Kindergarten



|Grade |

|7 |

|Seventh Grade – Number, Number Sense and Operations Standard |

|Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and |

|pencil, technology-supported and mental methods. |

|Benchmarks |Grade level Indicators |Strategies/Resources |

|Use order of operations, including use |Meaning of Operations |4. properties – commutative |

|of parenthesis and exponents to solve |Use order of operations and properties to simplify numerical expressions |associative |

|multi-step problems, and verify |involving integers, fractions and decimals. (4) |distributive |

|and interpret the results. (E) | |properties of zero |

| | |Mnemonic Device: |

| | |Please Excuse My Dear Aunt Sally |

| | |Do operations in parentheses first |

| | |Rewrite numbers with exponents |

| |Computation and Estimation |Do all multiplication & division from left to right |

|Apply and explain the use of prime |Represent and solve problem situations that can be modeled by and solved |Do all addition & subtraction from left to right |

|factorizations, |using concepts of absolute value, exponents and square roots (for perfect| |

|common factors, and |squares). (9) |9. absolute value – distance from 0 on the number line |

|common multiples in problem situations. | | |

|(G) | | |

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| | |-6 -5 -4 -3 -2 -1 0 1 2 |

| | |absolute value of -5 is 5 |

| | |Helpful to have students memorize perfect squares up to 25. |

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| | |5. Use a number line to model adding and subtracting integers. |

|Use and analyze the steps in standard | | |

|and non-standard | |ex. -2 + (-3) = -5 |

|algorithms for | | |

|computing with fractions, decimals and | |l -3 l l |

|integers. (H) |Meaning of Operations |l l -2 l |

| |Explain the meaning and effect of adding, subtracting, multiplying and |l l l |

| |dividing integers such as, how adding two integers can result in a lesser|l l l |

| |value. (5) | |

| | |-5 -4 -3 -2 -1 0 1 2 3 |

| |Computation and Estimation |To develop rules for multiplication of integers show patterns by decreasing one factor |

| |Develop and analyze algorithms for computing with percents and integers, |continuously: |

| |and demonstrate fluency in their use. (8) |Ex:: To develop PosX Neg or Neg X Neg |

| | |+4 X +3 = +12 +4 X –2 = -8 |

|Use a variety of strategies, including | |+4 X +2 = +8 +3 X –2 = -6 |

|proportional reasoning, to estimate, | |+4 X +1 = +4 +2 X –2 = -4 |

|compute, solve and explain solutions to |Computation and Estimation |+4 X 0 = 0 +1 X –2 = -2 |

|problems involving integers, fractions, |Simplify numerical expressions involving integers and use integers to |+4 X –1 = -4 0 X –2 = 0 |

|decimals and percents. (I) |solve real-life problems. (6) |+4 X –2 = -8 -1 X –2 = +2 |

| | |hence… Pos X Neg = Neg and Neg X Neg = Pos |

| |Solve problems using the appropriate form of a rational number (fraction,| |

| |decimal or percent). (7) |⅓ - no decimal equivalent - use fraction in computation |

| | |Convert fraction to decimal to % interchangably: |

| |Represent and solve problem situations that can be modeled by and solved |Ex.: ½ = 0.5 = 50% |

| |using concepts of absolute value, exponents and square roots (for perfect| |

| |squares). (9) | |

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| |Note: There are instances where a grade-level indicator is linked to a | |

| |benchmark for a grade band that does not include the grade level of the | |

| |indicator. See Grade 8 for indicator 1, 2, 3, 5. | |

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|Seventh Grade – Measurement Standard |

|Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies |

|Benchmarks |Grade level Indicators |Strategies/Resources |

|Select appropriate units to measure |Measurement Units | |

|angles, circumference, surface area, |Select appropriate units for measuring derived measurements such as, |1. This is often found in textbooks under “ratios expressed in per unit form”. |

|mass and volume, using: |miles per hour, revolutions per minute. (1) | |

|U.S. customary units; such as, degrees, | | |

|square feet, pounds, and other units as | | |

|appropriate; | | |

|Metric units; such as, square meters, | | |

|kilograms and other units as | | |

|appropriate. (A) | | |

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|Convert units of length, area, volume, | | |

|mass and time within the same | | |

|measurement system. (B) |Measurement Units | |

| |Convert units of area and volume within the same measurement system using| |

| |proportional reasoning and a reference table when appropriate such as, |2. Use appropriate conversion factors. |

| |square feet to square yards, cubic meters to cubic centimeters. (2) |Helpful to teach cancellation of units |

| | |Ex 8 sq.ft. X 144 sq. in. = 1152 sq. in. |

| | |1 1 sq. ft. |

|Identify appropriate tools and apply |Use Measurement Techniques and Tools |The trapezoid and a congruent copy can be put together to form a parallelogram. Find the area |

|appropriate techniques for measuring |Use strategies to develop formulas for finding area of trapezoids and |of the parallelogram & divide by 2 to get the area of one trapezoid. |

|angles, perimeter or |volume of cylinders and prisms. (6) | |

|circumference and area of triangles, | | |

|quadrilaterals, circles, and composite |Develop strategies to find the area of composite shapes using the areas | |

|shapes, and surface area |of triangles, parallelograms, circles and sectors. (7) |b2 b1 |

|and volume of prisms and | | |

|cylinders. (C) |Note: There are instances when a grade-level indicator for one standard | |

| |is linked to a benchmark for a different standard. See also correlation |b1 b2 |

| |for Patterns, Functions and Algebra for indicator 6. | |

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|Select a tool and measure accurately to |Use Measurement Techniques and Tools |A = ½ (b1 + b2 ) |

|a specified level of precision. (D) |Estimate a measurement to a greater degree of precision than the tool | |

| |provides. (3) | |

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|Use problem solving | | |

|techniques and technology as needed to |Use Measurement Techniques and Tools | |

|solve problems involving length, weight,|Solve problems involving proportional relationships and scale factors | |

|perimeter, area, volume, time and |such as, scale models that require unit conversions within the same |4. map scale - 1” = 10 miles |

|temperature. (E) |measurement system. (4) | |

|Analyze and explain what happens to area| | |

|and perimeter or surface area and volume|Use Measurement Techniques and Tools | |

|when the dimensions of an object are |Describe what happens to the surface area and volume of a | |

|changed. (F) |three-dimensional object when the measurements of the object are changed | |

| |such as, length of sides are doubled. (9) | |

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|Understand and demonstrate the |Use Measurement Techniques and Tools | |

|independence of perimeter and area for |Understand the difference between surface area and volume, and | |

|two-dimensional shapes and of surface |demonstrate that two objects may have the same surface area, but | |

|area and volume for three-dimensional |different volumes or they may have the same volume, but different surface| |

|shapes. (G) |areas. (8) | |

| | |8. Build shapes with unifix cubes – find volume and surface area. |

| |Note: There are instances where a grade-level indicator is linked to a | |

| |benchmark for a grade band that does not include the grade level of the | |

| |indicator. See Grade 8 for indicator 5. | |

|Seventh Grade – Geometry and Spatial Sense Standard |

|Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of |

|geometric objects, and transformations to analyze mathematical situations and solve problems. |

|Benchmarks |Grade level Indicators |Strategies/Resources |

|Identify, describe and classify types of|Characteristics and Properties | |

|line pairs, angles, two-dimensional |Determine sufficient (not necessarily minimal) properties that define a |2. Possible to use Venn diagram to help students visualize these ideas. |

|figures and three-dimensional objects |specific two-dimensional figure or three-dimensional object. For | |

|using their properties. (D) |example: | |

| |a. determine when one set of figures is a subset of another such as, all | |

| |squares are rectangles; | |

| |b. develop a set of properties that eliminates all but the desired figure| |

| |such as, only squares are quadrilaterals with all sides congruent and all| |

| |angles congruent. (2) | |

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| | |1. Which figures are similar to the shaded rectangle? |

|Use proportions to express relationships|Characteristics and Properties |6 |

|among corresponding parts of similar |Use proportional reasoning to describe and express relationships between | |

|figures. (E) |parts and attributes of similar and congruent figures. (1) |4 |

| | |12 |

| |Spatial Relationships |6 |

| |Determine and use scale factors for similar figures to solve problems |4 3 |

| |using proportional reasoning. (6) |8 |

| | |4 3 |

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| | |6. To represent an inequality on a coordinate plane, graph it as though it was an equality |

|Describe and use the concepts of | |using a dashed line, then shade above or below to make the inequality true. |

|congruence, | | |

|similarity and symmetry to solve | |4. SSS HL Postulate |

|problems. (F) | |SAS |

| | |ASA |

| | |AAS |

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| |Characteristics and Properties |7. Degrees of rotation are usually measured in a counterclockwise direction. |

| |Determine necessary conditions for congruence of triangles. (4) | |

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| |Transformations and Symmetry | |

| |Identify the line and rotation symmetries of two-dimensional figures to | |

| |solve problems. (7) | |

|Describe and use properties of triangles|Characteristics and Properties | |

|to solve problems involving angle |Use and demonstrate understanding of the properties of triangles. For |3. a + b + c = 180º |

|measures and side lengths of right |example: | |

|triangles. (G) |a. use Pythagorean Theorem to solve problems involving right triangles; |To demonstrate understanding of this idea it is helpful to cut out a triangle, have students |

| |b. use triangle angle sum relationships to solve problems. (3) |“tear” the 3 angles from the triangle, and join the vertices at the common vertex to show that |

| | |the sum is 1800. |

| |Apply properties of congruent or similar triangles to solve problems | |

| |involving missing lengths and angle measures. (5) |[pic][pic] |

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| |Note: There are instances when a grade-level indicator for one standard | |

| |is linked to a benchmark for a different standard. See also correlation | |

| |for Patterns, Functions and Algebra for indicator 3. | |

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| |Transformations and Symmetry | |

| |Perform translations, reflections, rotations and dilations of | |

| |two-dimensional figures using a variety of methods (paper folding, |8. Ask, “How are rotations, reflections, and translations alike? How are they different? Give |

|Predict and describe results (size, |tracing, graph paper). (8) |specific examples and draw illustrations to support your response.” |

|position, orientation) of | | |

|transformations of two-dimensional | | |

|figures. (H) | | |

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| | |9. |

| |Visualization and Geometric Models |[pic] |

| |Draw representations of three-dimensional geometric objects from | |

| |different views. (9) | |

|Identify and draw three-dimensional | | |

|objects from different views (top, side,| | |

|front and perspective). (I) | | |

|Apply properties of equality and |Characteristics and Properties | |

|proportionality to solve problems |Use proportional reasoning to describe and express relationships between | |

|involving congruent or similar figures; |parts and attributes of similar and congruent figures. (1) | |

|such as, create a scale drawing. (J) | | |

| |Spatial Relationships | |

| |Determine and use scale factors for similar figures to solve problems | |

| |using proportional reasoning. (6) |6. When a figure is enlarged, the scale factor is greater than 1. |

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| | |A scale factor indicates the ratio of size of two similar figures. |

|Seventh Grade – Patterns, Functions and Algebra |

|Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such|

|as, tables, graphs and equations. |

|Benchmarks |Grade level Indicators |Strategies/Resources |

|Represent, analyze and generalize a |Use Patterns, Relations and Functions |1. function – where the value of one variable depends on the value of another variable |

|variety of patterns and functions with |Represent and analyze patterns, rules and functions with words, tables, | |

|tables, graphs, words and symbolic |graphs and simple variable expressions. (1) |f(x) = x + 1 |

|rules. (B) | | |

| |Generalize patterns by describing in words how to find the next term. (2)|“in words” this means “ a number plus one” |

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| | |as a “graph” note drawing : |

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| |Use Algebraic Representation |[pic] |

| |Recognize a variety of uses for variables such as, placeholder for an | |

|Use symbolic algebra to represent and |unknown quantity in an equation, generalization for a pattern, formula. |as a “table” note table: |

|explain mathematical relationships. (D) |(9) | |

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| | |[pic] |

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| | |as a “variable expression” : y = x + 1 |

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|Use rules and variables to describe | |3. Linear – Change in one quantity always results in a corresponding proportional change in |

|patterns, functions and other | |other variables. If placed on a graph, a linear question will result in a straight line. |

|relationships. (E) | | |

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| | |6. To represent an inequality on a coordinate plane, graph it as though it was an equality |

| | |using a dashed line, then shade above or below to make the inequality true. |

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|Use representations, such as, tables, |Use Patterns, Relations and Functions | |

|graphs and equations, to model |Recognize and explain when numerical patterns are linear or nonlinear | |

|situations and to solve problems, |progressions such as, 1,3,5,7...is linear and 1,3,4,8,16...is nonlinear. | |

|especially those that involve linear |(3) | |

|relationships. (F) | | |

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| |Use Algebraic Representation | |

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| |Represent linear equations by plotting points in the coordinate plane. | |

| |(5) | |

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| |Represent inequalities on a number line or a coordinate plane. (6) | |

|Write, simplify and |Use Patterns, Relations and Functions | |

|evaluate algebraic |Represent and analyze patterns, rules and functions with words, tables, | |

|expressions. (G) |graphs and simple variable expressions. (1) | |

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| |Use Algebraic Representation | |

| |Justify that two forms of an algebraic expression are equivalent, and | |

| |recognize when an expression is simplified such as, |7. combining like terms |

| |4m = m + m + m + m or a · 5 + 4 = 5a + 4. (7) | |

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|Solve linear equations | | |

|and inequalities symbolically, | | |

|graphically and numerically. (H) | |4, To create a “visual representation” use a balance beam. Put an object (“unknown quantity) |

| | |plus a 5 gram weight on one side and enough gram weights on the other side to balance this. To |

| |Use Algebraic Representation |determine the “unknown weight”, remove the 5-gram weight (so the “unknown” stands alone) and |

| |Create visual representations of equation-solving processes that model |remove 5 grams from the other side to balance. The “unknown” becomes the total of the remaining|

| |the use of inverse operations. (4) |weights. |

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|Explain how inverse operations are used | | |

|to solve linear equations. (I) | | |

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| |Use Algebraic Representation | |

| |Create visual representations of equation-solving processes that model | |

| |the use of inverse operations. (4) | |

|Use formulas in problem-solving |Use Algebraic Representation | |

|situations. (J) |Use formulas in problem-solving situations. (8) | |

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| |Use strategies to develop formulas for finding area of trapezoids and | |

| |volume of cylinders and prisms. (6) Measurement | |

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| |Use and demonstrate understanding of the properties of triangles. For | |

| |example: | |

|Graph linear equations and inequalities.|Use Pythagorean theorem to solve problems involving right triangles. | |

|(K) |Use triangle sum relationships to solve problems. | |

| |Geometry and Spatial Sense | |

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| |Use Algebraic Representation | |

| |Represent linear equations by plotting points in the coordinate plane. | |

|Analyze functional |(5) | |

|relationships, and explain how a change | | |

|in one |Represent inequalities on a number line or a coordinate plane. (6) | |

|quantity results in a change in the | | |

|other. (L) | | |

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| |Analyze Change | |

| |Analyze linear and simple nonlinear relationships to explain how a change| |

| |in one variable results in the change of another. (10) | |

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|Approximate and interpret rates of | |Ex.: y = x2 |

|change from graphical and numerical | |If x changes from 3 to 4, then y changes from 9 to 16. |

|data. (M) | | |

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| |Analyze Change | |

| |Use graphing calculators or computers to analyze change such as, | |

| |distance-time relationships. (11) | |

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|Seventh Grade – Data Analysis & Probability Standard |

|Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data. |

|Benchmarks |Grade level Indicators |Strategies/Resources |

|Read, create and use line graphs, |Data Collection |1. Include experiences with: |

|histograms, circle |Read, create and interpret box-and-whisker plots, stem-and-leaf plots, |-scatter plots |

|graphs, box and whisker plots, |and other types of graphs, when appropriate. (1) |-histograms |

|stem-and-leaf plots, and other | |-frequency tables |

|representations | | |

|when appropriate. (A) | |Note: This is the first time that box-and-whisker plots and stem-and-leaf plots are introduced |

| | |to students. |

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| | |Students need to master how to read, create and interpret box-and-whisker plots and |

| | |stem-and-leaf plots by the end of the school year. |

| |Statistical Methods | |

| |Construct opposing arguments based on analysis of the same data, using |Ask students to describe the steps in making a box-and-whisker plot and a stem-and-leaf plot. |

|Interpret data by looking for patterns |different graphical representations. (4) | |

|and relationships, draw and justify | |Use data to predict future outcomes. |

|conclusions, and answer related | | |

|questions. (B) | | |

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| |Statistical Methods | |

| |Compare data from two or more samples to determine how sample selection | |

|Compare increasingly complex displays of|can influence results. (5) | |

|data, such as, multiple sets of data on | | |

|the same graph. (D) | | |

|Collect, organize, display, and |Data Collection | |

|interpret data for a specific purpose or|Analyze how decisions about graphing affect the graphical representation | |

|need. (E) |such as, scale, size of classes in a histogram, number of categories in a| |

| |circle graph. (2) | |

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| |Statistical Methods | |

| |Analyze a set of data by using and comparing combinations of measures of | |

|Determine and use the range, mean, |center (mean, mode, median) and measures of spread (range, quartile, |3. quartile– separation of data into four equal parts |

|median and mode to analyze and compare |interquartile range), and describe how the inclusion or exclusion of | |

|data, and explain what each |outliers effect those measures. (3) |interquartile range – the difference between the minimum value of the data |

|indicates about the data. (F) | | |

| | |outliers – data that is much greater or less than the other data |

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| | |Ask student to explain how to determine if a number is an outlier. |

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| |Data Collection | |

| |Analyze how decisions about graphing affect the graphical representation | |

|Evaluate conjectures and predictions |such as scale, size of classes in a histogram, number of categories in a | |

|based upon data presented in tables and |circle graph. (2) |6. Data can be represented so that it is misleading to the consumer. Common misleading data |

|graphs, and identify misuses of | |presentations may include: irregular intervals in the data, a break in one of the axis |

|statistical data and displays. (G) |Identify misuses of statistical data in articles, advertisements, and |presented, an axis may not start at zero, use of an inappropriate scale. Data may be displayed |

| |other media. (6) |in such a way as to distort the information in order to persuade the consumer in a certain way. |

|Describe the probability of an event |Probability |7. Probability of events can be expressed as a ratio, fraction or decimal. |

|using ratios, including fractional |Compute probabilities of compound events such as multiple coin tosses or | |

|notation. (I) |multiple rolls of number cubes, using such methods as organized lists, | |

| |tree diagrams and area models. (7) | |

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|Make and justify | |8. As the number of experiments is increased to test a prediction, the probability will move |

|predictions based on | |closer to the theoretical probability. |

|experimental and theoretical | | |

|probabilities. (K) | |theoretical probability – |

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| | |# of favorable outcomes |

| | |total # of possible outcomes |

| |Probability | |

| |Make predictions based on theoretical probabilities, design and conduct | |

| |an experiment to test the predictions, compare actual results to | |

| |predicted results, and explain differences. (8) | |

|Seventh Grade – Mathematical Processes Standard |

|Students use mathematical processes and knowledge to solve problems. Students apply problem-solving and decision-making techniques, and communicate mathematical ideas. The benchmarks for mathematical |

|processes articulate what students should demonstrate in problem solving, representation, communication, reasoning and connections at key points in their mathematics program. |

|Benchmarks |Grade level Indicators |Strategies/Resources |

|Clarify problem-solving situation and | |Problem-Solving Strategies |

|identify potential solution processes; | |choose a method of computation |

|such as, consider different strategies | |draw a diagram |

|and approaches to a problem, restate | |guess and check |

|problem from various perspectives. (A) | |look for a pattern |

| | |make a list |

|Apply and adapt problem-solving | |make a model |

|strategies to solve a variety of |Specific grade-level indicators have not been included for the |solve a simple problem |

|problems, including unfamiliar and |mathematical processes standard because content and processes should be |use logical reasoning |

|non-routine problem situations. (B) |interconnected at the indicator level. Therefore, mathematical processes|work backwards |

| |have been embedded within the grade-level indicators for the five content|eliminate possibilities |

|Use more than one strategy to solve a |standards. |reasonable answers |

|problem, and recognize there are | | |

|advantages associated with various | |compare: to determine how two things are alike and/or different; the common/critical attributes |

|methods. (C) | |must be identified. |

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|Recognize whether an estimate or an | |Compare is involved in ALL of the following: |

|exact solution is appropriate for a | | |

|given problem situation. (D) | |analyze: to investigate by breaking it down so as to more clearly understand the impact to the |

| | |situation |

|Use deductive thinking to construct | | |

|informal arguments to support reasoning | |describe: to analyze into its parts but less detailed than explain |

|and to justify solutions to problems. | | |

|(E) | |determine: to reach a decision after a thorough investigation; to find the cause of and then |

| | |to solve or set limits to a situation |

|Use inductive thinking to generalize a | | |

|pattern of observations for particular | |identify: to show or prove the sameness of |

|cases, make conjectures, and provide | | |

|supporting arguments for conjectures. | |interpret: a student must 1st analyze and then make an inference; this is more subjective than |

|(F) | |an evaluation |

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| | |predict: to state what one believes will happen (based on data) |

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| | |recognize: to examine closely & identify the common/critical attributes |

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| | |Other Stated Verbs in the Indicators: |

| | |demonstrated apply convert |

| | |estimate use perform |

| | |simplify draw construct |

| | |solve generalize compute |

| | |develop create select |

| | |represent justify |

|Relate mathematical ideas to one another| | |

|and to other content areas; such as, use| | |

|area models for adding fractions, | | |

|interpret graphs in reading, science and| | |

|social studies. (G) | | |

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|Use representations to organize and | | |

|communicate mathematical thinking and |Specific grade-level indicators have not been included for the | |

|problem solutions. (H) |mathematical processes standard because content and processes should be | |

| |interconnected at the indicator level. Therefore, mathematical processes| |

|Select, apply, and translate among |have been embedded within the grade-level indicators for the five content| |

|mathematical representations to solve |standards. | |

|problems; such as, representing a number| | |

|as a fraction, decimal or percent as | | |

|appropriate for a problem. (I) | | |

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|Communicate mathematical thinking to | | |

|others and analyze the mathematical | | |

|thinking and strategies of others. (J) | | |

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|Recognize and use mathematical language | | |

|and symbols when reading, writing and | | |

|conversing with others. (K) | | |

|Seventh Grade Student Vocabulary |

|Number, Number Sense and Operations |Measurement Standard |Geometry and Spatial Sense Standard |Patterns, Functions and Algebra Standard |Data Analysis & Probability Standard |

|Standard | | | | |

|properties |proportional reasoning |conditions |simple variable |box-and-whisker plots |

|integers |reference table |rotation symmetries |expressions |stem-and-leaf plots |

|absolute value |square feet |Pythagorean Theorem |linear/nonlinear |measures of spread- |

|square roots |square yards |triangle angle sum |progressions |quartile |

|appropriate form of a |cubic meters |relationships |points in the |interquartile |

|rational number |cubic centimeters |*MEPCV |coordinate plane |outliers (inclusion or |

|*MEPCV |area of trapezoids | |simplified |exclusion of) |

| |volume of cylinders/ | |inverse operations |misuses of statistical data |

| |prisms | |distance-time |probabilities |

| |composite shapes | |relationships |compound events |

| |area of triangles/ | |*MEPCV |tree diagrams |

| |parallelograms | | |area models |

| |proportional relationships | | |*MEPCV |

| |scale factors | | | |

| |unit conversions | | | |

| |*MEPCV | | | |

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|*MEPCV – Maintain and Enhance Previous Content Vocabulary – Previous Content Vocabulary is now enhanced to the current grade appropriate indicators. |

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B

Ohio Academic Content Standards

Mathematics Curriculum Guide

D

C

A

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