MAFS.4.G.1.2
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Draw and identify lines and angles, and...__

MAFS.4.G.1.3
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Draw and identify lines and angles, and...__

MAFS.4.MD.1.1
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

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**Content Complexity:**
Level 1: Recall

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve problems involving measurement and...__

MAFS.4.MD.1.2
Use the four operations to solve word problems1 involving distances, intervals of time, and money, including problems involving simple fractions or decimals2. Represent fractional quantities of distance and intervals of time using linear models. (1See glossary Table 1 and Table 2) (2Computational fluency with fractions and decimals is not the goal for students at this grade level.)

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve problems involving measurement and...__

MAFS.4.MD.1.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Solve problems involving measurement and...__

MAFS.4.MD.2.4
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Represent and interpret data. (Supporting...__

MAFS.4.MD.3.5
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles.An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

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**Content Complexity:**
Level 1: Recall

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Geometric measurement: understand concepts...__

MAFS.4.MD.3.7
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Geometric measurement: understand concepts...__

MAFS.4.NBT.1.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 10 by applying concepts of place value and division.

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**Content Complexity:**
Level 1: Recall

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Generalize place value understanding for...__

MAFS.4.NBT.1.2
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using , =, and symbols to record the results of comparisons.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Generalize place value understanding for...__

MAFS.4.NBT.2.4
Fluently add and subtract multi-digit whole numbers using the standard algorithm.

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**Content Complexity:**
Level 1: Recall

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Use place value understanding and properties...__

Remarks/Examples:

**Fluency Expectations or Examples of Culminating Standards **

Students’ work with decimals (4.NF.3.5–3.7) depends to some extent on concepts of fraction

MAFS.4.NBT.2.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Use place value understanding and properties...__

Remarks/Examples:

**Examples of Opportunities for In-Depth Focus **

When students work toward meeting this standard, they combine prior understanding of multiplication with deepening understanding of the base-ten system of units to express the product of two multi-digit numbers as another multi-digit number. This work will continue in grade 5 and culminate in fluency with the standard algorithms in grade 6.

MAFS.4.NBT.2.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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**More Information**

**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Use place value understanding and properties...__

Remarks/Examples:

**Examples of Opportunities for In-Depth Focus **

When students work toward meeting this standard, they combine prior understanding of multiplication and division with deepening understanding of the base-ten system of units to find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors. This work will develop further in grade 5 and culminate in fluency with the standard algorithms in grade 6.

MAFS.4.NF.1.1
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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**Content Complexity:**
Level 3: Strategic Thinking & Complex Reasoning

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Extend understanding of fraction equivalence...__

Remarks/Examples:

**Examples of Opportunities for In-Depth Focus **

Extending fraction equivalence to the general case is necessary to extend arithmetic from whole numbers to fractions and decimals.

MAFS.4.NF.1.2
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.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Extend understanding of fraction equivalence...__

MAFS.4.NF.2.3
Understand a fraction a/b with a 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.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.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.

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**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Build fractions from unit fractions by...__

Remarks/Examples:

**Examples of Opportunities for In-Depth Focus **

This standard represents an important step in the multi-grade progression for addition and subtraction of fractions. Students extend their prior understanding of addition and subtraction to add and subtract fractions with like denominators by thinking of adding or
subtracting so many unit fractions.

MAFS.4.NF.2.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 (1/4), recording the conclusion by the equation 5/4 = 5 (1/4).Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b) = (n a)/b.)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. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

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**More Information**

**Content Complexity:**
Level 2: Basic Application of Skills & Concepts

**Date Adopted/Revised:**
02/14

**Belongs to:**
__Build fractions from unit fractions by...__

Remarks/Examples:

**Examples of Opportunities for In-Depth Focus **

This standard represents an important step in the multi-grade progression for multiplication and division of fractions. Students extend their developing understanding of multiplication to multiply a fraction by a whole number.

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