Grade 7 NJSLS-Math Prerequisite Concepts and Skills · Web viewGrade 7: New Jersey Student Learning Standards for Mathematics - Prerequisite Standards and Learning Objectives Description

Grade 7 NJSLS-Math Prerequisite Concepts and Skills

Grade 7: New Jersey Student Learning Standards for Mathematics - Prerequisite Standards and Learning Objectives

August 2020

Grade 7: New Jersey Student Learning Standards for Mathematics - Prerequisite Standards and Learning Objectives Description

Included here are the prerequisite concepts and skills necessary for students to learn grade level content based on the New Jersey Student Learning Standards in mathematics. This tool is intended to support educators in the identification of any gaps in conceptual understanding or skill that might exist in a student’s understanding of mathematics standards. The organization of this document mirrors that of the mathematics instructional units, includes all grade level standards, and reflects a grouping of standards and student learning objectives.

The tables are divided into three columns. The first column contains the grade level standard and student learning objectives, which reflect the corresponding concepts and skills in that standard. The second column contains standards from prior grades and the corresponding learning objectives, which reflect prerequisite concepts and skills essential for student attainment of the grade level standard as listed in the first column. Given that a single standard may reflect multiple concepts and skills, all learning objectives for a prior grade standard may not be listed. Only those prior grade learning objectives that reflect prerequisite concepts and skills important for attainment of the associated grade level standard is listed. The third column contains Student Achievement Partners’ recommendations (SAP) for the 2020-21 school year regarding preserving or reducing time as compared to a typical academic year.

Content Emphases Key: : Major Cluster: Supporting Cluster : Additional Cluster

Unit 1: Operations with Rational Numbers Rationale for Unit Focus

Unit 1 focuses on operations with rational numbers and algebraic expressions. Learners extend previous understandings of addition and subtraction to add and subtract rational numbers. Similarly, they extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. They solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. They apply properties of operations to calculate with numbers in any form and convert between forms as appropriate.

Note: Double asterisks (**) indicate that the example(s) included within the New Jersey Student Learning Standard may be especially informative when considering the Student Learning Objective.

Unit 1, Module A

Standard and Student Learning Objectives

Previous Grade(s) Standards and Student Learning Objectives

Instructional Considerations

SAP recommendation to preserve or reduce time in 20-21 as compared to a typical year

7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

a. Describe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20 points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round?

b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending 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.

We are learning to/that…

· apply previous understandings of addition to add rational numbers

· describe situations in which opposites combine to make zero

· show by modeling, a number and its opposite have a sum of zero (additive inverse)

· p + q is the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative (e.g. 5 + -4 is 4 units in the negative direction from 5 and, similarly, 5 + 4 is also 4 units away in the positive direction)

· represent addition and subtraction of signed rational numbers on a vertical or horizontal number line

· interpret sums of rational numbers in real world situations

6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.


· use positive and negative numbers to represent quantities in real-world contexts and explain the meaning of zero in context

6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

We have learned to/that…

· locate numbers with opposite signs as points on opposite sides of zero on the number line

6.NS.C.7 Understand ordering and absolute value of rational numbers.

a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.

c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.


· represent the relative position of two numbers on a number line diagram using inequality statements

· absolute value of a rational number is its distance from zero on the number line

Incorporate foundational work on understandings of rational numbers (6.NS.C.5, 6.NS.C.6 and 6.NS.C.7) to build towards operations with rational numbers (7.NS.A) as detailed by the cluster.

7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

c. Understand subtraction of rational numbers as adding the additive inverse, p − q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in real-world contexts.

d. Apply properties of operations as strategies to add and subtract rational numbers.


· apply previous understandings of subtraction to subtract rational numbers

· subtraction of rational numbers is the same as adding the additive inverse, p − q = p + (-q)

· show by modeling on a number line that the distance between two rational numbers is the absolute value of their differences and apply the concept in real world contexts

· apply properties of operations as strategies to add and subtract rational numbers

5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)


· add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fraction


7.NS.A.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.

a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading 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.


· apply previous understandings of multiplication of fractions to multiply signed rational numbers

· operations on signed rational numbers continue to satisfy the properties of operations

· the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers

· interpret the products of signed rational numbers in real world situations

· apply previous understandings of division of fractions to divide signed rational numbers

· integers can be divided as long as the divisor is not zero

· division of integers results in a signed rational number

· If p and q are integers, then -(p/q) = (-p)/q = p/(-q)

· interpret quotients of signed rational numbers by describing real world contexts

5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a part of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)


· apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

· interpret the product of a fraction and a fraction as (a/b) × (c/d) = ac/bd **

5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.


· solve word problems involving division of whole numbers resulting in a fraction or mixed number quotient


7.NS.A.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.

c. apply properties of operations as strategies to multiply and divide rational numbers.

d. convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.


· apply properties of operations as strategies to multiply and divide signed rational numbers

· convert a rational number to a decimal using long division

· the decimal form of a rational number terminates in zeros or eventually repeats

6.NS.A.1 Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.


· compute quotients of fractions

6.NS.B.2. Fluently divide multi-digit numbers using the standard algorithm.


· divide multi-digit numbers using the standard algorithm working towards accuracy and efficiency

5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.


· apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction

5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.


· interpret a fraction as division of the numerator by the denominator using visual fraction models or equations


7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.


· solve real-world and mathematical problems involving the four operations with rational numbers in fraction form

· solve real-world and mathematical problems involving the four operations with rational numbers in decimal form

6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation


· add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation

5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)


· add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fraction

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.


· solve word problems involving measurement that includes simple fractions or decimals, using the four operations


Unit 1, Module B

Standard and Student Learning Objectives

Previous Grade(s) Standards and Student Learning Objectives

Instructional Considerations

SAP recommendation to preserve or reduce time in 20-21 as compared to a typical year

7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients


· apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients

6.EE.A.3 Apply the properties of operations to generate equivalent expressions.


· generate equivalent expressions using the properties of operations.

Incorporate foundational work on writing and transforming linear expressions from grade 6 (6.EE.A) into the work of using properties of operations to generate equivalent expressions, as detailed by cluster (7.EE.A).

7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”.


· rewriting an expression in different forms can clarify the problem and how the quantities are related

6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).


· two expressions are equivalent when they name the same number regardless of which value is substituted into them

· identify when two expressions are equivalent

Incorporate foundational work on writing and transforming linear expressions from grade 6 (6.EE.A) into the work of using properties of operations to generate equivalent expressions, as detailed by cluster (7.EE.A).

7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; 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 an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation


· convert between forms (fractions, decimals, and whole numbers) as appropriate to solve multi-step real life and mathematical problems with positive and negative rational numbers in any form

· apply the properties of operations to calculate with numbers in any form when solving multi-step real-life and mathematical problems, and assess the reasonableness of answers using mental computation and estimation strategies

n/a

For curricula and lessons that are well aligned to solving multi-step real-life and mathematical problems as detailed by the standard, no special considerations for shifting how time is dedicated are recommended.

Time spent on instruction and practice should not be reduced.

6

Updated August 2020

Documents

Grade 7 NJSLS-Math Prerequisite Concepts and Skills · Web viewGrade 7: New Jersey Student Learning Standards for Mathematics - Prerequisite Standards and Learning Objectives Description