1
MC
7
Multiply integers and rational numbers in mathematical
and real world problems.
3
MC
8
Divide integers in mathematical and real world problems.
Understand that the divisor cannot be zero and that
dividing creates rational numbers.
2
MC
6
MC
9
MC
10
1
Convert rational numbers to decimals using long division
and understanding that the decimal eventually repeats.
2
3
7.EE.A.1
7.EE.A.2
7.EE.B.3
7.EE.B.4
7.EE.B.4a
7.EE.B.4b
2013-2014
Apply properties of operations as strategies to
add, subtract, factor, and expand linear
expressions with rational coefficients.
Understand that rewriting an expression in
different forms in a problem context can shed
light on the problem and how the quantities in it
are related.
Solve multi-step real-life and mathematical
problems posed with positive and negative
rational numbers in any form (whole numbers,
fractions, and decimals), using tools
strategically. Apply properties of operations to
calculate with numbers in any form; convert
between forms as appropriate; and assess the
reasonableness of answers using mental
computation and estimation strategies.
Use variables to represent quantities in a realworld or mathematical problem, and construct
simple equations and inequalities to solve
problems by reasoning about the quantities.
Solve word problems leading to equations of the
form px + q = r and p(x + q) = r, where p, q, and r
are specific rational numbers. Solve equations of
these forms fluently. Compare an algebraic
solution to an arithmetic solution, identifying
the sequence of the operations used in each
approach.
Solve word problems leading to inequalities of
the form px + q > r or px + q < r, where p, q, and
r are specific rational numbers. Graph the
solution set of the inequality and interpret it in
the context of the problem.
MC
10
Apply the properties of operations as strategies to add,
subtract, factor, and expand linear expressions with
rational coefficients.
MC
11
Re write expressions to help analyze and solve them.
3
12
Solve multi-step real life and mathematical problems with
rational numbers in any form (fractions, decimals,
percents) by applying properties of operations and
converting rational numbers between forms as needed,
and then assess the reasonableness of results using mental
computation and estimation strategies.
3
MC
13
Use variables to represent quantities in a real-world or
mathematical problem by constructing simple equations
and inequalities to represent problems.
2
MC
14
Solve problems using the distributive property. Compare
the algebraic solution to the arithmetic solution.
3
MC
15
Solve and graph inequalities in both math and real world
problems
3
MC
3
Mathematic
al Practice #
1
Selected Opportunities for Connections to Mathematical Practices
Make sense of problems and persevere in solving them. SLO 11 Compare arithmetic and algebraic solutions to the same real-world
problems.
2
Reason abstractly and quantitatively. SLO 9 Find simpler but equivalent expressions
3
Construct viable arguments and critique the reasoning of others. SLO #3 Present oral and written arguments.
4
Model with mathematics. SLOs #1 and #4 Apply the mathematics to describe situations that arise from their environments.
5
Use appropriate tools strategically.
6
Attend to precision.
Look for and make use of structure. SLO #6 Discern a structure then perform calculations appropriate for the structure. SLO 7
Examine the formation of rational expressions then performs appropriate arithmetic operations.
7
8


2013-2014
Look for and express regularity in repeated reasoning.
Big Ideas
 Converting between fractions and decimals
 Adding, subtracting, multiplying and dividing integers in both math and real world contexts
 Setting up and solving algebraic equations from both math and real world contexts
 Setting up, solving and graphing inequalities from both math and real world contexts
Use the order of operations and the distributive property to re write math expressions in different ways
Essential Questions
How do I compute (add, subtract, multiply and divide) with both rational and integers numbers? What does this look like on a number line?
 How do I represent fractions, decimals and percent in different forms?
 What strategies can be used to solve for unknowns in algebraic equations?
 What strategies can be used to solve for unknowns in algebraic inequalities? What do my answers look like on a number line?
 How can I use mathematical properties to represent expressions in different ways?
 How do I represent real world situations as mathematical equations?
Key
Vocabulary

Rational number
 Integer
 Equation
 Expression
 Inequality
 Distributive property
Suggested Resources (list specific chapters and or page numbers from existing text that correspond to the SLOs and Standards)
1. ACCENTUATE THE NEGATIVE: Investigations 1.3 and 1.2
2. ACCENTUATE THE NEGATIVE: Investigations 1.1 and 1.4
3. ACCENTUATE THE NEGATIVE page 26 (Investigation 2.2)
4. ACCENTUATE THE NEGATIVE: Investigations 2.2, 2.3, 2.4
5. ACCENTUATE THE NEGATIVE: Investigation 2.1
6. Supplemental material (suggested Glencoe Math course 1 pages 67, 68, 71, 72
7. ACCENTUATE THE NEGATIVE 3.1, 3.2 and 3.4
8. ACCENTUATE THE NEGATIVE: investigation 3.3
9. Supplemental material (suggested Glencoe Math course 1 page 56)
10. ACCENTUATE THE NEGATIVE: Investigations 4.2 and 4.3
11. ACCENTUAGE THE NEGATIVE: Investigation 4.1
12. MOVING STRAIGHT AHEAD: Investigations 3.2, 3.3, 3.4
13. COMMONG CORE: Investigation 3
14. ACCENTUAGE THE NEGATIVE: 4.2 and 4.3
15. COMMON CORE: Investigation 3
16. Learnzillion: learnzillion.com/lessonsets/140-describe-situations-in-which-opposite-quantities-combine-to-make-0-understanding-p-q-asthe-number-q-from-p-1
17. Learnzillion: learnzillion.com/lessonsets/193-solve-realworld-problems-involving-the-four-operations-with-rational-numbers-1
18. IXL ABS Value Game: www.math-play.com/Absolute-Value-Equations/Absolute-Value-Equations.html
19. Other various integer activities here: www.math-play.com/7th-grade-math-games.html
20. Video here: www.teachingchannel.org/videos/adding-integers-lesson-idea
21.
2013-2014
2013-2014