| 1 |
- divide whole objects into parts and identify and describe, through investigation, equal-sized parts of the whole, using fractional names (e.g., halves; fourths or quarters).
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| 2 |
- determine, through investigation using concrete materials, the relationship between the number of fractional parts of a whole and the size of the fractional parts (e.g., a paper plate divided into fourths has larger parts than a
paper plate divided into eighths) (Sample problem: Use paper squares to show which is bigger, one half of a square or one fourth of a square.).
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| 2 |
- regroup fractional parts into wholes, using concrete materials (e.g., combine nine fourths to form two wholes and one fourth);
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| 3 |
- divide whole objects and sets of objects into equal parts, and identify the parts using fractional names (e.g., one half; three thirds; two fourths or two quarters), without using numbers in standard fractional notation.
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| 4 |
- represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of
fractional parts being considered;
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| 4 |
- count forward by halves, thirds, fourths, and tenths to beyond one whole, using concrete materials and number lines (e.g., use fraction circles to count fourths: “One fourth, two fourths, three fourths, four fourths, five
fourths, six fourths, ...”);
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| 5 |
- represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using
standard fractional notation;
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| 5 |
- demonstrate and explain the concept of equivalent fractions, using concrete materials (e.g., use fraction strips to show that 3⁄4
is equal to 9⁄12);
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| 6 |
- represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation;
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| 7 |
- use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals;
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| 7 |
- add and subtract fractions with simple like and unlike denominators, using a variety of tools and algorithms;
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| 8 |
- represent, compare, and order rational numbers;
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| 8 |
- use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
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| 8 |
- solve problems involving addition, subtraction, multiplication, and division with simple fractions.
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| 9D |
- simplify numerical expressions involving integers and rational numbers, with and without the use of technology;
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| 9D |
- solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;
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| 9D |
- solve for the unknown value in a proportion, using a variety of methods (e.g., concrete materials, algebraic reasoning, equivalent ratios, constant of proportionality) (Sample problem: Solve x⁄4 = 15⁄20.);
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| 9P |
- solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms
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| 9P |
- simplify numerical expressions involving integers and rational numbers, with and without the use of technology;*
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