Fractions Progressions by Gabby Goerlinger

Unit Fractions

goerlg58 — 2019-11-04 17:14:45 UTC

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Fractions on a Number Line

goerlg58 — 2019-11-04 17:16:38 UTC

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Fractions as numbers on a number line

goerlg58 — 2019-11-04 17:19:36 UTC

Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

Fractions as numbers on a number line

goerlg58 — 2019-11-04 17:20:32 UTC

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Equivalence of Fractions

goerlg58 — 2019-11-04 17:23:58 UTC

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Equivalence of Fractions

goerlg58 — 2019-11-04 17:27:15 UTC

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Extend Understanding of Fraction Equivalence and Ordering

goerlg58 — 2019-11-04 17:30:25 UTC

Understand decimal notation for fractions, and compare decimal fractions

goerlg58 — 2019-11-04 17:32:28 UTC

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.² For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Multiplying a Fraction by a Whole Number

goerlg58 — 2019-11-04 17:57:20 UTC

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Multiplying a Fraction by a Whole Number

goerlg58 — 2019-11-04 17:58:05 UTC

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Multiplying a Fraction by a Whole Number

goerlg58 — 2019-11-04 17:58:30 UTC

Understand a fraction a/b as a multiple of 1/b.

Build Fractions from Unit Fractions

goerlg58 — 2019-11-04 18:09:28 UTC

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem

Build Fractions from Unit Fractions

goerlg58 — 2019-11-04 18:11:09 UTC

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Build Fractions from Unit Fractions

goerlg58 — 2019-11-04 18:12:20 UTC

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

Build Fractions from Unit Fractions

goerlg58 — 2019-11-04 18:13:44 UTC

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Extend understanding of fraction equivalence and ordering

goerlg58 — 2019-11-04 18:15:37 UTC

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.

Apply and extend previous understandings of multiplication and division.

goerlg58 — 2019-11-04 18:18:48 UTC

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Apply and extend previous understandings of multiplication and division.

goerlg58 — 2019-11-04 18:19:42 UTC

Interpret division of a whole number by a unit fraction, and compute such quotients.

Apply and extend previous understandings of multiplication and division.

goerlg58 — 2019-11-04 18:20:14 UTC

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

Apply and Extend previous understandings of multiplication and division.

goerlg58 — 2019-11-04 18:27:01 UTC

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Interpret Multiplication as scaling

goerlg58 — 2019-11-04 18:29:38 UTC

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

Interpret multiplication as scaling

goerlg58 — 2019-11-04 18:33:02 UTC

Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

goerlg58 — 2019-11-04 18:34:19 UTC

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

goerlg58 — 2019-11-04 18:34:35 UTC

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.

Apply and Extend previous understandings of multiplication and division

goerlg58 — 2019-11-04 18:39:15 UTC

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Use equivalent fractions as a strategy to add and subtract fractions.

goerlg58 — 2019-11-04 18:43:57 UTC

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.

Use equivalent fractions as a strategy to add and subtract fractions.

goerlg58 — 2019-11-04 18:44:22 UTC

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.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

goerlg58 — 2019-11-04 18:47:05 UTC

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.