7th Grade Mathematics Quarter 1 Curriculum Map
2014-15
Unit 1: Number 1st 9 Weeks Suggested Instructional Days: 22 System Unit Summary (Learning Target/Goal): Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Instructional Materials: CCSS for Mathematical Practice: Prentice Hall Mathematics: Common Core Course 2 1. Make sense of problems and persevere in
solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unit & Timeline
Standards
Learning Expectation & Example
Vocabulary
Assessment Data 2013-14 District-wide data percentage of students choosing each answer *=correct answer
Resources: Prentice Hall Mathematics 1-1, 1-2 4 Review & Routines, day Preprocedures, review s assessment of basic computation
absolute value
Discovery Test A (see district assessment calendar for dates)
and fraction skills
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7th Grade Mathematics Quarter 1 Curriculum Map
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1 day
3 days
7.NS.1b Understand p + q as the number located a distance |q| from p in the positive or negative direction depending on whether 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. 7NS.1a 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. 7.NS.1b Understand p + q as the number located a distance |q|
integers positive negative opposites number line
To compare and order integers Example
Discovery C #71 A* 51.63 B 6.34 C 32.73 D 6.94 Moderate
Compare. Use , or =. 9 __ -4
To add and subtract integers Example
additive inverse addend sum difference
Discovery D #47 A 17.15 B* 46.84 C 24.12 D 11.48 Hard
The temperature in Caribou, Maine, was 8˚F at noon. By 10:00 p.m. the temperature changed by -8˚F. What was the temperature at 10:00 p.m.?
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7th Grade Mathematics Quarter 1 Curriculum Map
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from p in the positive or negative direction depending on whether 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. 7.NS.1c 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.1d Apply properties of operations as strategies to add and
Discovery C #50 A 26.39 B 8.39 C 6.4 D* 58.57 Easy
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7th Grade Mathematics Quarter 1 Curriculum Map
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subtract rational numbers.
Resources: Prentice Hall Mathematics 1-3, 1-4 7.NS.2a 2 days Understand To multiply and 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.’
divide integers
zero product property produce factors
Discovery D #65 A 25.76 B 13.29 C 13.64 D* 46.19 Hard
Example A scuba diver is 180 ft. below sea level and rises to the surface at a rate of 30 ft./minute. How long will the diver take to reach the surface?
7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and
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7th Grade Mathematics Quarter 1 Curriculum Map
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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.
Resources: Prentice Hall Mathematics 1-5, 1-6 7.NS.2d 2 Converting between terminating days Convert a decimals fractions & rational repeating number to a decimals, decimal using terminating/repeatin decimals long division; quotient g decimals know that the divisor decimal form of a rational number terminates in 0s or eventually repeats. 7.EE.3 Solve multistep, real life mathematical problems posed with positive and negative rational numbers in any form using tools strategically. Apply properties of
Discovery C #55 A 26.03 B 14.37 C 8.33 D* 50.79 Moderate
Example Write 3/16 as a decimal, using long division. Write 0.965 as a fraction in simplest form.
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7th Grade Mathematics Quarter 1 Curriculum Map
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operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonablenes s of answers using mental computation and estimation strategies.
2 day
7.NS.2b 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 Convert a rational number to a decimal using long division; know that the
Discovery C #51 A 23.31 B* 33.03 C 23.01 D 20.11 Moderate
Compare and order rational numbers Example List from least to greatest: 3/2, 0.25, 3/4, -1.0
rational numbers numerator denominator
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7th Grade Mathematics Quarter 1 Curriculum Map
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decimal form of a rational number terminates in 0s or eventually repeats.
2 days
7.NS.1b: Understand p + q as the number located as 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 zero (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on
Add and subtract rational numbers Example
mixed numbers improper fractions
A diver climbs a 12 ft. tower and walks 6 3/4 ft to the end of the diving board. Then he jumps 5 1/2 ft above the board and dives into the water. The water level is 1 1/4 ft below the base of the tower. How far does the diver travel from the top of the dive to the water?
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7th Grade Mathematics Quarter 1 Curriculum Map
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the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
2 day
Resources: Prentice Hall Mathematics 1-7, 1-8 7.NS.2a To multiply rational distributive Understand property numbers that commutativ multiplication e property is extended Example from fractions associative Marta is conducting to rational property numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to
a science experiment. She changes the temperature of a chemical solution by -3/4˚F each minute. What is the total change in the temperature of the
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7th Grade Mathematics Quarter 1 Curriculum Map
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2 days
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.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 7.NS.2b 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).
chemical solution after 11 minutes?
To divide rational numbers Example One can of iced tea holds 12 fl oz. A 2liter bottle holds 67 3/5 fl oz. How many cans of iced tea will you need to fill a 2-liter bottle.
reciprocal
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7th Grade Mathematics Quarter 1 Curriculum Map
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Interpret quotients of rational numbers by describing real-world contexts. 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
Discovery C #60 A* 30.86 B 12.74 C 13.16 D 41.97 Hard
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
1 day
7.NS.1a, b, c, d 7.NS.2a, b, c, d 7.NS.3 1 7.NS.1a, day b, c, d 7.NS.2a, b, c, d 7.NS.3 Unit 2: Expressions and Equations
REVIEW & REINFORCE
Math 7 Q1 CFA#1 (School created- can be given at the discretion of the teacher)
Discovery Education Assessment
Suggested Instructional Days: 18
1st 9 Weeks
Unit Summary (Learning Target/Goal): Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
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7th Grade Mathematics Quarter 1 Curriculum Map
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Unit & Timeline
Standards
Learning Expectation & Example
Resources: Prentice Hall Mathematics 2-1,2-2 7.EE.4 Use variables to 3 Write and days represent quantities in a evaluate real-world or mathematical problem and algebraic construct simple equations expressions and inequalities to solve problems by reasoning about the quantities.
Expression and Equations Use properties of operations to generate equivalent expressions. Solve reallife and mathematica l problems using numerical and algebraic expressions and equations
3 days
7.EE.1: Apply, factor, and expand linear expressions with rational coefficients.
Example Write a word phrase for the expression a5. Write an expression for the word phrase five times a number. Simplify algebraic expressions using properties of operations
Vocabulary
Assessment Data 2013-14 District-wide data percentage of students choosing each answer *=correct answer
variable algebraic expression order of operations equations
Discovery C #56 A 30.98 B 19.26 C* 30.50 D 18.24 Moderate
like terms coefficient terms
Discovery C #49 A* 19.2 B 23.97 C 32.07 D 24.34 Hard
Example
Simplify the expression: 3a+8+a-92a Resources: Prentice Hall Mathematics 2-3, 2-4
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7th Grade Mathematics Quarter 1 Curriculum Map
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4 days
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.
Solve onestep equations by adding, subtracting, multiplying, or dividing; Properties of Equality, inverse operations
properties of equality inverse operations solution
Discovery D #64 A* 36.01 B 15.11 C 30.09 D 17.56 Moderate
Example
Solve the equation: d + 261.9 = 48 1 day
7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x+q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
Write and evaluate 2step equations
Discovery C #63 A* 39.86 B 22.4 C 14.92 D 21.62 Easy
Example
A fitness club advertises a special for new members. Each month of membership is $19, with an initial enrollment fee of $75. Write an
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7th Grade Mathematics Quarter 1 Curriculum Map
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expression for the total cost. Then evaluate your expression for 8 months. Resources: Prentice Hall Mathematics 2-5,2-6 7.EE.4a: Solve word 3 Use inverse days problems leading to operations equations of the form px + q = r and p(x+q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. 7.EE.3: Solve the twostep equations using inverse operations and the distributive property
Discovery D #42 A* 61.48 B 5.09 C 27.11 D 6.21 Easy
to solve 2step equations Example You earn $20 per hour landscaping a yard. You pay $1.50 in bus fare each way. How many hours must you work to earn $117?
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7th Grade Mathematics Quarter 1 Curriculum Map
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2 days
2 days
7.EE.3: Solve the twostep equations using inverse operations and the distributive property 7.EE.4a: Solve word problems leading to equations of the form px + q = r and p(x+q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
Use distributive property to solve equations of the form p(x+q)
All standards
Unit 2 Review and Assessment
Discovery C #67 A 23.61 B 31.46 C* 25.42 D 17.87 Moderate
Example
-8(x+2)=10
PARCC Resources
Link to PARCC End of Year Sample Test http://epat-parcc.testnav.com/client/index.html#tests PARCC Sample Items http://parcconline.org/samples/mathematics/grade-7-mathematics
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