amador county unified - Amador Public Schools Curriculum and

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AMADOR COUNTY UNIFIED
7
Common Core Learning Objectives & Essential Tools
DataWORKS Educational Research has analyzed Common Core State Standards
(CCSS) and recognized the challenge educators face in creating Learning Objectives
from often text-dense standards.
In Common Core Learning Objectives & Essential Tools, DataWORKS takes CCSS
to a highly functional, teacher-friendly level. Each grade-level/subject-specific booklet
(Math and ELA only) offers one or more READY TO TEACH learning objectives for
each standard.
“With these explicit Learning Objectives, teachers can move quickly to designing
well-crafted and well-delivered lessons that focus on required skills and content.”
By deciphering individual skills and concepts in CCSS and organizing them to create
READY TO TEACH learning objectives, DataWORKS Common Core Learning
Objectives & Essential Tools helps teachers insure they teach the required skill and
content for each standard.
Side-by-Side
3rd Grade – Numbers
and
Operations
Fractions
Color-coded
Columns
Developing understanding of fractions as numbers.
Standard
3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part
when a whole is partitioned into b equal parts; understand a fraction
a/b as the quantity formed by a parts of size 1/b.
Learning Objective
1.1 Determine unit fractions of a whole.
1.2 Determine fractions of a whole.
Common Core State Standards may include:
Learning Objectives include:
• multiple objectives
• examples and directions
• non-specific language
• a skill (verb)
• a concept (bolded noun)
• brevity for ease of teaching
• consistency across grades
Teaching Tips
This lesson is the first time fractions are
addressed.
Teaching Tips include:
• examples for teaching concepts
• suggestions for lesson design
• definition of terms
• connections to other standards
Table of Contents
Introduction
2
3
Learning Objectives
Common Core Standards
Math Learning Objectives
5
6
7
8
9
10
Math Learning Objectives Overview
Ratios and Proportional Relationships
The Number System
Expressions and Equations
Geometry
Statistics and Probability
Essential Tools
12 Types of Vocabulary
14 Academic Vocabulary - Math
16 Content Vocabulary - Math
Common Core Posters
Solving Math Problems
Different Ways to Represent Ratios
DataWORKS Educational Research
©2012 All rights reserved.
Table of Contents
| 1
Introduction – Learning Objectives
Learning Objectives
A Learning Objective is a statement that describes what students will be able to do at the
end of the lesson, independently and successfully, as a result of instruction.
Importance of Learning Objectives
•
•
•
•
•
Defines the purpose of the entire lesson
Ensures that the Independent Practice matches
Verifies that the lesson matches a standard
Prevents lessons from becoming activities rather than content
Focuses students’ attention when taught
Crafting Learning Objectives from Common Core Standards
The Common Core Learning Objectives crafted from the Common Core Standards contain
three major parts:
Skills – measurable verbs that match Independent Practice (identify, write, calculate)
Concepts – topic or big idea of the lesson, usually nouns (decimal, figurative language)
Context – restricting condition or how to do it (using a number line, in a poem)
Introduction | 2
Introduction – Common Core Standards
1. Common Core Standards may contain multiple Objectives.
DataWORKS crafted separate Learning Objectives for each Common Core Standard that had more than
one Objective. Each Learning Objective can be used to create a new lesson.
Standard
Learning Objective
3.RI.3 Describe the relationship between a series of historical events, scientific ideas or
concepts, or steps in technical procedures in a text, using language that pertains to time,
sequence, and cause/effect.
3.1 Describe time relationships in text.
3.2 Describe sequence relationships in text.
3.3 Describe cause-and-effect relationships in text.
4.MD.6 Measure angles in whole number degrees using a protractor. Sketch angles of
specified measure.
6.1 Measure angles using a protractor.
6.2 Sketch angles of a specified measure.
2. Common Core Standards may contain Examples.
DataWORKS omitted the examples from the Learning Objectives. Teachers should use the examples as a
guide on how to write the Skill Development for the lesson.
Standard
Learning Objective
3.RL.3 Describe characters in a story (e.g., their traits, motivations, or feelings) and
3.0 Explain how character actions contribute to the sequence of events.
explain how their actions contribute to the sequence of events
4.MD.3 Apply the area and perimeter formulas for rectangles in real world and
3.1 Calculate the area of rectangles using formulas.
mathematical problems. For example, find the width of a rectangular room given the area of the
3.2 Calculate the perimeter of rectangles using formulas.
flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Introduction | 3
Introduction – Common Core Standards
3. Common Core Standards may contain Concept Definitions.
DataWORKS omitted the Concept definition and used the Concept name when crafting the Learning
Objective. Teachers should use the definition to create a bullet-proof definition for Concept Development.
Add the Concept name if it is missing.
Standard
3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is
partitioned into b equal parts; understand a fraction a/b as the quantity formed by a
parts of size 1/b.
8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10
to estimate very large or very small quantities…
1.L.1e Use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked
home; Today I walk home; Tomorrow I will walk home).
Learning Objective
1.1 Determine the unit fraction of a whole.
1.2 Determine fractions of a whole.
3.0 Write numbers in scientific notation.
1.0e.1 Use past tense verbs.
1.0e.2 Use present tense verbs.
1.0e.3 Use future tense verbs.
4. Common Core Standards may contain Context (restricting conditions or
teaching directions).
DataWORKS omitted the context. Teachers should use the restricting conditions or teaching directions to
create the Skill Development of the lesson.
Standard
Learning Objective
4.MD.1 Know relative sizes of measurement units within one system of units including 1.1 Identify relative sizes of measurement.
km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, 1.2 Record measurement equivalents.
express measurements in a larger unit in terms of a smaller unit. Record measurement
equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1
in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and
inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Introduction | 4
Grade 7 Math Learning Objectives Overview
Domain
Standards
Lettered Standards
Learning Objectives
3
4
4
3
8
5
Ratios and Proportional Relationships (RP)
Clusters
Analyze proportional relationships and use them to solve real-world and
mathematical problems.
The Number System (NS)
Clusters
Apply and extend previous understandings of operations with fractions to add,
subtract, multiply and divide rational numbers.
Expressions and Equations (EE)
Clusters
Use properties of operations to generate equivalent expressions.
2
Solve real-life and mathematical problems using numerical and algebraic
expressions and equations.
2
3
2
4
Geometry (G)
Clusters
Draw, construct, and describe geometrical figures and describe the relationships
between them.
3
3
Solve real-life and mathematical problems involving angle measure, area,
surface area, and volume.
3
4
Use random sampling to draw inferences about a population.
2
2
Draw informal comparative inferences about two populations.
2
2
4
5
6
24
19
33
Statistics and Probability (SP)
Clusters
Total
Grade 7 Mathematics
| 5
Grade 7 – Ratios and Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Standard
7.RP.1 Compute unit rates associated with ratios of fractions, including ratios
of lengths, areas and other quantities measured in like or different units. For
example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the
complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
7.RP.2 Recognize and represent proportional relationships between
quantities.
Learning Objective
1.0 Compute unit rates.
Example:
Given: 4 items cost $8 (4,8) and 2 items cost $4 (2,4).
The unit rate is 1 item costs $2 (1, 2).
a. Decide whether two quantities are in a proportional relationship, e.g., by
testing for equivalent ratios in a table or graphing on a coordinate plane
and observing whether the graph is a straight line through the origin.
2.0a Determine whether two
quantities are in a proportional
relationship.
b. Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional
relationships.
2.0bcd Represent proportional
relationships using equations.
8
(0, 0)
d. Explain what a point (x, y) on the graph of a proportional relationship
means in terms of the situation, with special attention to the points (0, 0)
and (1, r) where r is the unit rate.
price ($)
4
3
2
1
c. Represent proportional relationships by equations. For example, if total cost
is proportional to the number n of items purchased at a constant price p, the
relationship between the total cost and the number of items can be expressed as t =
pn.
7.RP.3 Use proportional relationships to solve multistep ratio and percent
problems. Examples: simple interest, tax, markups and markdowns, gratuities and
commissions, fees, percent increase and decrease, percent error.
Teaching Tips
Refer to 6.RP.1&2 for previous work with ratios, rates,
and unit rates.
3.0 Solve multistep problems using
proportions.
1 2 3 4
# of
items
Refer to 6.RP.3 for previous work with percentages.
Grade 7 Mathematics
| 6
Grade 7 – The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.
Standard
7.NS.1 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 diagram.
a. Describe situations in which opposite quantities combine to make 0. For
example, a hydrogen atom has 0 charge because its two constituents are oppositely
charged.
b. 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.
c. 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.
d. Apply properties of operations as strategies to add and subtract rational
numbers.
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.
d. 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.
7.NS.3 Solve real-world and mathematical problems involving the four
operations with rational numbers.
Learning Objective
Teaching Tips
Rational numbers are defined in the CCSS glossary for
mathematics (p. 86).
1.0abc Add and subtract rational
numbers on a number line.
1.0d Add and subtract rational
numbers using properties of
operations.
2.0abc Multiply and divide rational
numbers using properties of
operations.
Refer to the glossary (p. 90) for examples and
definitions of properties of operations.
Rational numbers are defined in the CCSS glossary for
mathematics (p. 86).
Refer to the glossary (p. 90) for examples and
definitions of properties of operations.
2.0d Convert a rational number to a
decimal.
3.0 Solve real-world problems using
the four operations.
CCSS notes that “computations with rational numbers
extend the rules for manipulating fractions to complex
fractions.”
Grade 7 Mathematics
| 7
Grade 7 – Expressions and Equations
Use properties of operations to generate equivalent expressions.
Standard
7.EE.1 Apply properties of operations as strategies to add, subtract, factor,
and expand linear expressions with rational coefficients.
Learning Objective
1.1 Add and subtract expressions.
1.2 Factor and expand expressions.
7.EE.2 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. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same
as “multiply by 1.05.”
2.0 Interpret expressions.
Teaching Tips
Refer to the glossary in the CCSS mathematics for
definition of properties of operations (p.90).
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Standard
7.EE.3 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. For example: If a woman making $25 an
hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50,
for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the
center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches
from each edge; this estimate can be used as a check on the exact computation.
7.EE.4 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.
a. 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. For example, the perimeter of a rectangle is 54 cm. Its length is 6
cm. What is its width?
b. 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. For example: As a salesperson, you are paid $50 per week plus $3 per
sale. This week you want your pay to be at least $100. Write an inequality for the
number of sales you need to make, and describe the solutions.
Learning Objective
3.0 Estimate and solve real-world
problems.
Teaching Tips
definition of properties of operations (p.90).
4.0a.1 Solve word problems using
equations.
4.0a.2 Compare the algebraic
solution to an arithmetic solution.
An arithmetic solution uses numbers under addition,
subtraction, multiplication, and division, whereas
algebra uses symbols or letters to represent numbers.
4.0b Solve word problems using
inequalities.
Graphing the solution set of the inequality is embedded
within the lesson of solving inequalities.
Grade 7 Mathematics
| 8
Grade 7 – Geometry
Draw, construct, and describe geometrical figures and describe the relationships between them.
Standard
7.G.1 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.
Learning Objective
1.0 Solve problems involving scale
drawings.
Teaching Tips
Use ratio reasoning to solve problems for reproducing a
scale drawing at a different scale.
7.G.2 Draw (freehand, with ruler and protractor, and with technology)
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.
2.0 Construct geometric shapes.
Lesson should focus on triangles using straight lines
and angles.
7.G.3 Describe the two-dimensional figures that result from slicing three
dimensional figures, as in plane sections of right rectangular prisms and
right rectangular pyramids.
3.0 Describe the two-dimensional
figures that result from slicing three
dimensional figures.
A section of a rectangular prism when sliced vertically:
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Standard
7.G.4 Know the formulas for the area and circumference of a circle and use
them to solve problems; give an informal derivation of the relationship
between the circumference and area of a circle.
Learning Objective
4.0 Solve problems for the area and
circumference of a circle
7.G.5 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.
5.0 Solve for an unknown angle using
properties of angles.
7.G.6 Solve real-world and mathematical problems involving area, volume
and surface area of two- and three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes, and right prisms.
6.1 Solve problems involving area of
two-dimensional objects.
6.2 Solve problems involving volume
and surface area of threedimensional objects.
Teaching Tips
This is the first time finding the area and circumference of
a circle is addressed.
Area formula: A = r2
Circumference formula: C = 2 r or C = d
In 6th grade, students calculate the volume of
rectangular prisms and find the surface area using
nets.
Grade 7 Mathematics
| 9
Grade 7 – Statistics and Probability
Standard
7.SP.1 Understand that statistics can be used to gain information about a
population by examining a sample of the population; generalizations about a
population from a sample are valid only if the sample is representative of that
population. Understand that random sampling tends to produce
representative samples and support valid inferences.
Learning Objective
1.0 Determine how statistics can be
used to gain information about a
population.
7.SP.2 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. For example, estimate the mean word length in a book by
randomly sampling words from the book; predict the winner of a school election based on
randomly sampled survey data. Gauge how far off the estimate or prediction might be.
2.0 Draw inferences about a
population using sampling.
Teaching Tips
For example, students should describe the difference
between randomly selecting 1,000 people from all
over the country versus 1,000 people from a particular
city.
Draw informal comparative inferences about two populations.
Standard
7.SP.3 Informally assess the degree of visual overlap of two numerical data
distributions with similar variabilities, measuring the difference between the
centers by expressing it as a multiple of a measure of variability. For example,
the mean height of players on the basketball team is 10 cm greater than the mean height of
players on the soccer team, about twice the variability (mean absolute deviation) on either
team; on a dot plot, the separation between the two distributions of heights is noticeable.
7.SP.4 Use measures of center and measures of variability for numerical data
from random samples to draw informal comparative inferences about two
populations. For example, decide whether the words in a chapter of a seventh-grade
science book are generally longer than the words in a chapter of a fourth-grade science book.
Learning Objective
3.0 Compare two numerical data
distributions.
Teaching Tips
Students should be interpreting the meaning of the
overlap in given graphs of data distributions. Center
refers to mean.
4.0 Compare the center and the
variation of numerical data sets.
Measure of center refers to mean and median. Variability
refers to inter quartile range and/or mean absolute
deviation in standard 6.SP.5.
Grade 7 Mathematics
| 10
Standard
7.SP.5 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.
7.SP.6 Approximate the probability of a chance event by collecting data on
the chance process that produces it and observing its long-run relative
frequency, and predict the approximate relative frequency given the
probability. For example, when rolling a number cube 600 times, predict that a 3 or 6
would be rolled roughly 200 times, but probably not exactly 200 times.
7.SP.7 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.
a. Develop a uniform probability model by assigning equal probability to all
outcomes, and use the model to determine probabilities of events. For
example, if a student is selected at random from a class, find the probability that Jane
will be selected and the probability that a girl will be selected.
b. Develop a probability model (which may not be uniform) by observing
frequencies in data generated from a chance process. For example, find the
approximate probability that a spinning penny will land heads up or that a tossed
paper cup will land open-end down. Do the outcomes for the spinning penny appear to
be equally likely based on the observed frequencies?
7.SP.8 Find probabilities of compound events using organized lists, tables,
tree diagrams, and simulation.
a. 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.
Learning Objective
5.0 Determine the probability of a
chance event.
Teaching Tips
This is the concept of theoretical probability. Refer to
the glossary in the CCSS mathematics for definition of
probability (p.86).
6.0 Compare theoretical probability
to experimental probability.
This standard requires students to compare theoretical
probability (chance event) to experimental probability.
7.0a Develop a uniform probability
model and use it to find probabilities
of events.
7.0b Develop a non-uniform
probability model from model to
observed frequencies.
definition of probability model (p.86) and uniform
probability model (p. 87).
8.0ab Find probabilities of
compound events.
Example of a tree diagram used to represent sample
spaces for “flipping a coin with three heads in a row”:
Flip 1:
b. 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.
c. Design and use a simulation to generate frequencies for compound
events. For example, use random digits as a simulation tool to approximate the
answer to the question: If 40% of donors have type A blood, what is the probability
that it will take at least 4 donors to find one with type A blood?
H
Flip 2:
Flip 3:
T
H
H
T
T
H
H
T
H
T
T
H
T
8.0c Find probabilities of compound
events using simulations.
Grade 7 Mathematics
| 11
Types of Vocabulary
(Across Grades)
Academic
Vocabulary
Content
Vocabulary
Support
Vocabulary
- used across all disciplines
- content specific
- in specific textbooks and
worksheets; may be challenging for
EL students
(Often not taught in Textbooks)
DataWORKS
(Taught during Concept
Development in EDI Lessons)
(Often over-emphasized in Textbooks)
Examples:
distinguish, corresponds,
combine, separate, analysis,
symbolic
Examples:
main idea, thesis statement,
figurative language.
Examples:
halibut, hammock, port, starboard
denominator, linear equation,
addition, ratios, perimeter
Civil War, separation of powers,
legislative branch.
mitosis, cell wall, photosynthesis,
Solar System
Common Core
Tier One words
Tier Two words
Tier Three words
(everyday speech)
(general academic words)
(domain-specific words)
Beginning ELD
Examples in Informational text:
relative, vary, formulate,
specificity, accumulate
Examples in Technical text:
calibrate, itemize, periphery
Examples in Literary text:
misfortune, dignified, faltered,
unabashedly
Examples:
lava, legislature, circumference,
aorta
Grade 7 Mathematics
| 12
Types of Vocabulary
Reading Success
Readers can read effectively when they can understand at least 95% of the words they read. Knowing only
the most common 2000 words, studies show that readers should be able to comprehend about 80% of an
average academic text. Adding in a list of 570 Academic and Content Vocabulary* words brings that total up
to 90% comprehension (Nation & Waring, 1997). The remaining unknown words in academic text will
largely be Content and Support Vocabulary and should be learned within the context of lessons throughout
the school year.
Words Known
Comprehension
Most common 2000 words
80%
Plus 570 Academic Vocabulary Words
90%
Plus Remaining Content and Support Vocabulary
95-100%
* DataWORKS has taken the list of 570
words and further categorized them as
Academic or Content based on their
potential use. (e.g., area is an academic
vocabulary word when referring to area
of study, however, area is a content
vocabulary word when referring to the
space of a two-dimensional figure)
To compile this vocabulary list, DataWORKS has analyzed the text of the Common Core State Standards
and extracted the most important Academic and Content area vocabulary. These vocabulary lists:
• Should be used when designing Common Core
lessons.
• Are broken down into Academic and Content
Vocabulary. Some words can be both.
• Feature grade-appropriate definitions.
• Note the frequency of each word within the
standards (in parentheses after the word if the
word is used more than once).
Example
connection (2) – link, relationship
vocabulary from
the standards
frequency of
word within
the standards
grade-appropriate
definition
In addition, the DataWORKS Word Lists (by grade level) can
be found at www.dataworks-ed.com/resources/vocabulary.
Grade 7 Vocabulary List | 13
Academic Vocabulary – Grade 7 Math
(from the Common Core Standards)
A
appropriate – correct or relevant
approximate (2) – nearly correct
assess (2) – test or check
assign – give
C
complex – complicated
compound – having two or more parts
constant – remaining unchanged; a number with no
variable
constituents – parts
construct (2) – make or build from parts
context (3) – what is around a word, phrase, sentence, or
situation
convert (2) – change to something else
coordinate – numbers that represent position
D
data (5) – information about something
design – think of and create something for a specific job
develop – create
diagram (3) – a drawing that shows data
distribute (2) – break apart evenly; share
E
equivalent (2) – having the same value; of equal value
estimate (2) – calculate approximately
expand – make larger
F
focus – concentrate on
frequency (2) – how often something happens
G
generate (3) – create
I
identify (3) – find; look for
indicate – show or point out
inferences (3) – a conclusion drawn from information or
text, that is not explicitly stated
interpret (2) – tell what it means
involving (3) – having to do with
L
located – where something is
M
method – way of doing something
Academic Vocabulary – Grade 7 Math
O
occur (2) - happen
outcome (2) - result
overlap – occupy the same area in part
P
pose – ask
predict (2) – say something that you think will happen
based on evidence or patterns you see
previous (2) – coming before
process (2) – a series of actions to achieve a goal
purchased – bought
R
random (5) – without a clear pattern
reasonableness – not beyond what is usual or expected
requiring – needing
S
statistics – the study of collecting, organizing, and
interpreting data
strategically – doing something following a plan
strategies (3) – a plan on how to do something
T
technology – computers and computer programs
terminates – ends
U
uniform – the same across a group
unique – being the only one of its kind
V
valid – based on truth or fact
variability (2) – the quality of changing
variation – difference
verbal – said out loud
visual – able to be seen
sections – parts or pieces of something
selected – chosen
sequence – the order of things
similar – like something else
sources – where information comes from
specific – a certain kind
Content Vocabulary – Grade 7 Math
A
area (3) – the amount of space a shape covers
C
circumference – the distance around the outside of a
circle
coefficients – a number multiplied by one or more
variables
complementary angle – either of two angles that add up
to 90 degrees
compute (2) – figure out by doing math
cube – a solid figure with six congruent squares as sides
D
decimal (2) – a number written with a decimal point (1.03)
to show whole numbers and parts of a number less than
one
derivation – arrive at an answer through logic or a
mathematical process
diagram (3) – a drawing that shows data
dimension (2) – how far the sides of an object or shape
extend
discrepancy – something that is different or disagrees
divisor – the number by which a dividend is divided
E
equation (3) – numbers connected by operations and an
equal sign
F
factor – n. one of the numbers in a multiplication
problem;
v. to write a number as a product of smaller numbers
formulas – a mathematical rule used for computing (e.g.,
the formula for the area of a rectangle is A = l w)
fraction (4) – a number that represents part of a whole or
part of a set
freehand – done without mechanical aid
H
horizontal – side to side
Figure A
negative
0
positive
I
inequalities – a mathematical sentence that compares two
amounts; use symbols <, >, ,
integers – all whole numbers and their opposites (…-3, 2, -1, 0, 1, 2, 3…)
inverse (2) – an operation with the opposite effect (e.g.,
addition and subtraction are inverse operations)
L
linear – related to a line
M
multi-step (3) – a problem needing more than one step to
solve
N
negative (2) – a number less than zero; see Figure A
O
opposite – numbers on opposite sides of zero on the
number line
P
percent – a ratio that compares a number to 100
polygons – a closed shape with three or more straight
sides
positive (2) – a number greater than zero; see Figure A
proportional (3) – having the same or a constant ratio
protractor – a tool used to measure angles
Q
quadrilaterals – a closed figure with four straight sides
quotient – the answer to a division problem
R
ratio (3) – a relationship between two quantities
rational number (7) – an integer or a fraction
rectangular prisms – a solid figure that has two pairs of
opposite faces that are congruent rectangles
rectangular pyramids – a pyramid where the base is a
rectangle
rewrite – write again
S
slicing – cutting
supplementary angle – angles that add up to 180 degrees
surface area – the area on the surface of a 3-dimensional
object
V
variables – a letter used to represent an unknown amount
vertical (2) – up and down
volume –the amount of space an object takes up
Figure A
negative
0
positive
What am I trying to find?
“What do I already know about this idea?”
“What operation(s) will I need to use?”
“What amounts am I given?”
“Which numbers do I need?”
Larger-sized posters available for purchase at
www.dataworks-ed.com
“Does my answer make sense?”
“Did I answer the original question?”
WWW.DATAWORKS-ED.COM
3–7
“There are five boys
for every four girls.”
using
ratio form
5:4
6–7
Different Ways to Represent
Ratios
using
words
5
4
(10, 8)
Larger-sized posters available for purchase at
www.dataworks-ed.com
using a graph
boys
1 2 3 4 5 6 7 8 9 10
(5, 4)
using
pictures
10
9
8
7
6
5
4
3
2
1
using
fraction form
WWW.DATAWORKS-ED.COM
girls
Teacher Notes
Teacher Notes
READY TO TEACH™
EDI Lessons
If you like Common Core Learning
Objectives & Essential Tools, check out
DATAWORKS READY TO TEACH™
EDI Lessons.
READY TO TEACH™ EDI Lessons for Common Core State Standards
DataWORKS READY TO TEACH™ EDI® lessons for CCSS will be available to license and download beginning Spring 2013.
AT-A-GLANCE:
Common Core Learning Objective
& READY TO TEACH EDI Lesson
FREE LESSON DOWNLOADS
available along with fee-based
individual, school, or district licensing.
*Explicit Direct Instruction® (EDI®), is
a strategic collection of research-based,
instructional practices combined to help
teachers design and deliver well-crafted
lessons that explicitly teach grade-level
content and increase language acquisition
for all students.
2
AG
Embedded Grade-Level
Expository Text
E
2
LE
P
DataWORKS interactive,
multi-media lessons (K-12)
incorporate clear conceptual
definitions, academic vocabulary,
embedded grade-level expository
text, and higher-order questions,
along with the use of technology
to enhance students’ overall
learning experience.
1
3
Higher-Order Questions
MP
DataWORKS READY TO TEACH™
Explicit Direct Instruction® (EDI®)*
Lessons have always been rigorously
aligned to standards and strongly
focused on CCSS requirements.
Clear Conceptual Definitions
1
3
SA
Visit DataWORKS online Lesson
Catalog (www.dataworks-ed.com).
4
Academic Vocabulary
4
Free Downloads and Purchase Information
For free downloads or to purchase Common Core Learning Objectives & Essential Tools or READY TO TEACH® EDI® Lessons, visit www.dataworks-ed.com.
About DataWORKS Educational Research
Along with products and services, DataWORKS offers a variety of professional development training in Explicit Direct Instruction, lesson demonstrations in live classrooms,
interactive coaching, and after-school and summer acceleration programs (StepUP Academies). Implementation support is available for educators, administrators and parents.
Contact DataWORKS Client Relations Department for more information:
info@dataworks-ed.com
(800) 495-1550
John Hollingsworth and Dr. Silvia Ybarra co-founded DataWORKS with the single purpose of using real data to improve student learning, especially for English Language Learners
and other low-performing students. Now, DataWORKS focuses on GIFT–Great Initial First Teaching—so students learn more grade-level skills and content the first time a lesson
is taught. Analyzing test scores does not help improve student achievement; delivering great, grade-level lessons ... every lesson, every day ... helps improve student achievement.
John and Silvia’s new book, Explicit Direct Instruction for English Learners, publishes in December 2012 (Corwin). John and Silvia’s previous book, Explicit Direct Instruction: The Power
of the Well-Crafted, Well-Delivered Lesson (2009) is a Corwin Bestseller. Along with Joan Ardovino, John and Silvia co-authored Multiple Measures: Accurate Ways to Assess Student
Achievement (Corwin, 2000)
®
for English Learners
®
A Joint Publication
John R. Hollingsworth • Silvia E. Ybarra
7

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