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Aligning NJ Grade 7 Mathematics Curricula to the Common Core State Standards NEW OLD Common Core State Standards (CCSS) How is it related to 2008 NJ Core Curriculum Content If not related, where adopted June 16, 2010 the old content? Standards (NJ cccs) did old content go? Ratios and Proportional Relationships 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.1. Compute unit rates associated This CCSS moves Although possibly with ratios of fractions, including ratios of “rates” from grade 8 new in many 7th lengths, areas and other quantities (4.1.8.A.3) to grade 7. grade classes, the measured in like or different units. For It also moves content may have example, if a person walks 1/2 mile in each “compound NEW (to grade 7) been included in 1/4 hour, compute the unit rate as the measurement units” others as “a variety from grade 8 complex fraction 1/2/1/4 miles per hour, of situations” under (4.2.8.D.6) to grade 7. equivalently 2 miles per hour. NJ cccs 4.1.7.A.3. 7.RP.2. Recognize and represent Related, but the 4.1.7.A.3. Understand and use ratios, proportional relationships between new CCSS contain proportions, and percents (including quantities. more specific percents greater than 100 and less than 1) in a variety of situations. expectations a. Decide whether two quantities are in a 4.2.7.C.1. Use coordinates in four proportional relationship, e.g., by regarding quadrants to represent geometric testing for equivalent ratios in a table or proportional concepts. graphing on a coordinate plane and relationships. 4.3.7 B.1. Graph functions, and The new CCSS observing whether the graph is a understand and describe their general postpone straight line through the origin. behavior. introducing the Equations involving two variables concept of a 4.3.7.C.1. Analyze functional function until relationships to explain how a change in grade 8. one quantity can result in a change in another, using pictures, graphs, charts, and equations. b. Identify the constant of proportionality Related, but the 4.3.7.A.1. Recognize, describe, extend, (unit rate) in tables, graphs, equations, new CCSS move and create patterns involving whole diagrams, and verbal descriptions of “rates” from grade numbers, rational numbers, and integers. proportional relationships. 8 to grade 7. Descriptions using tables, verbal and symbolic rules, graphs, simple equations or expressions Finite and infinite sequences Without the formal terminology, sequences Generating sequences by using are introduced in grades calculators to repeatedly apply a 4 and 5 in the CCSS. formula The formal study of arithmetic and geometric sequences is postponed until HS. c. Represent proportional relationships by Although the new 4.3.7.C.2. Use patterns, relations, equations. For example, if total cost t CCSS postpone symbolic algebra, and linear functions to is proportional to the number n of items functions until model situations. purchased at a constant price p, the grade 8, the use of Using manipulatives, tables, graphs, relationship between the total cost and symbolic algebra verbal rules, algebraic expressions/ the number of items can be expressed (equations) to equations/inequalities as t = pn. model (represent) Growth situations, such as population Growth functions and relationships is growth and compound interest, using the formal study of recursive (e.g., NOW-NEXT) formulas arithmetic and explicit in bullet 1 of geometric sequences NJ cccs 4.3.7.C.2. (cf. science standards and social are postponed until HS. studies standards) d. Explain what a point (x, y) on the graph The new CCSS of a proportional relationship means in move “rates” from terms of the situation, with special grade 8 to NEW (to grade 7) attention to the points (0, 0) and (1, r) grade 7. where r is the unit rate. 7.RP.3. Use proportional relationships to Related, but the new [“Understand and use ratios, proportions, solve multistep ratio and percent problems. CCSS contain more and percents (including percents greater Examples: simple interest, tax, markups and specific expectations than 100 and less than 1) in a variety of markdowns, gratuities and commissions, fees, regarding proportional situations” from 4.1.7.A.3 above.] percent increase and decrease, percent error. relationships. Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later grades, or because it is not included at any grade in the new CCSS. 1 The Number System 7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.NS.1. Apply and extend previous Similar, but the 4.1.7.A.1. Extend understanding of the understandings of addition and subtraction new CCSS contain number system by constructing to add and subtract rational numbers; more specific meanings for the following: represent addition and subtraction on a expectations Rational numbers Exponents get more horizontal or vertical number line diagram. Percents attention in grades 6 regarding Whole numbers with exponents and HS in the CCSS. operations a. Describe situations in which opposite 4.1.7.B.1. Use and explain procedures Also linked to quantities combine to make 0. For involving negative for per-forming calculations with integers CCSS 7.NS.2 example, a hydrogen atom has 0 numbers. and all number types named above below for charge because its two constituents are (Rational numbers, Percents, Whole multiplication and oppositely charged. numbers with exponents) with: b. Understand p + q as the number Pencil-and-paper division located a distance |q| from p, in the Mental math positive or negative direction depending Calculator on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational 4.3.7 D.1. Use graphing techniques on a In Transition: numbers as adding the additive number line. Students coming to inverse, p – q = p + (–q). Show that the Absolute value seventh grade from classes in which the distance between two rational numbers Arithmetic operations represented by 2008 standards were on the number line is the absolute vectors (arrows) used may not yet have value of their difference, and apply this (e.g., “-3 + 6” is “left 3, right 6”) been introduced to principle in real-world contexts. absolute value. Until the curriculum change has been implemented at grade 6, teachers will need to continue introducing this concept at grade 7. d. Apply properties of operations as 4.3.7.D.4. Understand and apply the strategies to add and subtract rational properties of operations, numbers, numbers. equations, and inequalities. Additive inverse Multiplicative inverse 7.NS.2. Apply and extend previous Related, but the 4.1.7.B.1. Use and explain procedures Also linked to understandings of multiplication and new CCSS contain for performing calculations with integers CCSS 7.NS.1 division and of fractions to multiply and more specific and all number types named above above for addition divide rational numbers. (Rational numbers, Percents, Whole expectations and subtraction a. Understand that multiplication is numbers with exponents) with: extended from fractions to rational numbers regarding Pencil-and-paper by requiring that operations continue to operations Mental math satisfy the properties of operations, involving negative Calculator particularly the distributive property, leading numbers. to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as Related but much 4.3.7.D.4. Understand and apply the Also linked to the strategies to multiply and divide rational more specific properties of operations, numbers, new CCSS 7.EE.1 numbers. expectation equations, and inequalities. above Additive inverse Multiplicative inverse Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later grades, or because it is not included at any grade in the new CCSS. 2 d. Convert a rational number to a decimal Similar 4.1.7.A.6. Understand that all fractions using long division; know that the decimal can be represented as repeating or form of a rational number terminates in 0s terminating decimals. or eventually repeats. From the introduction to 4.1.7.A.5. Use whole numbers, While not explicitly Grade 7, critical area fractions, decimals, and percents to articulated in the (2): “Students develop represent equivalent forms of the same CCSS for grade 7, a unified understanding these expectations of number, recognizing number. from the 2008 NJ cccs fractions, decimals (that are part of the have a finite or a “understanding of repeating decimal 4.1.7.A.2. Demonstrate a sense of the representation), and number” as explained percents as different relative magnitudes of numbers (as in the CCSS Grade 7 representations of applied to rational numbers and introduction. rational numbers.” percents). 4.1.7.A.4. Compare and order numbers Compare & order are of all named types not explicitly articulated Rational numbers in the grade 7 CCSS. Percents Exponents get more Whole numbers with exponents attention in grades 6 and HS in the CCSS. 7.NS.3. Solve real-world and mathematical Similar, except 4.5.7.A.2. Solve problems that arise in problems involving the four operations with that manipulating mathematics and in other contexts. rational numbers. [“Computations with complex fractions Open-ended problems rational numbers extend the rules for is new at this Non-routine problems manipulating fractions to complex grade level. Problems with multiple solutions fractions.” (Footnote to Common Core Problems that can be solved in several State Standards)] ways [An application of CCSS 7.NS.1 and 7.NS.2 (NJ cccs 4.1.7.B.1) above] Expressions and Equations 7.EE 4.3.7.D.3. Create, evaluate, and simplify In CCSS, this is algebraic expressions involving variables. grade 6 content. Order of operations, including In Transition: appropriate use of parentheses Students coming to seventh grade from Substitution of a number for a classes in which the variable 2008 standards were used may not yet have mastered this content. Until the curriculum change has been implemented at grade 6, teachers will need to continue including this material at grade 7. Use properties of operations to generate equivalent expressions. 7.EE.1. Apply properties of operations as Related but more 4.3.7.D.4. Understand and apply the Also linked to the strategies to add, subtract, factor, and specific expectation properties of operations, numbers, new CCSS 7.NS.1d expand linear expressions with rational that goes beyond the equations, and inequalities. and 7.NS.2c above coefficients. 2008 NJ cccs for this Additive inverse grade level. Multiplicative inverse 7.EE.2. Understand that rewriting an Instructional 4.5.7.E.2. Select, apply, and translate expression in different forms in a problem guidance beyond the among mathematical representations to context can shed light on the problem and level of specificity solve problems. how the quantities in it are related. For provided in the example, a + 0.05a = 1.05a means that NJ cccs “increase by 5%” is the same as “multiply by 1.05.” 4.1.7 B.2. Use exponentiation to find CCSS move this from whole number powers of numbers. grade 7 to grade 6 (6.EE.1 & 2c). In Transition: Students coming to seventh grade from classes in which the 2008 standards were used may not yet have mastered this content. Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later grades, or because it is not included at any grade in the new CCSS. 3 Until the curriculum change has been implemented at grade 6, teachers will need to continue including this material at grade 7. 4.1.7 B.3. Understand and apply the In CCSS, this is standard algebraic order of operations, grade 6 content including appropriate use of parentheses. (6.EE.1 & 6.EE.2c). [Also including exponents, from NJ cccs In Transition: 4.1.7.A.1 and 4.1.7.B.2] Students coming to seventh grade from classes in which the 2008 standards were used may not yet have mastered this content. Until the curriculum change has been implemented at grade 6, teachers will need to continue including this material at grade 7. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 7.EE.3. Solve multi-step real-life and Similar but more 4.5.7.A.2. Solve problems that arise in mathematical problems posed with positive specific mathematics and in other contexts. and negative rational numbers in any form expectation Open-ended problems (whole numbers, fractions, and decimals), Non-routine problems using tools strategically. Apply properties of Problems with multiple solutions operations to calculate with numbers in any Problems that can be solved in several form; convert between forms as appropriate; ways and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary 4.1.7.C.1. Use equivalent an hour, or $2.50, for a new salary of representations of numbers such as $27.50. If you want to place a towel bar 9 fractions, decimals, and percents to 3/4 inches long in the center of a door that facilitate estimation. is 27 1/2 inches wide, you will need to 4.5.7.D.4. Rely on reasoning, rather than place the bar about 9 inches from each answer keys, teachers, or peers, to edge; this estimate can be used as a check check the correctness of their problem on the exact computation. solutions. 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to Somewhat similar, 4.3.7.D.2. Solve simple linear equations equations of the form px + q = r and p(x although CCSS informally and graphically. + q) = r, where p, q, and r are specific move fluent use of Multi-step, integer coefficients only rational numbers. Solve equations of algebraic methods (although answers may not be these forms fluently. Compare an from grade 8 to integers) algebraic solution to an arithmetic grade 7. Note also Using paper-and-pencil, calculators, solution, identifying the sequence of the that the new CCSS graphing calculators, spreadsheets, operations used in each approach. For are more limiting in and other technology example, the perimeter of a rectangle is terms of types of 54 cm. Its length is 6 cm. What is its equations to be width? solved. b. Solve word problems leading to Somewhat related 4.3.7.D.4. Understand and apply the Also linked to the inequalities of the form px + q > r or px + but much more properties of operations, numbers, new CCSS 7.EE.1, q < r, where p, q, and r are specific specific expectation. equations, and inequalities. 7.NS.1d, and rational numbers. Graph the solution set CCSS move the Additive inverse 7.NS.2c above of the inequality and interpret it in the solving of linear Multiplicative inverse context of the problem. For example: As inequalities from a salesperson, you are paid $50 per week grade 8 (4.3.8.D.3) plus $3 per sale. This week you want your to grade 7. pay to be at least $100. Write an inequality for the number of sales you need to NEW (to grade 7) make, and describe the solutions. Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later grades, or because it is not included at any grade in the new CCSS. 4 Geometry 7.G Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.1. Solve problems involving scale Similar although 4.2.7 A.2. Understand and apply the 3-D objects are drawings of geometric figures, including slightly more concept of similarity. not explicitly computing actual lengths and areas from a specific Using proportions to find missing measures included at this scale drawing and reproducing a scale expectation Scale drawings grade level. drawing at a different scale. Models of 3D objects 7.G.2. Draw (freehand, with ruler and Instructional 4.2.7.A.3. Use logic and reasoning to protractor, and with technology) geometric guidance beyond make and support conjectures about shapes with given conditions. Focus on the level of geometric objects. [Related to constructing triangles from three measures specificity provided Mathematical Process No. 3 description, of angles or sides, noticing when the that students “make conjectures and build a in the NJ cccs conditions determine a unique triangle, logical progression of statements to explore more than one triangle, or no triangle. the truth of their conjectures.”] 7.G.3. Describe the two-dimensional The new CCSS figures that result from slicing three- move this from grade dimensional figures, as in plane sections of 8 (NJ cccs 4.2.8.A.1) NEW (to grade 7) right rectangular prisms and right to grade 7. rectangular pyramids. 4.2.7.A.1. Understand and apply In the CCSS, properties of polygons. Identification and classification of two- Quadrilaterals, including squares, dimensional figures, rectangles, parallelograms, including quadrilaterals, trapezoids, rhombi are in grade 5 (5.G.3 Regular polygons and 4). Applying those properties is not explicitly articulated in CCSS at any grade. 4.2.7 B.2. Understand and apply CCSS move this transformations. from grade 7 to Finding the image, given the pre-image, grade 8. and vice-versa Sequence of transformations needed to map one figure onto another Reflections, rotations, and translations result in images congruent to the pre-image Dilations (stretching/shrinking) result in images similar to the pre-image 4.2.7.C.2. Use a coordinate grid to CCSS move this from model and quantify transformations (e.g., grade 7 to grade 8. translate right 4 units). 4.2.7.D.1. Solve problems requiring Not explicitly calculations that involve different units of articulated in CCSS measurement within a measurement system at any grade (e.g., 4’3” plus 7’10” equals 12’1”). Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 4.2.7.D.3. Recognize that all Although not explicitly measurements of continuous quantities articulated in the are approximations. CCSS, these are 4.2.7.D.2. Select and use appropriate critical understandings units and tools to measure quantities to for students to solve real-life problems at the degree of precision needed in a this grade particular problem-solving situation. 7.G.4. Know the formulas for the area and CCSS move area In Transition: circumference of a circle and use them to and circumference Students coming to solve problems; give an informal derivation seventh grade from of a circle from of the relationship between the classes in which the grade 6 (NJ cccs 2008 standards were circumference and area of a circle. 4.2.6.E.2) to used may already know grade 7. NEW (to grade 7) this content. Once the curriculum change has been implemented at grade 6, teachers can no longer assume previous familiarity with circumference and area of a circle. Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later grades, or because it is not included at any grade in the new CCSS. 5 4.2.7 E.1. Develop and apply strategies Although this 2008 for finding perimeter and area. CPI is somewhat Geometric figures made by combining related to CCSS triangles, rectangles and circles or parts 7.G.4 above, the of circles emphasis is very Estimation of area using grids of various different. sizes 7.G.5. Use facts about supplementary, CCSS move this complementary, vertical, and adjacent from grade 8 to angles in a multi-step problem to write and grade 7. NEW (to grade 7) solve simple equations for an unknown angle in a figure. 7.G.6. Solve real-world and mathematical CCSS move this problems involving area, volume and from grade 8 to surface area of two- and three-dimensional grade 7. objects composed of triangles, NEW (to grade 7) quadrilaterals, polygons, cubes, and right prisms. 4.2.7 E.2. Recognize that the volume of CCSS move volume a pyramid or cone is one-third of the of a cone from grade volume of the prism or cylinder with the 7 to grade 8. same base and height (e.g., use rice to Finding the volume compare volumes of figures with same of a pyramid is base and height). postponed until HS. Statistics and Probability 7.SP Use random sampling to draw inferences about a population. 7.SP.1. Understand that statistics can be Related but much 4.4.7 A.2. Make inferences and used to gain information about a population more specific formulate and evaluate arguments based by examining a sample of the population; expectations on displays and analysis of data. generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2. Use data from a random sample to CCSS move this draw inferences about a population with an from grade 8 unknown characteristic of interest. (4.4.8.A.4) to Generate multiple samples (or simulated grade 7. samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in NEW (to grade 7) a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Draw informal comparative inferences about two populations. 7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring 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 NEW deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later grades, or because it is not included at any grade in the new CCSS. 6 7.SP.4. Use measures of center and Related but much 4.4.7 A.1. Select and use appropriate Identification of measures of variability for numerical data more specific and representations for sets of data, and appropriate data from random samples to draw informal measures of central tendency (mean, displays is not explicitly more demanding included in the CCSS comparative inferences about two median, and mode). expectation. at any grade, but is populations. For example, decide whether Type of display most appropriate for critical throughout. the words in a chapter of a seventh-grade given data science book are generally longer than the Box-and-whisker plot, upper quartile, In CCSS, box plots words in a chapter of a fourth-grade lower quartile and interquartile range science book. are in grade 6 Scatter plot In CCSS, scatter plots are in grade 8 Calculators and computer used to Supportive of CCSS record and process information Mathematical Practice #5 Investigate chance processes and develop, use, and evaluate probability models. 7.SP.5. Understand that the probability of a CCSS move this chance event is a number between 0 and 1 from grade 6 that expresses the likelihood of the event NEW (to grade 7) (4.4.6.B.1) to occurring. Larger numbers indicate greater grade 7. likelihood. A probability near 0 indicates an 4.4.7.B.1. Interpret probabilities as unlikely event, a probability around 1/2 ratios, percents, and decimals. indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6. Approximate the probability of a Similar, but slightly 4.4.7.B.2. Model situations involving chance event by collecting data on the more specific probability with simulations (using chance process that produces it and expectation. spinners, dice, calculators and observing its long-run relative frequency, computers) and theoretical models. and predict the approximate relative Frequency, relative frequency frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled 4.4.7.B.3. Estimate probabilities and roughly 200 times, but probably not exactly make predictions based on experimental 200 times. and theoretical probabilities. 7.SP.7. Develop a probability model and Related to and an [“Estimate probabilities and make use it to find probabilities of events. extension of predictions based on experimental and Compare probabilities from a model to NJ cccs 4.4.7.B.3 theoretical probabilities” from 4.4.7.B.3 observed frequencies; if the agreement is above.] above not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end 4.4.7.B.4. Play and analyze probability- In CCSS, concepts down. Do the outcomes for the spinning based games, and discuss the concepts of fairness and penny appear to be equally likely based of fairness and expected value. expected value are on the observed frequencies? postponed until HS. Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later grades, or because it is not included at any grade in the new CCSS. 7 7.SP.8. Find probabilities of compound CCSS move this “Explore events using organized lists, tables, tree from grade 8 compound events” diagrams, and simulation. (4.4.8.B.2) to was included in a. Understand that, just as with simple grade 7. 2008 NJ cccs at events, the probability of a compound event is the fraction of outcomes in the grade 6 (4.4.6.B.3) sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language NEW (to grade 7) (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 4.4.7.C. Discrete Mathematics- In CCSS, Systematic Systematic Listing and Counting Listing and Counting Is postponed until HS 4.4.7.D. Discrete Mathematics- Vertex-Edge Graphs Vertex-Edge Graphs and Algorithms are not included in the new CCSS at any grade level Shaded content is not a focus in this grade because it has already been covered in previous grades, because it will be covered in later grades, or because it is not included at any grade in the new CCSS. 8