PROCESS STRANDS |
- Problem solving
- Reasoning and Proof
- Communication
- Connections
- Representation
|
| Problem solving |
| 7.PS.1 Explore, examine, and make observations about a social problem or mathematical situation |
| 7.PS.2 Understand that some ways of representing a problem are more helpful than others |
| 7.PS.3 Interpret information correctly, identify the problem, and generate possible solutions |
| 7.PS.4 Act out or model with manipulatives activities involving mathematical content from literature |
| 7.PS.5 Formulate problems and solutions from everyday situations |
| 7.PS.6 Translate from a picture/diagram to a numeric expression |
| 7.PS.7 Represent problem solving situations in oral, written, concrete, pictorial, and graphical forms |
| 7.PS.8 Select an appropriate representation of a problem |
| 7.PS.9 Use trial and error to solve problems |
| 7.PS.10 Use process of elimination to solve problems |
| 7.PS.11 Make pictures/diagrams of problems |
| 7.PS.12 Use physical objects to model problems |
| 7.PS.13 Work in collaboration with others to solve problems |
| .PS.14 Make organized lists to solve numerical problems |
| 7.PS.15 Make charts to solve numerical problems |
| 7.PS.16 Analyze problems by identifying relationships |
| 7.PS.17 Analyze problems by identifying relevant versus irrelevant information |
| 7.PS.18 Analyze problems by observing patterns |
| 7.PS.19 State a problem in their own words |
| 7.PS.20 Determine what information is needed to solve a problem |
| 7.PS.21 Discuss with peers to understand a problem situation |
| 7.PS.22 Discuss the efficiency of different representations of a problem |
| 7.PS.23 Verify results of a problem |
| 7.PS.24 Recognize invalid approaches |
| 7.PS.25 Determine whether a solution is reasonable in the context of the original problem |
|
|
| Reasoning and Proof |
| 7.RP.1 Use representations to support mathematical ideas |
| 7.RP.2 Determine whether a mathematical statement is true or false and explain why |
| 7.RP.3 Investigate the use of knowledgeable guessing by generalizing mathematical ideas |
| 7.RP.4 Make conjectures from a variety of representations |
| 7.RP.5 Justify general claims or conjectures, using manipulatives, models, and expressions |
| 7.RP.6 Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms
|
| 7.RP.7 Discuss, listen, and make comments that support or reject claims made by other students |
| 7.RP.8 Support an argument by trying many cases |
|
|
| Communication |
| 7.CM.1 Understand and explain how to organize their thought process |
| 7.CM.2 Verbally explain their rationale for strategy selection |
| 7.CM.3 Provide reasoning both in written and verbal form |
| 7.CM.4 Organize and accurately label work |
| 7.CM.5 Share organized mathematical ideas through the manipulation of objects, drawings, pictures, charts, graphs,
tables, diagrams, models, symbols, and expressions in written and verbal form |
| 7.CM.6 Answer clarifying questions from others |
| 7.CM.7 Listen for understanding of mathematical solutions shared by other students |
| 7.CM.8 Consider strategies used and solutions found in relation to their own work |
| 7.CM.9 Increase their use of mathematical vocabulary and language when communicating with others |
| 7.CM.10 Describe objects, relationships, solutions and rationale using appropriate vocabulary |
| 7.CM.11 Decode and comprehend mathematical visuals and symbols to construct meaning |
|
| Connections |
| 7.CN.1 Recognize, understand, and make connections in their everyday experiences to mathematical ideas |
| 7.CN.2 Compare and contrast mathematical ideas |
| 7.CN.3 Connect and apply mathematical information to solve problems |
| 7.CN.4 Understand multiple representations and how they are related |
| 7.CN.5 Model situations with objects and representations and be able to make observations |
| 7.CN.6 Recognize the presence of mathematics in their daily lives |
| 7.CN.7 Apply mathematics to solve problems that develop outside of mathematics |
| 7.CN.8 Recognize and apply mathematics to other disciplines |
|
| Representation |
| 7.R.1 Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as
representations |
| 7.R.2 Share mental images of mathematical ideas and understandings |
| 7.R.3 Recognize and use external mathematical representations |
| 7.R.4 Use standard and nonstandard representations with accuracy and detail |
| 7.R.5 Understand similarities and differences in representations |
| 7.R.6 Connect mathematical representations with problem solving |
| 7.R.7 Construct effective representations to solve problems |
| 7.R.8 Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in
a tree) |
| 7.R.9 Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a
field trip) |
| 7.R.10 Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd
and even number problems) |
| The Process Strands highlight ways of acquiring and using content knowledge. Though the Process Strands are not
individually covered, students are required to problem solve, reason, and apply their knowledge throughout. |
|
|
CONTENT STRANDS |
Number Sense and Operations Strand |
| Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number
systems. |
| Number Systems |
| 7.N.1 - Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers,
rational numbers, and irrational numbers) |
| 7.N.2 - Recognize the difference between rational and irrational numbers (e.g., explore different approximations of |
| 7.N.3 - Place rational and irrational numbers (approximations) on a number line and justify the placement of them |
| 7.N.4 - Develop the laws of exponents for multiplication and division |
| 7.N.5 - Write numbers in scientific notation |
| 7.N.6 - Translate numbers from scientific notation into standard form |
| 7.N.7 - Compare numbers written in scientific notation |
|
| Number Theory |
| 7.N.8 - Find the common factors and greatest common factor of two or more numbers |
| 7.N.9 - Determine multiples and least common multiple of two or more numbers |
| 7.N.10 - Determine the prime factorization of a given number and write in exponential form |
| |
| Students will understand meanings of operations and procedures, and how they relate to one another. |
| Operations |
| 7.N.11 - Simplify expressions using order of operations (Note: Expressions may include absolute value and/or
integral exponents greater than 0.) |
| 7.N.12 - Add, subtract, multiply, and divide integers |
| 7.N.13 - Add and subtract two integers (with and without the use of a number line) |
| 7.N.14 - Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to
fractions and decimals (e.g., 10-2 = .01 = 1/100) |
| 7.N.15 - Recognize and state the value of the square root of a perfect square (up to 225) |
| 7.N.16 - Determine the square root of non-perfect squares using a calculator |
| 7.N.17 - Classify irrational numbers as non-repeating/non-terminating decimals |
|
| Students will compute accurately and make reasonable estimates. |
| Estimation |
| 7.N.18 - Identify the two consecutive whole numbers between which the square root of a non-perfect square whole
number less than 225 lies (with and without the use of a number line) |
| 7.N.19 - Justify the reasonableness of answers using estimation |
|
|
Algebra Strand |
| Students will represent and analyze algebraically a wide variety of problem solving situations. |
| Variables and Expressions |
| 7.A.1 - Translate two-step verbal expressions into algebraic expressions |
| Students will perform algebraic procedures accurately. |
| Variables and Expressions |
| 7.A.2 - Add and subtract monomials with exponents of one |
| 7.A.3 - Identify a polynomial as an algebraic expression containing one or more terms |
|
| Students will perform algebraic procedures accurately. |
| Equations and Inequalities |
| 7.A.4 - Solve multi-step equations by combining like terms, using the distributive property, or moving variables to
one side of the equation |
| 7.A.5 - Solve one-step inequalities (positive coefficients only) |
| 7.A.6 - Evaluate formulas for given input values (surface area, rate, and density problems) |
| |
| Students will recognize, use, and represent algebraically patterns, relations, and functions. |
| Patterns, Relations, and Functions |
| 7.A.7 - Draw the graphic representation of a pattern from an equation or from a table of data |
| 7.A.8 - Create algebraic patterns using charts/tables, graphs, equations, and expressions
|
| 7.A.9 - Build a pattern to develop a rule for determining the sum of the interior angles of polygons |
| 7.A.10 - Write an equation to represent a function from a table of values |
Geometry Strand |
| Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric
shapes. |
| Shapes |
| 7.G.1 - Calculate the radius or diameter, given the circumference or area of a circle |
| 7.G.2 - Calculate the volume of prisms and cylinders, using a given formula and a calculator |
| 7.G.3 - Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms,
cylinders, cones, and pyramids) |
| 7.G.4 - Determine the surface area of prisms and cylinders, using a calculator and a variety of methods |
|
| Students will identify and justify geometric relationships, formally and informally. |
| Geometric Relationships |
| 7.G.5 - Identify the right angle, hypotenuse, and legs of a right triangle |
| 7.G.6 - Explore the relationship between the lengths of the three sides of a right triangle to develop the
Pythagorean Theorem |
| 7.G.7 - Find a missing angle when given angles of a quadrilateral |
| 7.G.8 - Use the Pythagorean Theorem to determine the unknown length of a side of a right triangle |
| 7.G.9 - Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a
calculator |
| |
| Students will apply coordinate geometry to analyze problem solving situations. |
| Coordinate Geometry |
| 7.G.10 - Graph the solution set of an inequality (positive coefficients only) on a number line |
Measurement Strand |
| Students will determine what can be measured and how, using appropriate methods and formulas. |
| Units of Measurement |
| 7.M.1 - Calculate distance using a map scale |
| 7.M.2 - Convert capacities and volumes within a given system |
| 7.M.3 - Identify customary and metric units of mass |
| 7.M.4 - Convert mass within a given system |
| 7.M.5 - Calculate unit price using proportions |
| 7.M.6 - Compare unit prices |
| 7.M.7 - Convert money between different currencies with the use of an exchange rate table and a calculator |
| 7.M.8 - Draw central angles in a given circle using a protractor (circle graphs) |
|
| Tools and Methods |
| 7.M.9 - Determine the tool and technique to measure with an appropriate level of precision: mass |
|
| Students will develop strategies for estimating measurements. |
| Estimation |
| 7.M.10 - Identify the relationships between relative error and magnitude when dealing with large numbers (e.g.,
money, population) |
| 7.M.11 - Estimate surface area |
| 7.M.12 - Determine personal references for customary /metric units of mass |
| 7.M.13 - Justify the reasonableness of the mass of an object |
Statistics and Probability Strand |
| Students will collect, organize, display, and analyze data. |
| Collection of Data |
| 7.S.1 - Identify and collect data using a variety of methods |
| Organization and Display of Data |
| 7.S.2 - Display data in a circle graph |
| 7.S.3 - Convert raw data into double bar graphs and double line graphs |
|
| Analysis of Data |
| 7.S.4 - Calculate the range for a given set of data |
| 7.S.5 - Select the appropriate measure of central tendency |
| 7.S.6 - Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph,
double line/bar graphs or circle graph) |
|
| Students will make predictions that are based upon data analysis. |
| Predictions from Data |
| 7.S.7 - Identify and explain misleading statistics and graphs |
|
| Students will understand and apply concepts of probability. |
| Probability |
| 7.S.8 - Interpret data to provide the basis for predictions and to establish experimental probabilities |
| 7.S.9 - Determine the validity of sampling methods to predict outcomes |
| 7.S.10 - Predict the outcome of an experiment |
| 7.S.11 - Design and conduct an experiment to test predictions |
| 7.S.12 - Compare actual results to predicted results |
