Geometry 
3.G: Reason With Shapes And Their Attributes. 
3.G.1  Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 
4.G: Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles. 
4.G.1  Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. 

4.G.2  Classify twodimensional 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. 

4.G.3  Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. 
Measurement And Data 
3.MD: Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects. 
3.MD.2  Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 
4.MD: Solve Problems Involving Measurement And Conversion Of Measurements From A Larger Unit To A Smaller Unit. 
4.MD.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. 
5.MD: Geometric Measurement: Understand Concepts Of Volume And Relate Volume To Multiplication And To Addition. 
5.MD.3  Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 

5.MD.3.b  A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 
Number And Operations In Base Ten 
3.NBT: Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic.4 
3.NBT.1  Use place value understanding to round whole numbers to the nearest 10 or 100. 
5.NBT: Perform Operations With MultiDigit Whole Numbers And With Decimals To Hundredths. 
5.NBT.7  Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 
Understand The Place Value System. 
5.NBT.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 wholenumber exponents to denote powers of 10. 
4.NBT: Generalize Place Value Understanding For MultiDigit Whole Numbers. 
4.NBT.3  Use place value understanding to round multidigit whole numbers to any place. 
Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic. 
4.NBT.4  Fluently add and subtract multidigit whole numbers using the standard algorithm. 

4.NBT.5  Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit 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. 
Number And Operations—Fractions 
5.NF: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions. 
5.NF.3  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. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? 

5.NF.4  Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 
4.NF: Extend Understanding Of Fraction Equivalence And Ordering. 
4.NF.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. 
Understand Decimal Notation For Fractions, And Compare Decimal Fractions. 
4.NF.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. 

4.NF.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. 
3.NF: Develop Understanding Of Fractions As Numbers. 
3.NF.1  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. 

3.NF.3  Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 

3.NF.3.b  Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. 
Operations And Algebraic Thinking 
3.OA: Multiply And Divide Within 100. 
3.OA.7  Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. 
Represent And Solve Problems Involving Multiplication And Division. 
3.OA.1  Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. 

3.OA.4  Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = � ÷ 3, 6 × 6 = ?. 
4.OA: Gain Familiarity With Factors And Multiples. 
4.OA.4  Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1–100 is prime or composite. 
5.OA: Write And Interpret Numerical Expressions. 
5.OA.1  Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 

5.OA.2  Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. 