5th Grade

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GGeometry Standards
GGeometry Standards
Geometry Logo. Includes four pictures of solids on an orange background.
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
G.1.1
Geometry Logo. Includes four pictures of solids on an orange background.
Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures.
G.2.4
Geometry Logo. Includes four pictures of solids on an orange background.
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
G.1.2
Geometry Logo. Includes four pictures of solids on an orange background.
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
G.2.3
MDMeasurement and Data Standards
MDMeasurement and Data Standards
Measurement and Data Logo. Includes a measuring tape symbol on a green background.
Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
MD.1.1
Measurement and Data Logo. Includes a measuring tape symbol on a green background.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 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.
MD.3.3.b
Measurement and Data Logo. Includes a measuring tape symbol on a green background.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. b. Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
MD.3.5.b
Measurement and Data Logo. Includes a measuring tape symbol on a green background.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
MD.2.2
Measurement and Data Logo. Includes a measuring tape symbol on a green background.
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
MD.3.4
Measurement and Data Logo. Includes a measuring tape symbol on a green background.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
MD.3.5.c
Measurement and Data Logo. Includes a measuring tape symbol on a green background.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
MD.3.3.a
Measurement and Data Logo. Includes a measuring tape symbol on a green background.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
MD.3.5.a
NBTNumbers and Operations in Base Ten Standards
NBTNumbers and Operations in Base Ten Standards
Numbers and Base Ten Logo
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.
NBT.1.1
Numbers and Base Ten Logo
Read, write, and compare decimals to thousandths. b. Compare two decimals to thousandths based on meanings of the digits in each place, using greater than, equal to, and less than symbols to record the results of comparisons.
NBT.1.3.b
Numbers and Base Ten Logo
Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.
NBT.2.6
Numbers and Base Ten Logo
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.
NBT.1.2
Numbers and Base Ten Logo
Use place value understanding to round decimals to any place.
NBT.1.4
Numbers and Base Ten Logo
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.
NBT.2.7
Numbers and Base Ten Logo
Read, write, and compare decimals to thousandths. a. 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).
NBT.1.3.a
Numbers and Base Ten Logo
Fluently multiply multi-digit whole numbers using the standard algorithm.
NBT.2.5
NFNumbers and Operations - Fraction Standards
NFNumbers and Operations - Fraction Standards
Fractions Logo. Includes a pie chart on a pink background.
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.)
NF.1.1
Fractions Logo. Includes a pie chart on a pink background.
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. 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. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
NF.2.4.a
Fractions Logo. Includes a pie chart on a pink background.
Interpret multiplication as scaling (resizing), by: b. 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.
NF.2.5.b
Fractions Logo. Includes a pie chart on a pink background.
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
NF.2.7.b
Fractions Logo. Includes a pie chart on a pink background.
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. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 is less than 1/2.
NF.1.2
Fractions Logo. Includes a pie chart on a pink background.
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. b. 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.
NF.2.4.b
Fractions Logo. Includes a pie chart on a pink background.
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
NF.2.6
Fractions Logo. Includes a pie chart on a pink background.
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. c. 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. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
NF.2.7.c
Fractions Logo. Includes a pie chart on a pink background.
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 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
NF.2.3
Fractions Logo. Includes a pie chart on a pink background.
Interpret multiplication as scaling (resizing), by: a. 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.
NF.2.5.a
Fractions Logo. Includes a pie chart on a pink background.
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
NF.2.7.a
OAOperations and Algebraic Thinking Standards
OAOperations and Algebraic Thinking Standards
Operations and Algebraic Thinking Logo. Includes symbols for add, subtract, multiply, divide on a blue background.
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
OA.1.1
Operations and Algebraic Thinking Logo. Includes symbols for add, subtract, multiply, divide on a blue background.
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.
OA.1.2
Operations and Algebraic Thinking Logo. Includes symbols for add, subtract, multiply, divide on a blue background.
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.
OA.2.3
Additional Course Resources
Additional Course Resources
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FAIM Assessment Form 1A
FAIM Form 1A
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FAIM Assessment Form 2B
FAIM Form 2B
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FAIM Answer Key Form 2A
FAIM Answer Key 2A
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FAIM Assessment Form 1B
FAIM Form 1B
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FAIM Answer Key Form 1A
FAIM Answer Key 1A
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FAIM Answer Key Form 2B
FAIM Answer Key 2B
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FAIM Assessment Form 2A
FAIM Form 2A
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FAIM Answer Key Form 1B
FAIM Answer Key 1B
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Click to access several fraction videos to help with fraction instruction.
Fraction Video Resources