7TH GRADE PACING GUIDE
MATH INNOVATIONS UNIT 1: LET’S BE RATIONAL
August-September
Standards:
7.EE.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 ¾ inches long in the center of a door that is 27 ½ 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.
7.NS.1abc 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, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 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. 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.
7.NS.2a 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.
7.NS.2b Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. B) Understand that integers can be divided provided that the divisor is not zero and every quotient of integers (with nonzero 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.
7.NS.2d Apply and extend previous understandings of multiplication and division of fractions 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 zeroes or eventually repeats.
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
Standard/Target / Section/Lesson / # Days / Formative Assessment /Section 1: Fractions and Decimals / 1st of Sept.
Pretest / 1.1: BIG Numbers / 1 / ACT #1
Pretest / 1.2: Little Numbers / 1
Multiplication Facts Quiz: 2’s, 3’s, 5’s and 10’s
7.NS.3 Knowledge Target: Add rational numbers. Knowledge Target: Subtract rational numbers. / 1.3: Adding and Subtracting Fractions / 2 / ACT #12, 54, 51, 5, 14, 14B, 119
7.NS.3 Knowledge Target: Multiply rational numbers. Knowledge Target: Divide rational numbers. Reasoning Target: Solve real-world and mathematical problems by adding, subtracting, multiplying, and dividing rational numbers, including complex fractions. / 1.4: Multiplying and Dividing Fractions
*Need to add complex fractions. / 2 / ACT #7, 4, 83, 4A, 5
Multiplication Facts Quiz: Square Numbers
7.EE.3 Knowledge Target: Convert between numerical forms as appropriate.
7.NS.2d Knowledge Target: Convert a rational number to a decimal using long division. Knowledge Target: Explain that the decimal form of a rational number terminates (stops) in zeroes or repeats. / 1.5: Writing Fractions as Decimals / 2 / ACT#5
1.6: Decimal Patterns / 3 / ACT #3, 9, 6, 33
Study Guide / 1
Percent Proficiency: / Quiz / 1 / ACT #13
Section 2: Making Sense of Signed Numbers / Mid Sept.
2.1: Signed Numbers / 1 / PARCC #5
7.NS.1 Knowledge Target: Describe situations in which opposite quantities combine to make 0. Knowledge Target: Represent and explain how a number and its opposite have a sum of 0 and are additive inverses. Knowledge Target: Demonstrate and explain how adding two numbers, p + q, if q is positive, the sum of p and q will be |q| spaces to the right of p on the number line. Reasoning Target: Represent the distance between two rational numbers on a number line is the absolute value of their difference and apply this principle in real-world contexts. / 2.2: Integers / 3 / PARCC #12, 14; ACT #37, 43, 119
Multiplication Facts Quiz: Nines
Pretest / 2.3: Coordinate Graphing / 1 / ACT #17
Study Guide / 1
Percent Proficiency: / Quiz / 1
Section 3: Computation with Signed Numbers / 3rd Wk in Oct.
7.NS.1 Knowledge Target: Demonstrate and explain how adding two numbers, p + q, if q is negative, the sum of p and q will be |q| spaces to the left of p on the number line. Reasoning Target: Interpret sums of rational numbers by describing real-world contexts. Reasoning Target: Explain and justify why the sum of p + q is located a distance of |q| in the positive or negative direction from p on a number line. / 3.1: Adding Signed Numbers / 3
3.2: Integer Games / 2
Multiplication Facts Quiz: Last Six Facts
7.NS.1 Knowledge Target: Identify subtraction of rational numbers as adding the additive inverse to subtract rational numbers, p – q = p + (-q). Reasoning Target: Apply and extend previous understanding to represent addition and subtraction problems of rational numbers with a horizontal or vertical number line. / 3.3: Linking Subtraction to Addition / 3 / PARCC #12; ACT #2
7.NS.1 Reasoning Target: Apply the principle of subtracting rational numbers in real-world contexts. Reasoning Target: Apply properties of operations as strategies to add and subtract rational numbers. / 3.4: Subtracting Signed Numbers / 3 / PARCC #6, 8, 14
7.NS.2a Knowledge Target: Recognize that the process for multiplying fractions can be used to multiply rational numbers including integers. Knowledge Target: Know and describe the rules when multiplying signed numbers. Reasoning Target: Interpret the products of rational numbers by describing real-world contexts. / 3.5: Multiplying Signed Numbers / 1 / ACT #11; PARCC #4, 2, 11
7.EE.3 Reasoning Target: 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. Reasoning Target: Apply properties of operations to calculate with numbers in any form. Reasoning Target: Assess the reasonableness of answers using mental computation and estimation strategies.
7.NS.2b Knowledge Target: Explain why integers can be divided except when the divisor is 0. Knowledge Target: Describe why the quotient is always a rational number. Knowledge Target: Know and describe the rules when dividing signed numbers, integers. Knowledge Target: Recognize that
-(p/q) = -p/q = p/-q. Reasoning Target: Interpret the quotient of rational numbers by describing real-world contexts. / 3.6: Dividing Signed Numbers / 3 / PARCC #10
Study Guide / 1
Percent Proficiency: / Quiz / 1
Study Guide / 1
Percent Proficiency: / Unit Exam / 1
Lewis County Middle School