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Our Savior Christian Academy Curriculum …...Number and Operations Our Savior Christian Academy...

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  • Number and Operations

    Our Savior Christian Academy

    Curriculum Framework for: Math Our Savior Christian Academy’s “Curriculum Framework for Math” is designed as a tool that will follow the same format for all grades K-4. Each grade level will have a separate section based on classroom structure, and it will be up to each individual teacher to design a lesson plan that fits their classroom needs

    based on these standards and suggestions. Our Savior Christian Academy’s “Curriculum Framework for Math” is offered to the glory of God that it may be a blessing among Lutheran school educators and their students.

    PHILOSOPHY God has created an orderly, systematic universe. Mathematics is a useful and unique God-given universal language that facilitates the ability to appreciate the

    created order God has given us and further advances the understanding of our modern, high-tech world. The development of mathematics abilities prepares

    students for lives of responsible Christian service to His church and the community.

  • Number and Operations

    Our Savior Christian Academy

    Broad Goals

    Our Savior Christian Academy’s Science goals include:

    Incorporating Jesus Christ in all core areas of Science.

    Providing the children with a wide range of knowledge, skills, and related activities that help him/her to develop an understanding of the physical world.

    Encouraging the children to be confident and to communicate Science effectively through reading, writing, speaking, and listening.

    Using higher order thinking skills including comprehension, application, analysis, evaluation, and synthesis in the learning concepts in life science, earth science, and physical science.

    Displaying respect in their interactions with the environments of which they are members.

    Exhibiting organizational skills, intellectual curiosity and growth, and application of what has been learned in science both to future schoolwork and to lifelong learning.

    Providing learning experiences in which students will recognize, develop, and apply effective communication skills at or above grade level in the areas of Science.

    Students are shown strategies on how to be knowledgeable and proficient thinkers who will make positive Christ-like contributions to society.

    Our Savior Christian Academy obtains this through:

    Keeping Our Savior, Jesus Christ, as the center focus on our campus and in our curriculum

    Fascinating and significant Science experiences through multi-sensory activities that incorporate the world around them.

    Applying Science to other core areas of learning.

    Adapting other subjects to add valuable perspectives to the Science curriculum.

    Teaching on an individual basis with the knowledge that children acquire an understanding of Science in an uneven way.

    Continuous assessment for analysis and planning in Science. o Focuses on the identification of the children's existing knowledge and strategies. o Updating curriculum to meet changing state standards along with student needs. o Provides information that will enable the teacher to cater for individual differences in ability, previous learning and learning style, and to resist pressure to push the child to

    premature mastery.

    Work samples and results that are shared with the parents, congregants, and community.

    6th

    grade

    7th

    grade

  • Number and Operations

    1. Understand numbers, ways of representing numbers, relationships among numbers and number systems Grade 6 Grade 7

    A apply and understand whole numbers to millions, fractions and decimals to the thousandths (including location on the number line) Curriculum N1A7 Comparing and Ordering Rational Numbers N1A8 *compare and order all rational numbers including percents, and find their location on a number line http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=300 Fraction Garden (Comparing Fractions) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1004 Modeling Decimals (Area and Grid Models) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1007 Ordering Percents, Fractions and Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=263 Ordering Percents, Fractions and Decimals Greater Than 1 http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=306 Real Number Line - Activity A http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=122 Treasure Hunter (Decimals on the Number Line) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1003 6.NS.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 7.NS.1.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.1.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.

    compare and order all positive rational numbers and find their approximate location on a number line N1A8 Curriculum Comparing and Ordering Rational Numbers http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=300 Fraction Garden (Comparing Fractions) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1004 Modeling Decimals (Area and Grid Models) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1007 Ordering Percents, Fractions and Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=263 Ordering Percents, Fractions and Decimals Greater Than 1 http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=306 Real Number Line - Activity A http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=122 Treasure Hunter (Decimals on the Number Line) 6.NS.7.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. 6.NS.7.b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3° C > –7° C to express the fact that –3° C is warmer than –7°C. 6.NS.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. http://illustrativemathematics.org/illustrations/277 http://illustrativemathematics.org/illustrations/278 6.NS.6.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.

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  • Number and Operations

    B

    recognize and generate equivalent forms of fractions, decimals and benchmark percents to solve problems

    6.RP.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means

    times the

    quantity); solve problems involving finding the whole, given a part and the percent. Curriculum Fraction Garden (Comparing Fractions) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1004 Ordering Percents, Fractions and Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=263 Ordering Percents, Fractions and Decimals Greater Than 1 http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=306 Percents and Proportions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=266

    recognize and generate equivalent forms of fractions, decimals and percents N1b5 N1B7 Curriculum Fraction Garden (Comparing Fractions) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1004 Ordering Percents, Fractions and Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=263 Ordering Percents, Fractions and Decimals Greater Than 1 http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=306 Percents and Proportions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=2667.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 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.) http://illustrativemathematics.org/illustrations/2987.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. 7.NS.2.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.

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    C *recognize equivalent representations for the same number and generate them by decomposing and composing numbers Curriculum Ordering Percents, Fractions and Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=263 Ordering Percents, Fractions and Decimals Greater Than 1 http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=306

    *recognize equivalent representations for the same number and generate them by decomposing and composing numbers, including exponential notation N1C7 Curriculum Ordering Percents, Fractions and Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=263 Ordering Percents, Fractions and Decimals Greater Than http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=306 7.EE.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.”

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  • Number and Operations

    2. Understand meanings of operations and how they relate to one another

    Grade 6 Grade 7

    B describe the effects of multiplication and division on fractions and decimals Curriculum N2B6

    (shade parts of a region to represent fractional parts, decode a message using information from a secret code, play a board game, and divide words into letters using fractional terms) 6.NS.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.

    *describe the effects of all operations on rational numbers including integers N2B7 Curriculum

    parts of a region to represent fractional parts, decode a message using information from a secret code, play a board game, and divide words into letters using fractional terms) 7.NS.1.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.2.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 – = = .

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  • Number and Operations

    C

    *apply properties of operations (including order of operations) to positive rational numbers N2C6 N2C7 N3B5 N2C7 Curriculum Dividing Fractions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212 Dividing Mixed Numbers http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=213 Fractions with Unlike Denominators http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=220 Multiplying Decimals (Area Model) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1026 Multiplying Fractions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=344 Multiplying Mixed Numbers http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=227 Multiplying with Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=228 Order of Operations http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=255 Sums and Differences with Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=237 6.EE.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 6.NS.7.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.. 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. 7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.1.d Apply properties of operations as strategies to add and subtract rational numbers.

    apply properties of operations (including order of operations) to positive rational numbers and integers N2C8 inverse operations Dividing Fractions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212 Dividing Mixed Numbers http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=213 Fractions with Unlike Denominators http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=220 Multiplying Decimals (Area Model) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1026 Multiplying Fractions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=344 Multiplying Mixed Numbers http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=227 Multiplying with Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=228 Order of Operations http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=255 Sums and Differences with Decimals http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=237 7.NS.1.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. 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.

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  • Number and Operations

    2. Understand meanings of operations and how they relate to one another -- continued Grade 6 Grade 7

    D identify square and cubic numbers and determine whole number roots and cubes N2D6 Curriculum Square Roots http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=103 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. http://illustrativemathematics.org/illustrations/532

    *approximate the value of square roots to the nearest whole number Curriculum Square Roots http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=103

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    3. Compute fluently and make reasonable estimates -- continued

    Grade 6 Grade 7

    D *estimate and justify the results of multiplication and division of positive rational numbers N3D7 Curriculum Dividing Fractions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212 Dividing Mixed Numbers http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=213 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.

    *estimate and justify the results of all operations on rational numbers Curriculum Dividing Fractions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212 Dividing Mixed Numbers http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=213

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  • Number and Operations

    E

    solve problems using ratios and rates N3E6 N3E6 Curriculum Part:Part and Part:Whole Ratios http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=264 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every two wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” http://illustrativemathematics.org/illustrations/76

    6.RP.2 Understand the concept of a unit rate

    associated with a ratio a:b with b ≠ 0, and

    use rate language in the context of a ratio relationship. For example, “This recipe has a ratio

    of 3 cups of flour to 4 cups of sugar, so there is

    cup of flour for each cup of sugar.” “We

    paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.) http://illustrativemathematics.org/illustrations/77 http://illustrativemathematics.org/illustrations/549 6.RP.3.b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.6.RP.3.c Find a percent of a quantity

    as a rate per 100 (e.g., 30% of a quantity means

    times the quantity); solve problems

    involving finding the whole, given a part and the percent.6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

    solve problems involving proportions, such as scaling and finding equivalent ratios N3E7

    Part:Part and Part:Whole Ratios

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=264 6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 7.RP.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. http://illustrativemathematics.org/illustrations/107

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  • Number and Operations

    3. Compute fluently and make reasonable estimates Grade 6 Grade 7

    C multiply and divide positive rational numbers N3C6 Curriculum Dividing Fractions

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212

    Dividing Mixed Numbers

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=213

    Multiplying Decimals (Area Model)

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1026

    Multiplying Fractions

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=344

    Multiplying Mixed Numbers

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=227

    Multiplying with Decimals

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=228

    6.NS.2 Fluently divide multi-digit numbers using the standard algorithm http://illustrativemathematics.org/illustrations/271 http://illustrativemathematics.org/illustrations/270 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. http://illustrativemathematics.org/illustrations/274 6.NS.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. For example, create

    a story context for (

    ) ÷ (

    ) and use a visual fraction model to show the quotient; use the relationship

    between multiplication and division to explain that (

    ) ÷ (

    ) =

    because

    of

    is

    . (In general, (

    ) ÷ (

    ) =

    How much chocolate will each person get if 3 people share

    lb of chocolate equally? How many

    -cup

    servings are in

    of a cup of yogurt? How wide is a rectangular strip of land with length

    mi and area

    square mi? http://illustrativemathematics.org/illustrations/463

    apply all operations on rational numbers including integers N3C7

    Curriculum

    Dividing Fractions

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212

    Dividing Mixed Numbers

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=213

    Multiplying Decimals (Area Model)

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=102

    6

    Multiplying Fractions

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=344

    Multiplying Mixed Numbers

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=227

    Multiplying with Decimals

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=228 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.) 7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers. 7.EE.4.b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. 7.NS.1.d Apply properties of operations as strategies to add and subtract rational numbers. 7.EE.4.a 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.

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    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=213http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1026http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=344http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=227http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=228http://illustrativemathematics.org/illustrations/271http://illustrativemathematics.org/illustrations/270http://illustrativemathematics.org/illustrations/274http://illustrativemathematics.org/illustrations/463http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=213http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1026http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1026http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=344http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=227http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=228

  • Number and Operations

    6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line

    diagrams, or equations. http://illustrativemathematics.org/illustrations/135 http://illustrativemathematics.org/illustrations/498 http://illustrativemathematics.org/illustrations/79 http://illustrativemathematics.org/illustrations/134

    6.NS.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.

    6.NS.7 Understand ordering and absolute value of rational numbers. http://illustrativemathematics.org/illustrations/288 http://illustrativemathematics.org/illustrations/286

    6.NS.7.d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

    7.NS.1

    7.NS.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. http://illustrativemathematics.org/illustrations/314 http://illustrativemathematics.org/illustrations/310 http://illustrativemathematics.org/illustrations/46

    7.NS.1.a 7.NS.1.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.

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

    http://illustrativemathematics.org/illustrations/135http://illustrativemathematics.org/illustrations/498http://illustrativemathematics.org/illustrations/79http://illustrativemathematics.org/illustrations/134http://illustrativemathematics.org/illustrations/288http://illustrativemathematics.org/illustrations/286http://illustrativemathematics.org/illustrations/314http://illustrativemathematics.org/illustrations/310http://illustrativemathematics.org/illustrations/46

  • Algebraic Relationships 1. Understand patterns, relations and functions

    Grade 6 Grade 7

    B represent and describe patterns with tables, graphs, pictures, symbolic rules or words Curriculum Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid.

    analyze patterns represented graphically or numerically with words or symbolic rules, including recursive notation Curriculum Build & analyze a pattern to complete a sequence of patterns. Analyze a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid

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    C *compare various forms of representations to identify patterns Curriculum Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.

    compare and contrast various forms of representations of patterns Curriculum Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.

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    1. Understand patterns, relations and functions -- continued

    Grade 6 Grade 7

    D *identify functions as linear or nonlinear from tables or graphs A1D7

    Curriculum Identify Fractions

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=133 7.RP.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

    identify functions as linear or nonlinear from tables, graphs or equations

    Curriculum Identify Fractions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=133

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  • Algebraic Relationships 2. Represent and analyze mathematical situations and structures using algebraic symbols

    Grade 6 Grade 7

    A use symbolic algebra to represent unknown quantities in expressions or equations and solve one-step equations A2A6 A2A7 Curriculum Solve one-step equations using an area model. 6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. http://illustrativemathematics.org/illustrations/425 6.EE.2.a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. 7.RP.2.c Represent proportional relationships by equations. 7.EE.4.a 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. 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

    use symbolic algebra to represent unknown quantities in expressions or equations and solve linear equations with one variable A2A8 A2A7 A2A7 A2A8 Curriculum Solve one-step equations using an area model. 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. http://illustrativemathematics.org/illustrations/673 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. http://illustrativemathematics.org/illustrations/425 7.RP.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.EE.4.b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

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    B

    use the commutative, distributive and associative properties to generate equivalent forms for simple algebraic expressions A2B6 A2B8Curriculum Chocomatic (Multiplication, Arrays, and Area) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1014 6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).http://illustrativemathematics.org/illustrations/257 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. http://illustrativemathematics.org/illustrations/532 6.EE.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). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. http://illustrativemathematics.org/illustrations/542 6.EE.3 Apply the properties of operations to generate equivalent expressions. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

    use properties to generate equivalent forms for simple algebraic expressions that include positive rationals and integers A2B7 Curriculum Chocomatic (Multiplication, Arrays, and Area) http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1014 7.NS.2.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.

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  • Algebraic Relationships

    3. Use mathematical models to represent and understand quantitative relationships Grade 6 Grade 7

    A model and solve problems, using multiple representations such as tables, expressions and one-step equations A3A6 A3A5

    Curriculum

    Solve one-step equations using an area model. 6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. http://illustrativemathematics.org/illustrations/532 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

    model and solve problems, using multiple representations such as graphs, tables, expressions, and linear equations

    Curriculum Solve one-step equations using an area model.

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  • Algebraic Relationships 4. Analyze change in various contexts

    Grade 6 Grade 7

    A *construct and analyze representations to compare situations with constant or varying rates of change

    Curriculum Distance-Time http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=260

    compare situations with constant or varying rates of change

    Curriculum Distance-Time http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=260

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    6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c

    have infinitely many solutions; represent solutions of such inequalities on number line diagrams. http://illustrativemathematics.org/illustrations/642

    7.RP.2 7.RP.2 Recognize and represent proportional relationships between quantities. http://illustrativemathematics.org/illustrations/100 http://illustrativemathematics.org/illustrations/101 http://illustrativemathematics.org/illustrations/104 http://illustrativemathematics.org/illustrations/95 http://illustrativemathematics.org/illustrations/181 http://illustrativemathematics.org/illustrations/180

    7.RP.2.d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=260http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=260http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=260http://illustrativemathematics.org/illustrations/642http://illustrativemathematics.org/illustrations/100http://illustrativemathematics.org/illustrations/101http://illustrativemathematics.org/illustrations/104http://illustrativemathematics.org/illustrations/95http://illustrativemathematics.org/illustrations/181http://illustrativemathematics.org/illustrations/180

  • Geometric and Spatial Relationships 1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

    Grade 6 Grade 7

    A Identify similar and congruent shapes

    Curriculum Given a variety of shapes, identify similar and congruent shapes

    *identify the 2-diimensional cross-section of a 3-dimensional shape G1A7

    Curriculum Given a variety of shapes, identify similar and congruent shapes 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids

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    B describe relationships between corresponding sides, corresponding angles and corresponding perimeters

    of similar polygons

    Curriculum

    Similar Figures http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=271

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  • Geometric and Spatial Relationships

    2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems Grade 6 Grade 7

    A use coordinate systems to construct geometric shapes G2A6 Curriculum

    Demonstrate understanding through drawlings 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

    use coordinate geometry to construct and identify geometric shapes in the coordinate plane using their properties G2A7

    Curriculum

    complete problems from Houghton Mifflin Math (ISBN: 0-618-33867-5) 6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.NS.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 6.NS.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

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    3. Apply transformations and use symmetry to analyze mathematical situations Grade 6 Grade 7

    A *describe the transformation from a given pre-image using the terms reflection/flip, rotation/turn, and translation/Slide G3A8 reposition shapes under formal transformations such as reflection, rotation and translation

    CurriculumGive students different shapes. On lined paper, have student change shape as goes from one side of paper to next. Describe transformation 6.NS.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

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    B describe the relationship between the scale factor and the perimeter of the image using a dilation (contractions- magnifications; stretching/shrinking) G3B8 G3B7

    Curriculum Describe the relationship through class discussion using website

    http://www.mathopenref.com/dilate.html 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

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  • Geometric and Spatial Relationships

    C *create polygons and designs with rotational symmetry Curriculum Through experimentation and exploration, students will gain an understanding of rotational symmetry by designing a city.

    *determine all lines of symmetry of a polygons

    CurriculumWork with partner to create pictures with shapes that have symmetry. Identify

    all the lines

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    4. Use visualization, spatial reasoning and geometric modeling to solve problems Grade 6 Grade 7

    A *use spatial visualization to identify isometric representations of mat plans Curriculum

    3D and Orthographic Views - Activity A http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=281

    *use spatial visualizations to identify various 2-dimensional views of isometric drawings

    Curriculum

    3D and Orthographic Views - Activity A http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=281

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    draw or use visual models to represent and solve problems G4B6

    Curriculum

    3D and Orthographic Views - Activity A

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    Using graph paper, draw bus size so that all buses are full and no students are left

    behind. This is a nice illustration of division with remainders. 6.NS.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. 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

    draw or use visual models to represent and solve problems

    Curriculum

    3D and Orthographic Views - Activity A

    http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=281

    Using graph paper, draw bus size so that all buses are full and no students are left behind. This

    is a nice illustration of division with remainders.

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  • Geometric and Spatial Relationships 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

    G2A5 *use coordinate systems to specify location, describe paths and find distance between points along horizontal and vertical lines

  • Measurement 1. Understand measurable attributes of objects and the units, systems and processes of measurement

    Grade 6 Grade 7

    A identify and justify the unit of measure for area and volume (customary and metric) M2C5 determine volume by finding the total number of the same size units needed to fill a space without gaps or overlaps

    Curriculum complete problems from Houghton Mifflin Math (ISBN: 0-618-33867-5) http://www.biblestudy.org/beginner/bible-weights-and-measures.html 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. .

    *identify and justify the unit of measure for volume (customary and metric)

    Curriculum complete problems from Houghton Mifflin Math (ISBN: 0-618-33867-5) http://www.biblestudy.org/beginner/bible-weights-and-measures.html

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    identify the equivalent area and volume measures within a system of measurement (e.g., sq ft. to sq in, m3 to c m3) M1B7

    Curriculum complete problems from Houghton Mifflin Math (ISBN: 0-618-33867-5)

    using various measuring tools to identify the equivalent area and volume 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

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    C *solve problems involving elapsed time (hours and minutes)

    Curriculum complete problems from Houghton Mifflin Math (ISBN: 0-618-33867-5)

    Use flashcards to tell stories and find elapsed time

    *solve problems involving addition and subtraction of time (hours, minutes and seconds)

    Curriculum complete problems from Houghton Mifflin Math (ISBN: 0-618-33867-5)

    Use flashcards to tell stories and find elapsed time

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    6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

    6.EE.2.b 6.EE.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

  • Data and Probability 2. Apply appropriate techniques, tools and formulas to determine measurements

    Grade 6 Grade 7

    B *identify and justify an angle as acute, obtuse, straight, or right Curriculum

    Complete problems from Houghton Mifflin Math (ISBN: 0-618-33867-5)

    *use tools to measure angles to the nearest degree and classify the angle as acute, obtuse, right, straight, or reflex M2B8

    Curriculum Use items around the room and objects around school to measure angles and classify 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

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    C solve problems involving the area or perimeter of polygons M2C6 M2C6 Curriculum Complete problems from Houghton Mifflin Math (ISBN: 0-618-33867-5) 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

    solve problems involving circumference and/or area of a circle and surface area/volume of a rectangular or

    triangular prism, or cylinder M2C7 M2C7 Curriculum Complete problems from Houghton Mifflin Math

    (ISBN: 0-618-33867-5) 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply techniques in the context of solving real-world and mathematical problems. 6.EE.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 7.G.4 Know formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

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    2. Apply appropriate techniques, tools and formulas to determine measurements -- continued Grade 6 Grade 7

    E convert from one unit to another within a system of measurement (mass and

    weight) M2E6 Curriculum Lead the class in a review of the basic concepts and procedures involved in measuring length, weight, and volume. After whole group instruction, small groups and individuals practice measuring by completing a variety of fun activities and experiments. They also practice converting from one unit to another

    by using multiplication and division.6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

    convert from one unit to another within a system of measurement (capacity) and convert square or cubic units within the same system of measurement M2E7

    Curriculum Lead the class in a review of the basic concepts and procedures involved in measuring length, weight, and volume. After whole group instruction, small groups and individuals practice measuring by completing a variety of fun activities and experiments. They also practice converting from one unit to another by using multiplication and division. 6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. U

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  • Data and Probability 1. Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them

    Grade 6 Grade 7

    A formulate questions, design studies and collect data about a characteristic D1A6 D1A6 Curriculum Survey members of other classes on cross-curricular topics Complete cross-curricular experiments

    Evaluate the method used 6.SP.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.. 6.SP.5.a Reporting the number of observations. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

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    C interpret circle graphs; create and interpret stem-and-leaf plots Curriculum

    record observations over a week’s time (or more). (for example: weather, temperature)

    circle graphs and stem-and leaf plots

    select, create and use appropriate graphical representation of data, including circle graphs,

    histograms (including scatter plots) and box plots (box and whiskers) D1C8 D1C7 D1A8 Curriculum Study the weather over a period of time. record observations over a week’s time (or more). Use appropriate graphical representation

    of data 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 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.

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    2. Select and use appropriate statistical methods to analyze data Grade 6 Grade 7

    A find the range and measures of center, including median, mode and mean D2A6

    Curriculum survey classmates; organize data (for example: favorite color, food, etc.) record observations over a week’s time (or more). (for example: weather, temperature) create a table or graph based on what was learned.

    Compare the related data sets 6.SP.5.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

    find, use and interpret measures of center and spread, including ranges D2A8 find, use and interpret measures of center, outliers and spread including range and interquartile range D2A7

    Curriculum survey classmates; organize data (for example: favorite color, food, etc.) record observations over a week’s time (or more). (for example: weather, temperature) create a table or graph based on what was learned.

    Compare the related data sets and interpret measures of center 6.SP.5.d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. 6.SP.5.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 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. 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

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  • Data and Probability 6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

    M2E5 convert from one unit to another within a system of linear measurement (customary and metric)

    6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

    G2A5 *use coordinate systems to specify location, describe paths and find distance between points along horizontal and vertical lines

    6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

    G4A5 given a net of a prism or cylinder, identify the 3-dimensional shape

    6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

    G1C5 predict and justify the results of subdividing, combining and transforming shapes

    6.SP.5 Summarize numerical data sets in relation to their context, such as by:

    6.SP.5.b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

    D1C5 *describe methods to collect, organize and represent categorical and numerical data

    6.SP.5.d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

    D2B8 compare different representations of the same data and evaluate how well each representation shows important aspects of the data

  • Data and Probability 3. Develop and evaluate inferences and predictions that are based on data

    Grade 6 Grade 7

    A

    use observations about differences between 2 samples to make conjectures about the populations from which the samples were taken D3A7 A2A8 use symbolic algebra to represent and solve problems that involve linear relationships

    Curriculum Encourage students to plot many data sets and look for relationships in the plots; computer graphing software and graphing calculators can be very helpful in this work. Students should see a range of examples in which plotting data sets suggests linear relationships, nonlinear

    relationships, and no apparent relationship at all. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; 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.EE.4.b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

    use observations about differences between samples to make conjectures about the populations from which the samples were taken

    Curriculum Encourage students to plot many data sets and look for relationships in the plots; computer graphing software and graphing calculators can be very helpful in this work. Students should see a range of examples in which plotting data sets suggests linear relationships, nonlinear relationships, and no apparent relationship at all.

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  • Data and Probability

    4. Understand and apply basic concepts of probability Grade 6 Grade 7

    A use a model (diagrams, list, sample space, or area model) to illustrate the possible outcomes of an event D4A6

    Curriculum Students learn what probability is by predicting the outcome of planned experiments,

    and playing racing games. They use diagrams to illustrate possible outcomes 7.SP.8.b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

    use models to compute the probability of an event and make conjectures (based on theoretical probability) about the results of experiments D4A7 D4A5 *describe the degree of likelihood of events using such words as certain, equally likely and impossible

    Curriculum Students learn what probability is by predicting the outcome of planned experiments, and playing

    racing games. They use diagrams to compute the probability. 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. 7.SP.7.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. 7.SP.7.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. 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers

    indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around indicates an

    event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

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    7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. http://illustrativemathematics.org/illustrations/343

    7.SP.8.a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

    7.SP.8.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?

    http://illustrativemathematics.org/illustrations/343

  • Data and Probability Integrating Faith: All four mathematical operations are recorded in Genesis 1-2 creation account. For example, God made a day and he divided it into evening and morning. He made one day; then He added something to it. He commanded animals to multiply upon the earth, adding numbers of "like things" to His creation. He subtracted a rib from Adam; then He added another human, Eve. Mathematically, addition is the basis of all other operations. So we start there. The first thing God did was to add something to the nothing that existed—the heavens and the earth (Gen. 1:1). His first act was one of addition. Addition is generally used in connection with added blessings, usually a result of obedience. However, sometimes the term “add” has an undesirable connotation such as when God adds a curse as a result of disobedience. Addition and subtraction are operational inverses. Inverse means "reverse order." In other words, it is a doing/undoing relationship. Addition is related to multiplication in that multiplication is simply a quick way to do addition. For example, when we say "3x5," all we're saying is "3 added together 5 times" or "5 added together 3 times." Multiplication is based upon addition. Therefore, scripturally speaking, it too is viewed in terms of blessings. An example of this is God's command to "be fruitful and multiply" to fill the earth. God multiplied His creation in the initial six-day period. Now we are commanded to imitate what He has done, in obedience to His law of replenishing His kingdom and exercising dominion over it. Division is related to multiplication in the same way subtraction is to addition. In division, you unmultiply. In other words, you split up what has been multiplied. Division implies a result. For example, God's division of mankind at the tower of Babel was a result of disobedience to His law. (For a treat, use a concordance to look up all the instances of God's exercising His mathematical laws in the basic operations.) Mathematics, then, demonstrates that God has given us His law with blessings and curses. Addition and multiplication are generally related to blessings as a result of obedience; subtraction and division are often related to curses as a result of disobedience. We can also see God in the mathematical notion of place. Just as God designed a dwelling place for Himself—the Tabernacle—so He designed a dwelling place for numbers. The mathematical notion of place is the understanding that numbers make sense only in their notational context. In other words, just as a string of words in language means nothing without grammar and syntax, so place value determines the meaning of numbers in notation. This is the "decently and in order" principle (1 Cor. 14:40) which is the key to the placement of numbers in their meaningful context. Furthermore, in place value, you have the recognition of the cyclical nature of numbers in the cycle of the moon, year, and seasons—all God-ordained according to His law. From the position of convenience, as well as reflecting order in the universe, we need to realize that numbers do occur in patterns and cycles. God's nature is also revealed through the patterns and cycles of fractions, time, and money. Fractions are essentially division problems. Fractions take a whole and divide it into parts, whether it's one pie divided into eight pieces or one apple divided into halves. This simply reflects that wholes are made up of parts. This is reflective of God's unity and His plurality—three Persons in one God. That aspect of God's creation which we call time, we also enumerate. We divide it into parts of the whole. Time is created by God with a beginning and an ending. However, God does not reside in time, which is the passage of one moment to the next, measuring the duration of actions. Time deals with God's plan for the universe. He works all things after the counsel of His own will (Eph. 1:11). Measurement and passage of time are constant reminders that man is not autonomous. God appoints the time of our birth and time of our death (Heb. 9:27). We cannot escape time. God expects us to look at its patterns and use it His way and for His glory! Like the psalmist, we should exclaim, "What is man that thou art mindful of him? . . . As for man, his days are like grass; as a flower of the field, so he flourishes" (Ps. 8:4; 103:15). Money is another part of God's creation, which we enumerate. Money is simply an application of quantity and quality to the things God has made. It is related to weights and measures, which are numerical qualities of physical objects. In the Scriptures, money is derived from the weight of a valuable substance. Silver, gold, and copper are the metals valued highly enough to be used as coinage. The whole point of a coin is that it is the value of that weight of that particular precious metal. Money is necessary to the functioning of a commercial economy (viz., the accepted value of different animals as sacrifices in Levitical law). Gold and silver are seen as being created by God for use as money. Our modern notion of money being backed by the state is not found in Scripture. Correct use of money is one aspect of exercising dominion for Christ.

    practically in God's universe helps to fulfill His commandments to use all things lawfully. Solving word problems by taking the tools of math and applying them to practical situations is a major way of accomplishing that objective. Such an understanding is required for the exercise of wise stewardship over the resources God has given. If children have nothing but math facts in their heads and don't learn to apply these in a godly way for godly purposes, their knowledge is useless. Math values are taught over and over - "precept upon precept, line upon line, here a little, there a little" (Isa. 28:10). If they do happen to remember, their sin nature will quickly tempt them to

  • Data and Probability choose to forget. So then, if a child is prone to forget, should we stop teaching godly values because we feel "It's too hard" or "They'll never get this . . ."? For example, if some little children are consistently mean to one another, in spite of frequent godly admonitions, are we to simply quit teaching Ephesians 4:32 for awhile, and let them beat each other up in the meantime? The answer is obvious: "No way!" Math is truth because God made it that way. For God's creation is so reflective of His grandeur that it ought to bring us all to our knees shouting: "You, LORD, have made me glad through Your work; I will triumph in the works of Your hands. O LORD, how great are Your works! Your thoughts are very deep" (Ps. 92:4-5). Adapted from : http://www.christcentercurriculum.com/article-ccp-math-roots-in-scripture.php

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Our Savior Christian Academy Curriculum Framework for: Math Our Savior Christian Academy’s “Curriculum Framework for Math” is designed as a tool that will follow the same format for all grades K-4. Each grade level will have a separate section based on classroom structure, and it will be up to each individual teacher to design a lesson plan that fits their classroom needs based on these standards and suggestions. Our Savior Christian Academy’s “Curriculum Framework for Math” is offered to the gl ory of God that it may be a blessing among Lutheran school educators and their students. PHILOSOPHY God has created an orderly, systematic universe. Mathematics is a useful and unique God-given universal language that facilitates the ability to appreciate the created order God has given us and further advances the understanding of our modern, high-tech world. The development of mathematics abilities prepares students for lives of responsible Christian service to His church and the community.
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