Download Grade 7 Math DIG 2013-2014 - Prescott Unified School District

PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
Time Blocks and Assessments are Target Dates ONLY. These are subject to review and change.
Grade Level:7
Time
Block
Unit /
Theme
Q1-Q4
Q1
Ratios and
aug 7- Aug Proportion
28 (16
al
days)
Reasoning
Subject: Math
2013-2014 School Year
Content
Student Skills
(Nouns)
(Verbs)
Mathematical Practices
Rate
Unit Rate
Proportion
Dimensional Analysis
Complex Fraction
Constant of Proportionality
Slope
Direct Variation
2010
Common Resource Assessm
ents &
*Glencoe
Core
Course
2
Benchm
Standards
unless noted
arks
Make sense of problems and persevere in solving them.
7.MP.1
Reason abstractly and quantitatively.
7.MP.2
Construct viable arguments and critique the reasoning of
others.
7.MP.3
Model with mathematics.
7.MP.4
Use appropriate tools strategically.
7.MP.5
Attend to precision.
7.MP.6
Look for and make use of structure.
7.MP.7
Look for and express regularity in repeated reasoning.
7.MP.8
Recognize and represent proportional relationships between
quantities.
7.RP.2
Identify the constant of proportionality (unit rate) in tables,
graphs, equations, and verbal descriptions.
1. Determine unit rates (2 days)
7.RP.2b
Compute unit rates associated with ratios of fractions,
including ratios of lengths, areas, and other quantities.
7.1RP.1
Ch 1-1
Solve real-world and mathematical problems involving the four 7.NS.3
operations with rational numbers.
2. Simplify complex fractions and unit rates (2 days)
Ch 1-2
Q1 and Q2 Inquiry labs
Benchmar provide lead in
k Pretest to many
lessons, use
them if
needed.
Page 1 of 10
Form Rev. 6/18/12
PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
Use proportional relationships to solve multistep ratio and
percent problems.
3. Convert units of measure between derived units to solve
problems (2 days)
7.RP.3
Decide whether two quantities are in a proportional
relationship. Identify the constant of proportionality.
4. Identify proportional and nonproportional relationships (1
day)
5. Identify proportional relationships by graphing on a
coordinate plane (2 days)
7.RP.2a-b
Represent proportional relationships by equations.
6. Use proportions to solve problems. (1 day)
7.RP.2c
7.RP.3
Ch 1-3
Ch 1-4
Ch 1-5
Ch 1-6
Identify the constant of proportionality. Explain what a point
7.RP.3
(x,y) on the graph of a proportional relationship means in terms 7.RP.2b and d
of a situation.
7. Identify constant rates of change using tables and graphs. (1
Ch 1-7
day)
8. Identify slope using tables and graphs (2 days)
Ch 1-8
9. Use direct variation to solve problems (1 day)
Ch 1-9
Review
Test
Q1
Percent
aug
29-Sept 26
(17 days)
Percent of a Number
Percent Proportion
Percent Equation
Sales Tax
Tip
Markup
Discount
Simple Interest
Chapter 1
Test
8/28
Use proportional relationships to solve multistep ratio and
percent problems.
1. Find percent of a number (1 day)
2. Estimate percents using fractions and decimals (1 day)
3. Use the percent proportion (1 day)
7.RP.3
7.EE.3
Represent proportional relationships by equations.
4. Use the percent equation (1 day)
7.RP.2c
Ch 2-1
Ch 2-2
Ch 2-3
5. Find percent change and percent error (2 days)
7.RP.3
6. Solve problems involving sales tax, tips, and markup (3 days) 7.EE.2
7. Solve problems involving discount (1 day)
7.EE.3
Ch 2-4
Ch 2-5
Ch 2-6
Ch 2-7
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PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
8. Solve problems involving simple interest (2 days)
Ch 2-8
Ch 2 Test
Sept 26
Review (2 days)
Test
Q1
Benchmar
k
Sept 27
Integers
Q1-Q2
Sept
30-Oct 16
(9 days)
Integers
Absolute Value
Opposites
Addition of Integers
Subtraction of Integers
Multiplication of Integers
Division of Integers
Number Line
Solve real-world and mathematical problems involving the four 7.NS.3
operations with rational numbers.
7.EE.3
1. Read and write integers, and find the absolute value of an
integer. (1 day)
Ch 3-1
Apply and extend previous understandings of addition and
7.EE.3
subtraction to add and subtract rational numbers; represent
7.NS.1a, b,
addition and subtraction on a horizontal or vertical line diagram. and d
a. Describe situations in which opposite quantities combine to 7.NS.3
make 0.
b. Understand p+q as the number located a distance /q/ from p.
Interpret sums by describing real-world contexts.
d. apply properties of operations as strategies to add and
subtract rational numbers.
2. Add integers (1 day)
Ch 3-2
Understand subtraction of rational numbers as adding the
7.NS.1c
inverse. Show that the distance between two numbers on a
number line is the abs value of their difference and apply this to
real-world contexts.
3. Subtract integers (2 days)
Ch 3-3
Understand that multiplication is extended from fractions to
rational numbers by requiring that operations, prticularly the
distributive property, and the rules for multiplying signed
7.NS.3
7.NS.2a and c
7.EE.3
numbers. Interpret products in real-world contexts.
Apply properties of operations as strategies to multiply and
divide rational numbers.
4. Multiply integers (1 day)
Understand that integers can be divided, provided that the
divisor is not zero, and every quotient of integers is a rational
number.
5. Divide integers (1 day)
Ch 3-4
7.NS.2b and c
7.NS.3
Ch 3-5
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Form Rev. 6/18/12
PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
Ch 3 Test
Oct 16
Review
Test
Q2
Rational
Oct 17-NovNumbers
5
(14 days)
Rational Numbers
Terminating Decimals
Repeating Decimals
Convert a rational number to a decimal using long division;
7.NS.2d
know that the decimal form of a rational number terminates in 7.EE.3
0s or eventually repeats.
1. Write fractions as terminating or repeating decimals and
write decimals as fractions (1 day)
Understand that integers can be divided, provided that the
divisor is not zero and every quotient of integers is a rational
number.
2. Compare and order rational numbers (2 days)
Apply and extend previous understandings of addition and
subtraction to add and subtract rational numbers; represent
addition and subtraction on a horizontal or vertical number line.
3. Add and subtract rational numbers with like denominators (1
day)
4. Add and subtract rational numbers with unlike denominators
(2 day)
5. Add and subtract mixed numbers and rational numbers (2
days)
Ch 4-1
7.NS.2b
Ch 4-2
7.NS.1
7.NS.3
7.EE.3
Ch 4-3
Ch 4-4
Ch 4-5
Apply and extend previous understandings of multiplication and 7.NS.2
division and of fractions to multiply and divide rational numbers 7.NS.3
6. Multiply rational numbers (1 day)
7.EE.3
Use proportional relationships to solve multistep ratios and
7.RP.3
percent problems.
7.NS.2
7. Convert units of measure between the customary and metric 7.NS.3
systems. (2 days)
Ch 4-6
8. Divide rational numbers (1 day)
Ch 4-7
Review
Test
7.NS.2
7.NS.3
7.EE.3
Ch 4 Test
Nov 5
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Form Rev. 6/18/12
PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
Q2
Expressio Order of operations
Nov 6-Nov ns
Algebraic expression
22
Variable
(12 days)
Arithmetic Sequence
Properties of numbers
Distributive Property
Simplifying Expressions
Linear Expressions
Factoring
Apply properties of operations as strategies to add, subtract,
factor, and expand linear expressions with rational
coefficients.
7.EE.1
Understand that rewriting an expression in different forms in a 7.EE.2
problem context can shed light on the problem and how the
quantities in it are related.
1. Use numbers and symbols to represent mathematical ideas
as algebraic expressions (1 day)
2. Describe the relationships and extend terms in arithmetic
sequences. (1 day)
3. Identify and use mathematical properties to simplify
expressions. (1 day)
4. Apply the distributive property to rewrite algebraic
expressions (1 days)
5. Simplify algebraic expressions (1 day)
6. Adding/simplifying linear expressions (2 day)
7. Subtracting/simplifying linear expressions (1 day)
8. Use properties of mathematics to factor linear expressions
(1 day inquiry lab and 1 day)
Ch 5-1
Ch 5-2
Ch 5-3
Ch 5-4
Ch 5-5
Ch 6-6
Ch 6-7
Ch 6-8
Review
Test
Ch 5 Test
Nov 22
Q2
Benchmar
k
Nov 25 or
26
Q2-Q3
Dec 2-Jan
17
(24 days)
Equations
and
Inequalitie
s
Equations
-One Step Equations
-Two Step Equations
-Multi step
Inequalities
-One Step
-Two step
Use variables to represent quantities in a real-world or
mathematical problem, and construct simple equations and
inequalities to solve problems by reasoning about the
quantities.
7.EE.4
Solve word problems leading to equations of the form px + q = r 7.EE.4a
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.
1. Solve one step addition and subtraction equations (1 day
inquiry lab, 1 day practice)
2. Solve one step mulitplication and division problems (1 day
Ch 6-1
Ch 6-2
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Form Rev. 6/18/12
PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
inquiry lab, 1 day practice).
3. Solve equations with rational coefficients (1 day inquiry lab, 2
day practice)
4. Solve two step equations (1 day inquiry lab, 2 days practice)
5. Solve multi step equations (1 day inquiry lab, 2 days practice)
Ch 6-3
Ch 6-4
Ch 6-5
Solve word problems leading to inequalities of the form px + q > 7.EE.4b
7.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.
6.. Solve inequalities by addition and subtraction (1 day inquiry
lab, 1 day practice)
7. Solve inequalities by multiplication or division (1 day inquiry,
2 days practice)
8. Solve two step inequalities (1 day inquiry lab, 2 days practice)
Ch 6-6
Ch 6-7
Ch 6-8
Review
Test
Q3
Geometric Complementary Angles
Jan 21-Feb Figures
Supplementary Angles
6
Vertical Angles
Use facts about supplementary, complementary, vertical, and
adjacent angles in a multi-step problem to write and solve
simple equations for an unknown angle in a figure.
(12 days)
1.
Classify angles and identify vertical and adjacent angles (1
day)
2. Classify angles and identify vertical, adjacent,
complementary, supplementary angles (1 day)
Adjacent
TrianglesAngles
(classification)
Interior Angles of Polygons
Scale
3D figures
Cross Sections of 3D figures
Might need to
stop here,
review and
quiz
Ch 6 Test
7.G.5
Draw (freehand, with ruler and protractor, and with technology) 7.G.2
geometric shapes with given conditions. Focus on constructing
triangles from three measures of angles or sides, noticing
when the conditions determine a unique triangle, more than one
triangle, or no triangle.
3a.. Inquiry Lab-create triangles using given angles and side
lengths (1 day)
3b. Identify and classify triangles and find missing angle
measures (1 day)
3c. Sum of the interior angles of polygons (2 days)
Solve problems involving scale drawings of geometric figures,
including computing actual lengths and areas from a scale
drawing and reproducing a scale drawing at a different scale.
4. Solve problems involving scale drawings (2 days)
7.G.1
Ch 7-1
Ch 7-2
Ch 7-3 Inquiry
Ch 7-3
Ch 7-4
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Form Rev. 6/18/12
PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
Describe the two-dimensional figures that result from slicing
three-dimensional figures, as in plane sections of right
rectangular prisms and right rectangular pyramids.
1. Draw 3D figures given the top, side, and front views (1 day)
2. Identify and draw 3D figures and cross sections (1 day)
Ch 7-5
7.G.3
Ch 7-6
Ch 7 Test
2/4
Review
Test
Q3-Q4
Geometric Circumference
2/10-3/21 Measures Area
(23 days)
Circles
Composite Figures
Volume
-Prisms
-Pyramids
Surface Area
-Prisms
-Pyramids
-Composite Figures
Q3
Benchmar
k
2/7
Know the formulas for the area and circumference of a circle 7.G.4
and use them to solve problems; give an informal derivation of
the relationship between the circumference and area of a
circle.
1. Find the circumference of circles (1 day inquiry lab, 1 day
practice).
2. Find the area of circles (1 day inquiry lab, 1 day practice)
Solve real-world and mathematical problems involving area,
7.G.6
volume and surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and
right prisms.
3. Find the area of composite figures (3 days)
4. Find the volume of prisms (3 days)
5. Find the volume of pyramids (1 day inquiry lab, 2 days
practice)
6. Find the surface area of prisms (1 day inquiry lab, 2 days
practice)
7. Find the surface area of pyramids (1 day)
8. Find the surface area and volume of composite figures (3
days)
Review
Test
Q4
3/24-4/2
2
Probabil
ity
Probability
Simple Event
Experimental Probability
Theoretical Probability
Fair/Unfair
Counting Principle
Understand that the probability of a chance event is a
number between 0 and 1 that expresses the likelihood of the
event occurring. Larger numbers indicate greater likelihood.
A probability near 0 indicates an unlikely event, a probability
around 1/2 indicates an event that is neither unlikely nor
likely, and a probability near 1 indicates a likely event.
Ch 8-1
Ch 8-2
Ch 8-3
Ch 8-4
Ch 8-5
Ch 8-6
Ch 8-7
Ch 8-8
Ch 8 Test
3/21
7.SP.6
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Form Rev. 6/18/12
PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
Simulation
Compound Event
Independent/Dependent
Events
Develop a probability model and use it to find probabilities of
events. Compare probabilities from a model to observed
frequencies; if the agreement is not good, explain possible
sources of the discrepancy.
7.SP.7
Develop a uniform probability model by assigning equal
probability to all outcomes, and use the model to determine
probabilities of events
1. Find and interpret the probability of a simple event (1 day)
7.SP.7a
Develop a probability model (which may not be uniform) by
observing frequencies in data generated from a chance
process.
2a.. Find and compare the experimental and theoretical
probabilities (2 days)
2b. Use experimental and theoretical probability to determine
fair and unfair games (inquiry lab, 1 day)
7.SP.7b
Understand that, just as with simple events, the probability of
a compound event is the fraction of outcomes in the sample
space for which the compound event occurs.
7.SP.8a
Represent sample spaces for compound events using
methods such as organized lists, tables and tree diagrams.
For an event described in everyday language (e.g., “rolling
double sixes”), identify the outcomes in the sample space
which compose the event.
3. Find the probabilities of compound events (2 days)
7.SP.8b
Design and use a simulation to generate frequencies for
compound events.
4a. Perform probability simulations to model real world
situations (1 day)
4b. Inquiry lab-Simulate Compound Events (1 day)
7.SP.8c
Understand that the probability of a chance event is a
number between 0 and 1 that expresses the likelihood of the
event occurring. Larger numbers indicate greater likelihood.
A probability near 0 indicates an unlikely event, a probability
around 1/2 indicates an event that is neither unlikely nor
likely, and a probability near 1 indicates a likely event.
5. Use multiplication to count outcomes and find probabilities
(1 day)
7.SP.5
Ch 9-1
Ch 9-2
Ch 9-3
Ch 9-4
Ch 9-5
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Form Rev. 6/18/12
PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
6. Find the number of permutations of a set of objects and
find probabilities (2 days)
7. Find the probability of independent and dependent events
(3 days)
7.SP.8a
Ch 9-6
7.SP.8
Ch 9-7
Review
Test
Ch 9
Test
4/22
Q4
4/23-5/2
Statistic
s
(9 days)
Sample
Population
Understand that statistics can be used to gain information
about a population by examining a sample of the population;
Graphs
Statistics
Scatterplots
Trends
only if the sample
generalizations
about
is representative
a population from
of that
a sample
population.
are valid
Understand that random sampling tends to produce
representative samples and support valid inferences.
7.SP.1
Use data from a random sample to draw inferences about a
population with an unknown characteristic of interest.
Generate multiple samples (or simulated samples) of the
same size to gauge the variation in estimates or predictions.
1. Predict the actions of a larger group by using a sample (1
day)
2. Determine whether sample methods are valid (1 day)
3. Recognize when statistics and graphs are misleading (1
day)
7.SP.2
Use measures of center and measures of variability for
numerical data from random samples to draw informal
comparative inferences about two populations.
4. Compare two populations (1 day)
5a. Scatterplots and Trends (2 days)
5b. Select, organize, and construct appropriate displays of
data. (3 days)
7.SP.4
7.SP.3
Ch 10-1
Ch 10-2
Ch 10-3
Ch 10-4
Ch 10-5
Ch 10
Test
5/2
Review
Test
Q4
5/5-5-14
End of
Year
Review
End of Year Review
End of Year Benchmark 5/15-5/16
End of Year
Benchmar
k 5/15-5/16
End of
Year
Benchm
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Form Rev. 6/18/12
PRESCOTT UNIFIED SCHOOL DISTRICT
District Instructional Guide
Date Revised____June 2013______________
ark
5/15-5/1
6
*During Common Core transition, teachers may wish to document pre-2010 AZ standards that they are still responsible to teach for AIMS.
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Form Rev. 6/18/12