MP 1. Make Sense of Problems and Persevere in Solving Them

Grade Five—Mathematics

Mathematical Practices (MP)

MP 1. Make sense of problems and persevere in solving them.

MP 2. Reason abstractly and quantitatively.

MP 3. Construct viable arguments and critique the reasoning of others.

MP 4. Model with mathematics.

MP 5. Use appropriate tools strategically.

MP 6. Attend to precision.

MP 7. Look for and make use of structure.

MP 8. Look for and express regularity in repeated reasoning.

Operations and Algebraic Thinking (OA)
Write and interpret numerical expressions
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
OA 5.1 (DOK 1)
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols / Use order of operations including parentheses, brackets, or braces
Evaluate expressions using the order of operations (including using parentheses, brackets, or braces) / Lesson 24, 48
*No direct teaching of brackets or braces
*Direct teaching of order of operations is weak, NEEDS TO BE TAUGT AT LESSON 24 and put in the math journal / CT5, CT6, CT7, CT8, CT9, CT12, CT13/ET1, CT14, CT15/ET2/ET3, CT17/ET4, CT20/ET7, CT21/ET8, CT22, CT23/ET9/ET10
OA 5.2 (DOK 1, 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 X (8+7). Recognize that 3 X (18932 +921) is three times as large as 18932 + 921 without having to calculate the indicated sum or product. / Write numerical expressions for given numbers with operation words.
Write operation words to describe a given numerical expression
Interpret numerical expressions without evaluating them
Solve addition and subtraction word problems within 10 / Lesson 13, 24, 49 weak, 51
Keep a math journal that demonstrates the vocabulary with examples and notes / CT3
Analyze patterns and relationships
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
OA 5.3 (DOK 1, 2)
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. / Generate two numerical patterns using two given rules
Form ordered pairs consisting of corresponding terms for the two patterns
Graph generated ordered pairs on a coordinate plane
Analyze and explain the relationships between corresponding terms in the two numerical patterns / Investigation 4, 6, 8
Standards SuccessExtension Activity 3 / ET3
Gain familiarity with factors and multiples.
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
OA 5.4 (DOK 1, 2)
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 one-digit number.
Determine whether a given whole number in the range 1-100 is prime or composite. / 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 one-digit number.
Determine whether a given whole number in the range 1-100 is prime or composite. / ET3
Number and Operations in Base Ten (NBT)
Understand the place value system
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
NBT 5.1 (DOK 1)
Recognize that 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. / 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. / Lesson 3, 7, 52, 64, 106 / MATH PACKET
NBT 5.2 (DOK 1)
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. / Represent powers of 10 using whole number exponents
Translate between powers of 10 written as 10 raised to a whole number exponent, the expanded form, and standard notation
Explain the patterns in the number of zeros of the product when multiplying a number by powers of 10
Explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 10 / Lesson 29,
L. 64, 78, 106
111, 118
* Base ten needs to be directly taught and supplemented / CT23/ET9/ET10
NBT 5.3 (DOK 1)
Read, write, and compare decimals to thousandths. / Read and write decimal to thousandths using base-ten numerals, number names, and expanded form
Use <, =, and > symbols to record the results of comparisons between decimals
Compare two decimals to the thousandths, based on the place value of each digit / Examples of expanded form:
347.392 = (3 × 100) + (4 ×10) + (7 × 1) + (3 × 110) + (9 × 1100) + (2 × 11000 ).
347.392 = (3 x 100) + (4 x 10) + (7 x1) + (3 x 0.1) + (9 x 0.01) + (2 x 0.001)
347.392300 + 40 + 7 + 0.3 + 0.09 + 0.002 / MATH PACKET
NBT 5.3a (DOK 1)
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392=3X100+4X10+7X1+3 (1/10) + 9X (1/100) + 2 X (1/1000). / Read and write decimal to thousandths using base-ten numerals, number names, and expanded form / Lesson 64,66, 67, 68, 106 / CT14
NBT 5.3b (DOK 1)
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. / NBT 5.3b (DOK 1)
Use >, = and < symbols to record the results of comparisons between decimals
Compare two decimals to the thousandths, based on the place value of each digit / Lesson 69, 70, 71, 100, 106 / CT14, CT15/ET2/ET3, CT22
NBT 5.4 (DOK 1)
Use place value understanding to round decimals to any place. / Use knowledge of base ten and place value to round decimals to any place / Lesson 52, 62, 64, 88, 104, 106, 108
Standards success Activity 8 / CT21/ET8, CT22, CT23/ET9/ET10
Perform operations with multi-digit whole numbers and with decimals to hundredths.
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
NBT 5.5 (DOK 1)
Fluently multiply multi-digit whole numbers using the standard algorithm. / Mastery of the standard multiplication algorithm is expected at this stage. / Lesson 17, 29, 51, 55, 56 / CT6, CT7, CT8, CT9, CT10, CT11, CT12, CT13/ET1, CT14, CT17/ET4
NBT 5.6 (DOK 1, 2)
Using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. / The standard division algorithm is a 6th-grade standard. (6.NS.2) / Lesson 54
Lesson 92
Lesson 94
Standards Success Activity book: Activity 6 / CT11, CT12, CT13/ET1, CT17/ET4/ET6, CT19, CT20/ET7,CT21/ET8, CT23/ET9/ET10
NBT 5.7 (DOK 1, 2, 3)
Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, add, subtract, multiply, and divide decimals to hundredths.
Relate the strategy to a written method and explain the reasoning used. / 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 to solve decimal operation calculations / Lesson 13, 17, 26, 29, 51, 54, 56, 73, 99, 102, 109, 110, 111, 118, 119 / CT15/ET2/ET3, CT16, CT17/ET4, CT19, CT20/ET7, CT21/ET8, CT22, CT23/ET9/ET10
Number and Operations—Fractions (NF)
Use equivalent fractions as a strategy to add and subtract fractions.
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
NF 5.1 (DOK 1)
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.) / Solutions focus on equivalence, which may include, but does not require simplest form.
Example: 23 + 54 = 812 + 1512 = 2312. (In general, ????+???? = ??? + ?????? ) / Lesson 116 / MATH PACKET
NF 5.2 (DOK 1, 2, 3)
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 results 2/5 + 1/2 =3/7, by observing that 3/7 < 1/2. / Example of using a benchmark fraction to assess reasonableness: Recognize an incorrect result 25 + 12 = 37 by observing that 37 < 12. / Lesson 23, 29, 41, 43, 59, 60, 63, 75, 91, 116 / CT13/ET1
Apply and extend previous understandings of multiplication and division to multiply and divide fractions
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
NF 5.3 (DOK 1, 2)
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-poind sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? / 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? / Lesson 20, 40, 43, 46, 47, 49, 58, 91, 95 / CT13/ET1, CT14
NF 5.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
NF 5.4a (DOK 1, 2)
Interpret the product (a/b) X q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a X q ÷ b. For example, use a visual fraction model to show (2/3) X 4 = 8/3, and create a story context for this equation. Do the same with (2/3) X (4/5) = 8/15. (In general, (a/b) X (c/d) =ac/bd.) / Example: Use a visual fraction model to show
and create a story context for this equation.
Do the same with / Lesson 20, 40, 46, 76, 86 / MATH PACKET
NF 5.4 a
CT12, CT17/ET4, CT18/ET5/ET6, CT19, CT20/ET7, CT21/ET8, CT22, CT23/ET9/ET10
NF 5.4b (DOK 1, 2)
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. / Example:
/ Lesson 76/ Standards Success Activity 2, 86 (need more)
* In lesson 86 insert teaching the fractional area of a rectangle / ET2
NF 5.5a (DOK 1, 2, 3)
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. / Example: 22 x 36 < 22 x 50, because 36 < 50.
<14
Because1/7 is less than 1.
/ Lesson 86
Standards success Activity 9
*Need More / MATH PACKET
NF 5.5A
ET9
NF 5.5b (DOK 1, 2, 3)
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; / / Lesson 86, 120
Standards success Activity 9
* Need more / ET9
NF 5.5c (DOK 1, 2, 3)
Relating the principle of fraction equivalence a/b = (nXa)/(nXb) to the effect of multiplying a/b by 1. / 23 x 2/2 = 23 because 2/2 = 1.
/ Lesson 86, 120
Standards success Activity 9
* Need more / ET9
NF 5.6 (DOK 1, 2)
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. / See examples for 5.NF.4.
/ Lesson 76, 86, 120
Standards success Activity 10
* Need more / ET10
NF 5.7 Apply and extend previous understanding so division to divide unit fractions by whole numbers and whole numbers by unit fractions.
NF 5.7a (DOK 1, 2)
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) X 4 = 1/3. / Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
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. / Lesson 87, 96
Standard Success Activity 5
* Need more / NF5.7
MATH PACKET
NF5.7 A
ET5
NF 5.7b (DOK 1, 2)
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. / 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.
Interpret division of a whole number by a unit fraction and justify your answer using the relationship between multiplication and division, and by representing the quotient with a visual fraction model / Lesson 87, 96
Standard Success Activity 5
* Need more / ET5
NF 5.7c (DOK 1, 2)
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? / Examples: 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? / Lesson 87, 92, 93, 94, 95
Standards Success Activity 5
* Need more / ET5
Measurement and Data (MD)
Convert like measurement units within a given measurement system.
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
MD 5.1 (DOK 1, 2)
Convert among different-sized standard measurement units 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. / Include standard and metric systems.
Example: Convert 5 cm to 0.05 m
Solve multi-step, real world problems that involve converting units / Lesson 44, 46, 47, 65, 66, 74, 77, 85
* Beginning with L. 44 start to extend application of measuring (using packet we put together this year) / CT15, CT16, CT19, CT20/ET7, CT22
Represent and interpret data
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
MD 5.2 (DOK 1, 2)
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/3, 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. / 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. / Lesson 74
Investigation 5
Standards success Activity 4 / ET4,
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition
Standards / Skills / Suggested sample teacher activities/materials / Assessment / Notes
MD 5.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
MD 5.3a (DOK 1)
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. / Recognize that volume is the measurement of the space inside a solid three-dimensional figure
Recognize a unit cube has 1 cubic unit of volume and is used to measure volume of three-dimensional shapes / Lesson 103 / MATH PACKET
MD 5.3b 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 5.3b (DOK 1)
Recognize any solid figure packed without gaps or overlaps and filled with n unit cubes indicates the total cubic units or volume / Lesson 103 / MATH PACKET
MD 5.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. / MD 5.4 (DOK 1, 2)
Measure volume by counting unit cubes, cubic cm, cubic in, cubic ft, and improvised units / Lesson 103 / MATH PACKET
MD 5.5 (DOK 1, 2)
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
MD 5.5a (DOK 1, 2) 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. / Identify a right rectangular prism
Multiply the three dimensions in any order to calculate volume (Commutative and Associative properties)
Know that “B” is the area of the base
Recognize volume as additive
Develop volume formula for a rectangle prism by comparing volume when filled with cubes to volume by multiplying the height by the area of the base, or when multiplying the edge lengths (L x W c H)
Apply the following formulas to right rectangular prisms having whole number edge lengths in the context of real world mathematical problems : Volume =length x width x height Volume = area of base x height / Lesson 103, 104
Standards Success Activity 7 / MD 5.5,MD 5.5aMATH PACKET
MD 5.5b Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. / Solve real world problems by decomposing a solid figure into two non-overlapping right rectangular prisms and adding their volumes / Lesson 103, 104
MD 5.5c Apply the formulas V = l x w x h and V = v x 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. / Find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes / ET7, CT21/ET8, CT22
MD 5.5d (DOK 1, 2)
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. / Recognize volume as additive