Seventh Grade Math Scope and Sequence
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WHCSD Scope and Sequence 7th Grade Math 2021-2022
Seventh Grade Math Scope and Sequence
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Domain Number System Ratios and Proportions Statistics and Probability Geometry
Expressions and Equations
RATIOS AND 7.NS.1a. Describe situations in 7.RP.1. Compute unit rates 7.SP.5. Understand that the 7.G.5. Use facts about
PROPORTIONAL which opposite quantities associated with ratios of fractions, probability of a chance event is supplementary, complementary,
RELATIONSHIPS combine to make 0. For including ratios of lengths, areas a number between 0 and 1 that vertical, and adjacent angles in a
7.RP example, a hydrogen atom has and other quantities measured in expresses the likelihood of the multi-step problem to write and
0 charge because its two like or different units. For event occurring. Larger solve simple equations for an
1-3) Analyze constituents are oppositely example, if a person walks 1/2 numbers indicate greater unknown angle in a figure.
proportional charged. mile in each 1/4 hour, compute likelihood. A probability near 0
relationships and use the unit rate as the complex indicates an unlikely event, a 7.G.2 Draw (freehand, with ruler
them to solve real- 7.NS.1b. Understand p + q as fraction 1/2/1/4 miles per hour, probability around 1/2 indicates and protractor, and with
world and the number located a distance equivalently 2 miles per hour. an event that is neither unlikely technology) geometric figures
mathematical |q| from p, in the positive or nor likely, and a probability near with given conditions.
problems. negative direction depending on 7.RP.2a. Decide whether two 1 indicates a likely event. 2a. Focus on constructing
whether q is positive or quantities are in a proportional triangles from three measures of
THE NUMBER negative. Show that a number relationship, e.g., by testing for 7.SP.6. Approximate the angles or sides, noticing when the
and its opposite have a sum of 0 equivalent ratios in a table or probability of a chance event by conditions determine a unique
SYSTEM (are additive inverses). Interpret graphing on a coordinate plane collecting data on the chance triangle, more than one triangle,
7.NS sums of rational numbers by and observing whether the graph process that produces it and or no triangle.
1-3) Apply and extend describing real-world contexts. is a straight line through the observing its long-run relative 2b. Focus on constructing
previous origin. frequency, and predict the quadrilaterals with given
understandings of 7.NS.1c. Understand subtraction approximate relative frequency conditions noticing types and
operations with of rational numbers as adding 7.RP.2b. Identify the constant of given the probability. For properties of resulting
fractions to add, the additive inverse, p – q = p + proportionality (unit rate) in tables, example, when rolling a number quadrilaterals and whether it is
subtract, multiply, and (–q ). Show that the distance graphs, equations, diagrams, and cube 600 times, predict that a 3 possible to construct different
divide rational between two rational numbers verbal descriptions of proportional or 6 would be rolled roughly 200 quadrilaterals using the same
on the number line is the relationships. times, but probably not exactly conditions.
numbers. absolute value of their 200 times.
difference, and apply this 7.RP.2c. Represent proportional 7.G.4 Work with circles. a.
EXPRESSIONS AND principle in real-world contexts. relationships by equations. For 7.SP.7a. Develop a uniform Explore and understand the
EQUATIONS example, if total cost t is probability model by assigning relationships among the
7.EE proportional to the number n of equal probability to all circumference, diameter, area,
1-2) Use properties of 7.NS.2a. Understand that items purchased at a constant outcomes, and use the model to and radius of a circle. b. Know
operations to generate multiplication is extended from price p, the relationship between determine probabilities of and use the formulas for the area
equivalent fractions to rational numbers by the total cost and the number of events. For example, if a and circumference of a circle and
expressions. requiring that operations items can be expressed as t = pn. student is selected at random use them to solve real-world and
continue to satisfy the properties from a class, find the probability mathematical problems.
3-4) Solve real-life and of operations, particularly the that Jane will be selected and
7.RP.3. Use proportional
mathematical distributive property, leading to relationships to solve multistep the probability that a girl will be 7.G.6. Solve real-world and
problems using products such as (–1)(–1) = 1 ratio and percent problems. selected. mathematical problems involvingWHCSD Scope and Sequence 7th Grade Math 2021-2022
numerical and and the rules for multiplying Examples: simple interest, tax, area, volume and surface area of
algebraic expressions signed numbers. Interpret markups and markdowns, 7.SP.7b. Develop a probability two- and three-dimensional
and equations. products of rational numbers by gratuities and commissions, fees, model (which may not be objects composed of triangles,
describing real-world contexts. percent increase and decrease, uniform) by observing quadrilaterals, polygons, cubes,
percent error. frequencies in data generated and right prisms.
GEOMETRY 7.NS.2b. Understand that from a chance process. For
7.G integers can be divided, 7.G.1 Solve problems involving example, find the approximate 7.G.3. Describe the two-
1-3) Draw, construct, provided that the divisor is not similar figures with right triangles, probability that a spinning penny dimensional figures that result
and describe zero, and every quotient of other triangles, and special will land heads up or that a from slicing three-dimensional
geometrical figures integers (with non-zero divisor) quadrilaterals. tossed paper cup will land open- figures, as in plane sections of
and describe the is a rational number. If p and q 1a. Compute actual lengths and end down. Do the outcomes for right rectangular prisms and right
relationships between are integers, then –(p/q) = (–p)/q areas from a scale drawing and the spinning penny appear to be rectangular pyramids.
them. = p/(–q). Interpret quotients of reproduce a scale drawing at a equally likely based on the
4-6) Solve real-life and rational numbers by describing different scale. observed frequencies?
real world contexts. 1b. Represent proportional
mathematical
relationships within and between 7.SP.8a. Understand that, just
problems involving 7.NS.1d. Apply properties of similar figures. as with simple events, the
angle measure, operations as strategies to add probability of a compound event
circles, area, surface and subtract rational numbers. 7.RP.2d. Explain what a point (x, is the fraction of outcomes in the
area, and volume. y) on the graph of a proportional sample space for which the
7.NS.2c. Apply properties of relationship means in terms of the compound event occurs.
STATISTICS AND operations as strategies to situation, with special attention to
PROBABILITY multiply and divide rational the points (0, 0) and (1, r) where r 7.SP.8b. Represent sample
7.SP numbers. is the unit rate. spaces for compound events
Apply and extend previous using methods such as
1) Use sampling to understandings of operations organized lists, tables and tree
draw conclusions with fractions to add, subtract, 7.EE.3. Solve multi-step real-life diagrams. For an event
about a population. multiply, and divide rational and mathematical problems described in everyday language
2) Broaden numbers. posed with positive and negative (e.g., “rolling double sixes”),
understanding of rational numbers in any form identify the outcomes in the
statistical problem 7.NS.2d. Convert a rational (whole numbers, fractions, and sample space which compose
solving. number to a decimal using long decimals), using tools the event.
3-4) Summarize and division; know that the decimal strategically. Apply properties of
describe distributions form of a rational number operations to calculate with 7.SP.8c. Design and use a
terminates in 0s or eventually numbers in any form; convert simulation to generate
representing one between forms as appropriate;
repeats. frequencies for compound
population and draw and assess the reasonableness events. For example, use
informal comparisons 7.NS.3 Solve real-world and of answers using mental random digits as a simulation
between two mathematical problems computation and estimation tool to approximate the answer
populations. involving the four operations strategies. For example: If a to the question: If 40% of donors
5-8) Investigate with rational numbers. woman making $25 an hour gets have type A blood, what is the
chance processes and Computations with rational a 10% raise, she will make an probability that it will take at
develop, use, and numbers extend the rules for additional 1/10 of her salary an least 4 donors to find one with
manipulating fractions to hour, or $2.50, for a new salary of type A blood?
complex fractions. $27.50. If you want to place aWHCSD Scope and Sequence 7th Grade Math 2021-2022
evaluate probability towel bar 9 3/4 inches long in the 7.SP.1 Understand that
models. center of a door that is 27 1/2 statistics can be used to gain
inches wide, you will need to information about a population
place the bar about 9 inches from by examining a sample of the
each edge; this estimate can be population. a. Differentiate
used as a check on the exact between a sample and a
computation. population. b. Understand that
conclusions and generalizations
7.EE.1. Apply properties of about a population are valid only
operations as strategies to add, if the sample is representative of
subtract, factor, and expand linear that population. Develop an
expressions with rational informal understanding of bias.
coefficients.
7.SP.2 Broaden statistical
7.EE.2 In a problem context, reasoning by using the GAISE
understand that rewriting an model: a. Formulate Questions:
expression in an equivalent form Recognize and formulate a
can reveal and explain properties statistical question as one that
of the quantities represented by anticipates variability and can
the expression and can reveal be answered with quantitative
how those quantities are related. data. For example, “How do the
For example, a discount of 15% heights of seventh graders
(represented by p – 0.15p) is compare to the heights of eighth
equivalent to (1 – 0.15) p, which graders?” (GAISE Model, step
is equivalent to 0.85p or finding 1) b. Collect Data: Design and
85% of the original price. use a plan to collect appropriate
data to answer a statistical
7.EE.4a. Solve word problems question. (GAISE Model, step 2)
leading to equations of the form c. Analyze Data: Select
px + q = r and p(x + q) = r, where appropriate graphical methods
p, q, and r are specific rational and numerical measures to
numbers. Solve equations of analyze data by displaying
these forms fluently. Compare an variability within a group,
algebraic solution to an arithmetic comparing individual to
solution, identifying the sequence individual, and comparing
of the operations used in each individual to group. (GAISE
approach. For example, the Model, step 3) d. Interpret
perimeter of a rectangle is 54 cm. Results: Draw logical
Its length is 6 cm. What is its conclusions and make
width? generalizations from the data
based on the original question.
7.EE.4b. Solve word problems (GAISE Model, step 4)
leading to inequalities of the form
px + q > r or px + q < r, where p, 7.SP.3 Describe and analyze
q, and r are specific rational distributions.WHCSD Scope and Sequence 7th Grade Math 2021-2022
numbers. Graph the solution set 3a. Summarize quantitative data
of the inequality and interpret it in sets in relation to their context
the context of the problem. For by using mean absolute
example: As a salesperson, you deviationG (MAD), interpreting
are paid $50 per week plus $3 per mean as a balance point. 3b.
sale. This week you want your Informally assess the degree of
pay to be at least $100. Write an visual overlap of two numerical
inequality for the number of sales data distributions with roughly
you need to make, and describe equal variabilities, measuring
the solutions. 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 plotG (line plot),
the separation between the two
distributions of heights is
noticeable.
Resources Reveal Math Reveal Math Reveal Math Reveal Math
Modules 3, 4, 8, 9 Modules 1, 2, 8, 11 Modules 10-11 Modules 8 and 9
ODE Model Curriculum Expressions and Equations ODE Model Curriculum ODE Model Curriculum
GAISE model framework Modules 2, 3, 4, 5, 6, 7, 8, 9 GAISE model framework GAISE model framework
ODE Model Curriculum
GAISE model framework
CRITICAL AREAS
Critical Area 1: Developing understanding of and applying proportional relationships Students extend their understanding of ratios and develop understanding of proportionality
to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving
discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by
using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a
measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships.
Critical Area 2: Developing understanding of operations with rational numbers and working with expressions and linear equations Students develop a unified understanding of
number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percent as different representations of rational numbers. Students extend
addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and
multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts, e.g., amounts owed or temperatures below zero,
students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate
expressions and equations in one variable and use these equations to solve problems.WHCSD Scope and Sequence 7th Grade Math 2021-2022 Critical Area 3: Solving problems involving scale drawings and informal geometric constructions, angles, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Critical Area 4: Drawing inferences about populations based on samples Students build on their previous work with statistical problem solving through the use of the GAISE model framework. They summarize and describe distributions representing one population and informally compare two populations. Students interpret numerical data sets using mean absolute deviation. They begin informal work with sampling to generate data sets: learn about the importance of representative samples for drawing inferences and the impact of bias. Critical Area 5: Investigating chance Students build upon previous understandings as they develop concepts of probability. They investigate relevant chance events and develop models to determine and compare probabilities. They analyze the frequencies of the experimental results against their predictions, justifying any discrepancies. Students extend their investigations with compound events representing the possible outcomes in tree diagrams, tables, lists, and ultimately through designing and using simulations.
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