Download Standards

Session Seven: Developing Percent Concepts
Common Core Standards Addressed
Grade 3*
Multiply and divide within 100.
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CCSS.Math.Content.3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship
between multiplication and division or properties of operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.
Grade 4
Extend understanding of fraction equivalence and ordering.
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CCSS.Math.Content.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ even though the two fractions
themselves are the same size. Use this principle to recognize and generate equivalent fractions.
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CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g.,
by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.
Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of
comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Understand decimal notation for fractions, and compare decimal fractions.
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CCSS.Math.Content.4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator
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100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express
3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
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CCSS.Math.Content.4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example,
rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
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CCSS.Math.Content.4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize
that comparisons are valid only when the two decimals refer to the same whole. Record the results of
comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Grade 5
Analyze patterns and relationships.
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CCSS.Math.Content.5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent
relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two
patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting
number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and
observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain
informally why this is so.
Understand the place value system.
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CCSS.Math.Content.5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as
much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
*Fractions ,decimals, and percents are introduced at Grade 3, for that reason it is our starting point.
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CCSS.Math.Content.5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number
by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote powers of 10.
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CCSS.Math.Content.5.NBT.A.3 Read, write, and compare decimals to thousandths.
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CCSS.Math.Content.5.NBT.A.3a Read and write decimals to thousandths using base-ten
numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 ×
(1/10) + 9 × (1/100) + 2 × (1/1000).
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CCSS.Math.Content.5.NBT.A.3b Compare two decimals to thousandths based on meanings of
the digits in each place, using >, =, and < symbols to record the results of comparisons.
CCSS.Math.Content.5.NBT.A.4 Use place value understanding to round decimals to any place.
Use equivalent fractions as a strategy to add and subtract fractions.
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CCSS.Math.Content.5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of
fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad +
bc)/bd.)
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CCSS.Math.Content.5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the
same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to
represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess
the reasonableness of answers.
Grade 6
Understand ratio concepts and use ratio reasoning to solve problems.
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CCSS.Math.Content.6.RP.A.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 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received
nearly three votes.”
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CCSS.Math.Content.6.RP.A.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.
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CCSS.Math.Content.6.RP.A.3a Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the
coordinate plane. Use tables to compare ratios.
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CCSS.Math.Content.6.RP.A.3b 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?
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CCSS.Math.Content.6.RP.A.3c Find a percent of a quantity as a rate per 100; solve problems
involving finding the whole, given a part and the percent.
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CCSS.Math.Content.6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate
and transform units appropriately when multiplying or dividing quantities.
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
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CCSS.Math.Content.6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving
division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For
example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the
relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In
general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate
equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with
length 3/4 mi and area 1/2 square mi?.
Compute fluently with multi-digit numbers and find common factors and multiples.
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CCSS.Math.Content.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.