Download 7th Grade - St. Francis School District

7th Grade Math Learning Targets and “I Can” Statements
Ratios and Proportional Relationships
Students will be able to understand that two variable quantities are proportional if their values are in
a constant ratio and the relationship between proportional quantities can be represented as a linear
function.
Students will be able to analyze proportional relationships and use them to solve real-world and
mathematical problems.
I can compute unit rates associated with ratios of fractions, including lengths, areas, and other
quantities in like and different units.
I can determine whether two quantities are proportional from either a table or graph.
I can identify the unit rate in tables, graphs, equations, diagrams, and verbal descriptions.
I can identify the unit rate in tables, graphs, equations, diagrams, and verbal descriptions of
proportional relationships.
I can represent proportional relationships by equations.
I can draw a model for a proportional relationship and connect it to an equation to solve a
proportion.
I can interpret and explain what a point (x,y) means on a proportional graph, paying special
attention to (0,0) and (1,r), where r is the unit rate.
I can use proportions to solve multi-step ratio and percent problems, including interest, tax,
discounts, tips.
I can use proportions to solve multi-step ratio and percent problems, including simple interest,
tax, discounts, tips, and percent increase and decrease.
The Number System
Students will understand the set of real numbers has infinite subsets including the sets of whole
numbers, integers, rational numbers, and irrational numbers.
Students will understand that numerical quantities and calculations can be estimated by using
numbers that are close to the actual values, but easier to compute.
Students will be able to apply and extend previous understandings of operations with fractions to add,
subtract, multiply, and divide numbers.
I can add and subtract natural and whole numbers, integers, fractions, and decimals.
I can represent addition and subtraction on a number line diagram.
I can describe situations in which opposite quantities combine to make 0.
I can show that a number and its opposite have a sum of 0.
I understand subtraction of rational numbers as adding the additive inverse. For example p – q =
p + (-q).
I understand the distance between two rational numbers on the number line is the absolute
value of their differences.
I can multiply and divide natural and whole numbers, integers, fractions, and decimals.
I can explain the solutions for operations on integers (e.g. I can explain why
-2 multiplied by -3 is +6 or why -2 – (-6) is positive 4).
I can apply the properties of operations (commutative, associative, identity, distributive, and
inverse properties, along with order of operations) to operations with rational numbers.
I can convert a rational number to a decimal using long division.
I know the decimal form of a rational number terminates in 0s or eventually repeats.
I can solve real-world problems involving all four operations on rational numbers.
Expressions and Equations
Students will understand there are some mathematical relationships that are always true and that
these relationships are used as the rules of arithmetic and algebra for writing equivalent forms of
expressions and solving equations and inequalities.
Students will understand numbers, measures, expressions, and inequalities can represent
mathematical situations and structures in many equivalent forms.
Students will be able to use properties of operations to generate equivalent expressions.
I can add and subtract linear expressions with rational coefficients.
I can explain simplification of algebraic expressions (e.g. explain why 3x + x = 4x, but (3x)(x) is 3 x
2 or why 3x =2y cannot be simplified further, but (3x)(2y) can be simplified).
I can draw representations for addition, subtraction, multiplication, and factoring of algebraic
expressions and connect these drawings to symbolic representations.
I can factor and expand linear expressions with rational coefficients.
I understand rewriting an expression in different forms when solving a mathematical problem
can shed light on the problem and show how quantities in it are related (e.g. a + 0.05a = 1.05a
means that an increase by 5% is the same as “multiply by 1.05”).
Students will be able to solve real-life and mathematical problems using numerical and algebraic
expressions and equations.
I can solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers.
I can apply properties of operations to calculate with numbers in any form.
In multi-step real-life problems, I can convert between rational number forms (fractions,
decimals, and percents) as appropriate.
I can convert between rational number forms (fractions, decimals, and percents) as appropriate
to solve multi-step real-life and mathematical problems.
In multi-step real-life problems, I can determine if and explain why an answer is reasonable
using estimation and mental math.
I can determine if and explain why an answer is reasonable using estimation and mental math
when solving multi-step real-life and mathematical problems.
I can use variables to represent quantities in a real-world or mathematical problem and
construct simple equations and inequalities to solve problems.
I can solve word problems leading to equations of the forms px + q = r and
p(x+q) = r, where p, q, and r are specific rational numbers.
I can compare an algebraic solution to an arithmetic solution and identify the sequence of the
operations used in each approach.
I can 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.
I can solve a multi-step inequality and graph the solution on a number line (including those
using the distributive property). I can solve a multi-step inequality using real-life examples and
interpret the solution in the context of the problem.
I can graph the solution set of an inequality and interpret it in the context of a real-life or
mathematical problem.
Geometry
Students will be able to draw, construct, and describe geometrical figures and describe the
relationships between them.
I can solve problems with scale drawings of geometric figures, compute actual lengths and area
from a scale drawing, and reproduce a scale drawing using a different scale.
I can draw (freehand, with a ruler and protractor, and with technology) geometric shapes with
given conditions (focus on triangles).
I can draw (freehand, with a ruler and protractor, and with technology) geometric shapes with
given conditions. Focus on constructing triangles from three measures of angles or sides.
I can describe the two-dimensional figures that result from slicing three-dimensional figures.
Students will be able to solve real-life and mathematical problems involving angle measure, area,
surface area, and volume.
I know the formula for area and circumference of a circle and can use them to solve problems.
I can give an informal derivation of the relationship between the circumference and area of a
circle.
I can use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
I can solve real-world and mathematical problems involving two-dimensional area (triangles,
quadrilaterals, polygons) and three-dimensional volume and surface area (cubes, right prisms).
I can 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.
Statistics and Probability
Students will understand that some questions can be answered by collecting, representing, and
analyzing data, and the question to be answered determines the data to be collected, how best to
collect it, and how best to represent it.
Students will understand that numerical measures can describe the center and spread of numerical
data.
Students will be able to use random sampling to draw inferences about a population.
I understand statistics can be used to gain information about a population by examining a
sample of the population.
I can make generalizations from statistical data about a population sample.
I can answer questions related to sample size and validity: for example, "How large is a large
enough sample size?", "What makes a sample size valid?"
I can make reasonable arguments about whether or not conclusions drawn from a sample are
valid.
I understand generalizations about a population are valid only if the sample is representative of
that population.
I understand that random sampling tends to produce representative samples and support valid
inferences.
I can use data from a random sample to make inferences about a population with an unknown
character of interest (e.g. We can estimate the mean word length in a book by randomly
sampling words from the book).
I can generate multiple samples of the same size to gauge the variations in estimates or
predictions.
Students will be able to draw informal comparative inferences about two populations.
I can compare the degree of visual overlap of two data plots. I can describe the visual difference
and explain what that difference means.
I can compare the degree of visual overlap of two data distributions and describe the visual
difference and explain what the difference means.
I can compare and draw informal inferences about two populations using measures of center
(median, mean) and measures of variation (range, quartiles, interquartile range). (dot plots, box
plots, histograms are applicable).
I can compare and draw informal inferences about two populations using measures of center
(median, mean) and measures of variation (range, quartiles, interquartile range) for data from
random samples.
Students will understand the likelihood of an event occurring can be described numerically and used
to make predictions.
Students will be able to investigate chance processes and develop, use, and evaluate probability
models.
I can explain why the numeric probability of an event must be between 0 and 1. I can explain
the likeliness of an event occurring based on probability near 0, 1/2, and 1.
I can explain why the numeric probability of an event must be between 0 and 1. I can explain
the likelihood of an event occurring based on probability near 0, 1/2, and 1 with an
understanding that larger numbers indicate greater likelihood.
I can predict the probability of a chance event by collecting data on the chance process that
produces it and predict the approximate relative frequency given the probability (e.g. when
rolling a number cube 600 times, predict that a 3 or 6 would be rolled about 200 times, but
probably not exactly 200 times).
I can develop a probability model and use it to find probabilities of events and compare
probabilities from the model to observed frequencies of the events. If the agreement between
the model and observed frequencies is not good, I can explain possible sources for the
discrepancy.
I can find the probability of compound events by constructing models, i.e., lists, tables, tree
diagrams, and simulation.
I can find the probability of compound events using organized lists, tables, tree diagrams, and
simulation.
I can design and use a simulation to generate frequencies for compound events.