California Mathematics Standards, 7th Grade
Chapter Three of the CA Mathematics Framework states in part:
Implementation of the standards will be challenging, especially during the early phases, when many students will not have the necessary foundational skills to master all of the expected gradelevel mathematics content.
In the chapter there is a chart which identifies the key standards and the standards that are in bold here are those key standards. The Framework goes on to state:
The five strands in the Mathematics Content Standards (Number Sense; Algebra and Functions; Measurement and Geometry; Statistics, Data Analysis, and Probability; and Mathematical Reasoning) organize information about the key standards for kindergarten through grade seven. It should be noted that the strand of mathematical reasoning is different from the other four strands. This strand, which is inherently embedded in each of the other strands, is fundamental in developing the basic skills and conceptual understanding for a solid mathematical foundation. It is important when looking at the standards to see the reasoning in all of them. Since this is the case, this chapter does not highlight key topics in the Mathematical Reasoning strand.
For consistency and to emphasize the importance of the Mathematical Reasoning standards, all of them have been highlighted here.
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
1.1 read, write and compare rational numbers in scientific notation (positive and
negative powers of 10), approximate numbers using scientific notation
Weeks 2122
1.2 add, subtract, multiply and divide rational numbers, integers, fractions and decimals
and take rational numbers to whole number powers
Mountain Bike  That's Sum Triangle  A Square w/ Round Corners  Paper Folding Problem  Save My Place  Square Bowling
1.3 convert fractions to decimals and percents and use these representations in estimation,
computation and applications
Weeks 2122
1.4 differentiate between rational and irrational numbers
Weeks 1314
1.5 know that every fraction is either a terminating or repeating decimal and be able
to convert terminating decimals into reduced fractions representations of a decimal
Weeks 1314  Weeks 2122
1.6 calculate percent of increases and decreases
Weeks 2728
1.7 solve problems that involve discounts, markups, commissions, profit and simple
compound interest with decimals and money
Weeks 2728
2.0 Students use exponents, powers, and roots and use exponents in working with fractions:
2.1 understand negative whole number exponents. Multiply and divide expressions involving
exponents with a common base greater or less than a negative integer
2.2 add and subtract fractions using factoring to find common denominators numbers
Weeks 1314
2.3 multiply, divide, and simplify fractions using exponent rules
Weeks 1314
2.4 use the inverse relationship between raising to a power and root extraction for
perfect square integers; and, for integers which are not square, determine without
a calculator, the two integers between which its square root lies, and explain why
Weeks 2526
2.5 understand the meaning of the absolute value of a number, interpret it as the
distance of the number from zero on a number line and determine the absolute value
of real numbers
Weeks 2526
Algebra and Functions
1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs:
1.1 use variables and appropriate operations to write an expression, equation, inequality,
or system of equations or inequalities which represent a verbal description (e.g.,
three less than a number, half as large as area A)
Hop, Skip and Jump
1.2 use order of operations correctly to evaluate algebraic expressions such as 3(2x+5)^2
Hop, Skip and Jump
1.3 simplify numerical expressions by applying properties of rational numbers (identity,
inverse, distributive, associative, commutative), and justify the process used
Fruit for Thought
1.4 use algebraic terminology correctly (e.g., variable, equation, term, coefficient,
inequality, expression, constant)
Weeks 34  Fruit for Thought
1.5 represent quantitative relationships graphically and interpret the meaning of
a specific part of a graph in terms of the situation represented by the graph
Leonardo da Vinci Problem
2.0 Students interpret and evaluate expressions involving integer powers and simple roots:
2.1 interpret positive whole number powers as repeated multiplication and negative
whole numbers as repeated division or multiplication by the multiplicative inverse.
Simplify and evaluate expressions that include exponents.
Hop, Skip and Jump
2.2 multiply and divide monomials; extend the process of taking powers and extracting
roots to monomials, when the latter results in a monomial with an integer exponent.
3.0 Students graph and interpret linear and some nonlinear functions:
3.1 graph functions of the form y = n x 2 and y = n x 3 and use in solving problems
3.2 plot the values from the volumes of a 3D shape for various values of its edge
lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height
and a varying length equilateral triangle base)
3.3 graph linear functions, noting that the vertical change (change in yvalue) per
unit horizontal change (change in xvalue) is always the same and know that the ratio
("rise over run") is called the slope of a graph
3.4 plot values of the quantities whose ratio is always the same (cost vs. number
of an item, feet vs. inches, circumference vs. diameter of a circle). Fit a line
to the plot and understand that the slope of the line equals the quantities.
Leonardo da Vinci Problem
4.0 Students solve simple linear equations and inequalities over the rational numbers:
4.1 solve twostep linear equations and inequalities in one variable over the rational
numbers, interpret the solution(s) in terms of the context from which they arose
and verify the reasonableness of the results
4.2 solve multistep problems involving rate, average speed, distance and time, or direct variation
Measurement and Geometry
1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
1.1 compare weights, capacities, geometric measures, times and temperatures within
and between measurement systems (e.g., miles per hour and feet per second, cubic
inches to cubic centimeters)
Nutty Excursion
1.2 construct and read scale drawings and models
Weeks 3132
1.3 use measures expressed as rates (e.g., speed, density) and measures expressed
as products (e.g., persondays) to solve problems, checking units of the solutions;
and use dimensional analysis to check the reasonableness of the answer
2.0 Students compute the perimeter, area and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
2.1 routinely use formulas for finding the perimeter and areas of basic twodimensional
figures and for the surface area and volume of basic threedimensional figures, including
rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and circular cylinders
Weeks 1516  Weeks 1920
2.2 estimate and compute the area of more complex or irregular two and threedimensional
figures by breaking them up into more basic geometric objects
Weeks 1516  Weeks 1920
2.3 compute the length of the perimeter, the surface area of the faces, and the volume
of a 3D object built from rectangular solids. They understand that when the lengths
of all dimensions are multiplied by a scale factor, the surface area is multiplied
by the square of the scale factor and the volume is multiplied by the cube of the scale
factor
Cube/Rectangular Prism Activity
2.4 relate the changes in measurement under change of scale to the units used (e.g.,
square inches, cubic feet) and to conversions between units (1 square foot = 12 square
inches, 1 cubic inch = 2.54 cubic centimeters)
Weeks 2324
3.0 Students know the Pythagorean Theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
3.1 identify and construct basic elements of geometric figures, (e.g., altitudes,
midpoints, diagonals, angle bisectors and perpendicular bisectors; and central angles,
radii, diameters and chords of circles) using compass and straightedge
Weeks 1516  Weeks 3132
3.2 understand and use coordinate graphs to plot simple figures, determine lengths
and areas related to them, and determine their image under translations and reflections
Pentamino +1 = Hexamino
3.3 know and understand the Pythagorean Theorem and use it to find the length of the
missing side of a right triangle and lengths of other line segments, and, in some
situations, empirically verify the Pythagorean Theorem by direct measurement
Weeks 3132
3.4 demonstrate an understanding of when two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the
two figures
Weeks 1516  Paper Folding Problem
3.5 construct twodimensional patterns for threedimensional models such as cylinders,
prisms and cones
Pentamino +1 = Hexamino
3.6 identify elements of threedimensional geometric objects (e.g., diagonals of rectangular solids) and how two or more objects are related in space (e.g., skew lines, the possible ways three planes could intersect)
Weeks 1516  Weeks 1920
Statistics, Data Analysis and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
1.1 know various forms of display for data sets, including a stemandleaf plot or
boxandwhisker plot; use them to display a single set of data or compare two sets
of data
Weeks 910
1.2 represent two numerical variables on a scatter plot and informally describe how
the data points are distributed and whether there is an apparent relationship between
the two variables (e.g., time spent on homework and grade level)
Leonardo da Vinci Problem  Weeks 910
1.3 understand the meaning of and be able to compute the minimum, the lower quartile,
the median, the upper quartile and the maximum of a data set
Weeks 910
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns
Hop, Skip and Jump  POWs throughout year  Mountain Bike  That's Sum Triangle  A Square w/ Round Corners  Pentamino +1 = Hexamino  Rock, Scissors, Paper  Paper Folding Problem  Save My Place
1.2 formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed
Hop, Skip and Jump  Fruit for Thought  POWs throughout year  Leonardo da Vinci Problem  Mountain Bike  That's Sum Triangle  Pentamino +1 = Hexamino  Save My Place
1.3 determine when and how to break a problem into simpler parts
Hop, Skip and Jump  POWs throughout year  Rock, Scissors, Paper
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 use estimation to verify the reasonableness of calculated results
Fruit for Thought  That's Sum Triangle  A Square w/ Round Corners
2.2 apply strategies and results from simpler problems to more complex problems
Nutty Excursion  That's Sum Triangle  Pentamino +1 = Hexamino  Rock, Scissors, Paper  Paper Folding Problem  Cube/Rectangular Prism Activity
2.3 estimate unknown quantities graphically and solve for them using logical reasoning, and arithmetic and algebraic techniques
Fruit for Thought  Leonardo da Vinci Problem
2.4 make and test conjectures using both inductive and deductive reasoning
Fruit for Thought  POWs throughout year  Leonardo da Vinci Problem  That's Sum Triangle  A Square w/ Round Corners  Pentamino +1 = Hexamino   Rock, Scissors, Paper  Paper Folding Problem  Save My Place  Cube/Rectangular Prism Activity
2.5 use a variety of methods such as words, numbers, symbols, charts, graphs, tables, diagrams and models to explain mathematical reasoning
POWs throughout year  Pentamino +1 = Hexamino  Cube/Rectangular Prism Activity
2.6 express the solution clearly and logically using appropriate mathematical notation and terms and clear language, and support solutions with evidence, in both verbal and symbolic work
Hop, Skip and Jump  Fruit for Thought  POWs throughout year  Leonardo da Vinci Problem  That's Sum Triangle  A Square w/ Round Corners  Rock, Scissors, Paper
2.7 indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy
Save My Place
2.8 make precise calculations and check the validity of the results from the context of the problem
Mountain Bike  A Square w/ Round Corners  Cube/Rectangular Prism Activity
3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:
3.1 evaluate the reasonableness of the solution in the context of the original situation
POWs throughout year
3.2 note method of deriving the solution and demonstrate conceptual understanding of the derivation by solving similar problems
Nutty Excursion  POWs throughout year
3.3 develop generalizations of the results obtained and the strategies used and extend them to new problem situations
Nutty Excursion  Pentamino +1 = Hexamino
