# Operations and Algebraic Thinking OA

Hale County Schools

Grade 5 Math

**Hale County Schools**

Math 2010 COS

**Grade 5 Overview**

2013 – 2014

**Operations and Algebraic Thinking [OA] **

• Write and interpret numerical expressions.

• Analyze patterns and relationships.

**Number and Operations in Base Ten [NBT] **

• Understand the place value system.

• Perform operations with multi-digit whole numbers and with

decimals to hundredths.

**Number and Operations – Fractions [NF] **

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

• Apply and extend previous understandings of multiplication and

division to multiply and divide fractions.

**Measurement and Data [MD] **

• Convert like measurement units within a given measurement system.

• Represent and interpret data.

• Geometric measurement: understand concepts of volume and relate

volume to multiplication and to addition.

Geometry [G]

• Graph points on the coordinate plane to solve real-world and mathematical

problems.

• Classify two-dimensional figures into categories based on their properties.

Key:

** CCRS indicates 2010 Math Course of Study**

1st 9 weeks

Aug 19 – Oct 17

Ch 1 – 15 days

Aug 19 – Sept 9 / 1

8 / Lessons:1.1, 1.2

Lesson: 1.3, 1.8, 1.9

Lessons: 1.4, 1.5 / 5.4 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. [5-NBT1]

5.9Find 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. [5-NBT6]

5.5Explain 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. [5-NBT2] / determine that a digit represents ten times what it would be in the place to its right and one-tenth to its left.

divide four digit whole numbers by two digit whole numbers.

show the results of division using equations, arrays, or area models.

explain the pattern in placement of a decimal point using a power of ten. / 1.1 multiply, place value

1.2 period

1.3 Distributive Property, factor, product

1.8 inverse operations, Distributive Property, quotient

1.4 Base, exponent

Date / MP / Resource / CCRS / Student Can / Vocabulary

Chapter 1

(Continued) / Lessons: 1.6, 1.7

Lesson: 1.10

Lessons: 1.11, 1 / 5.8Fluently multiply multi-digit whole numbers using the standard algorithm. [5-NBT5]

5.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5-OA2]

5.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5-OA1] / multiply multi-digit of whole numbers.

write simple numerical expressions.

explain simple numerical expressions without finding the answer.

use algebraic expressions.

evaluate algebraic expressions using symbols. / 1.6 estimate

1.10 numerical expression

1.11 evaluate, order of operations

Date / MP / Resource / CCRS / Student Can / Vocabulary

1st 9 Weeks

**Aug 19 – Oct 17**

Ch 2 - 12 days

Sept 10 – Sept 25 / 1

4

7 / Lessons: 2.1 – 2.6, 2.8, 2.9

Lesson: 2.7 / 5.9 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. [5-NBT6]

5.13 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. [5-NF3] / divide four digit whole numbers by two digit whole numbers.

show the results of division using equations, arrays, or area models.

explain the results of division using equations, arrays, or area models.

explain a fraction as division of the numerator by the denominator.

solve word problems involving division and write the remainder as a fraction. / 2.1 dividend, divisor, quotient, remainder

2.2 inverse operations

2.3 partial quotients

2.4partial quotients

2.5 compatible numbers, estimate

Date / MP / Resource / CCRS / Student Can / Vocabulary

1st 9 Weeks

**Aug 19 – Oct 17**

Ch 3 –15 days

Sept 26 – Oct 16 / 3

8 / Lesson: 3.1

Lesson: 3.2

Lessons: 3.3

Lesson: 3.4

Lessons: 3.5- 3.12 / 5.4 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. [5-NBT1]

5.6.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). [5-NBT3a]

5.6.b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [5-NBT3b]

5.7 Use place value understanding to round decimals to any place. [5-NBT4]

5.10 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. [5-NBT7] / determine that a digit represents ten times what it would be in the place to its right and one-tenth to its left.

read decimals to thousandths using numerals, number names, and expanded form.

write decimals to thousandths using numerals, number names, and expanded form.

compare two decimals to thousandths using ˂, ˃, and =.

round decimals to any place.

add, subtract, multiply, and divide decimals to the hundredths using various methods.

explain how the answer was found. / 3.1thousandth, hundredth, tenth, place value

3.4 round

3.7 benchmark

3.10 sequence, term

Date / MP / Resource / CCRS / Student Can / Vocabulary

1st 9 Weeks

1 day – Oct 17

Chapter 4 / 7

8 / Lessons: 4.1, 4.3, 4.4, 4.7, 4.8

Lesons: 4.2 - 4.8 / 5.5Explain 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. [5-NBT2]

5.10 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. [5-NBT7]. / explain the powers of ten.

explain the pattern in placement of a decimal point using a power of ten.

add, subtract, multiply, and divide decimals to the hundredths using various methods.

explain how the answer was found. / 4.1. decimal, hundredths, multiplication, ones. Pattern, place value, product, tenths, thousandths

4.4 expanded form

Date / MP / Resource / CCRS / Student Can / Vocabulary

2nd 9 Weeks

Oct 18 – Dec 20

Ch 4 – 10 days

Oct 18 – Oct 31 / 4

7 / Lessons: 5.1, 5.4, 5.6

Lessons: 5.2- 5.8 / 5.5 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. [5-NBT2]

5.10 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. [5-NBT7] / explain the powers of ten.

explain the pattern in placement of a decimal point using a power of ten.

add, subtract, multiply, and divide decimals to the hundredths using various methods.

explain how the answer was found. / 5.1 decimal, decimal point, dividend, divisor, exponent, quotient

5.2 hundredth, tenth

5.3 compatible numbers, estimate

5.7 equivalent fractions, remainder

Date / MP / Resource / CCRS / Student Can / Vocabulary

2nd 9 Weeks

Oct 18 – Dec 20

Ch 4–10 days

Oct 18 – Oct 31 / 2

7 / Lessons: 5.1, 5.4, 5.6

Lessons: 5.2- 5.8 / 5.5Explain 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. [5-NBT2]

5.10 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. [5-NBT7]

5.13. 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. [5-NF3] / explain the powers of ten.

explain the pattern in placement of a decimal point using a power of ten.

add, subtract, multiply, and divide decimals to the hundredths using various methods.

explain how the answer was found.

explain a fraction as division of

the numerator by the denominator.

solve word problems involvingdivision and write the remainder as a fraction. / 5.1 decimal, decimal point, dividend, divisor, exponent, quotient

5.2 hundredth, tenth

5.3 compatible numbers, estimate

5.7 equivalent fractions, remainder

Date / MP / Resource / CCRS / Student Can / Vocabulary

2nd 9 weeks

**Oct 18 – Dec 20**

Ch 6– 13 days

Nov 19 – Dec 9 / 2

4 / Lessons: 6.1- 6.3, 6.9

Lessons: 6.4- 6.8, 6.10 / 5.12 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. [5-NF2]

5.11 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. [5-NF1] / solve word problems involving addition and subtraction of fractions including unlike denominators.

use benchmark fractions and number sense to estimate.

check for the reasonableness of my answers.

use equivalent fractions to add fractions with unlike denominators.

use equivalent fractions to subtract fractions with unlike denominators. / 6.1 sum

6.2 difference

6.3 benchmark

6.4 common denominator, common multiples, equivalent fractions

6.5 simplest form

6.6 mixed number

Date / MP / Resource / CCRS / Student Can / Vocabulary

2nd 9 Weeks

Oct 18 – Dec 20

(Ch 7- 9 days)

Dec 10 – Dec 20 / 3

5 / Lessons: 7.1-7.3, 7.6, 7.8

Lessons: 7.4, 7.7

Lessons: 7.5, 7.8

Lessons: 7.5, 7.8, 7.10

Lesson: 7.9 / 5.14.a Interpret the product (a/b) × q as a parts of a partition of q into b equal part equivalently, as the result of a sequence of operations a × q ÷ b. [5-NF4a]

5.14.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. [5-NF4b]

5.15.aInterpret multiplication as scaling (resizing), by: 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. [5-NF5a]

5.15.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. [5-NF5b]

5.16 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5-NF6] / explain the product of a whole number and a fraction using a visual fraction model.

explain the product of two fractions using a visual fraction model.

create a story to describe the equations.

find the area of a rectangle with fractional sides by tiling.

show the area is the same as would be found through multiplication.

multiply fractional side lengths to find the area of rectangles. show fraction products as rectangular areas.

compare the size of a product to the size of one factor based on the size of the other factor without multiplying.

explain why multiplying a number by a fraction greater than 1 results in a product greater than the number.

explain why multiplying a number by a fraction less than 1 results in a product smaller than the number.

solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models. / 7.1 denominator, numerator, product

7.4 equivalent fraction

7.6 simplest form

7.7 mixed number

Date / MP / Resource / CCRS / Student Can / Vocabulary

3rd 9 Weeks

Jan 3 – Mar 11

Ch 7 – 4 days

Jan 3 – Jan 8 / 3

5 / 5.16. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5-NF6]

15b. 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. [5-NF5b] / solve real-world problems

involving multiplication of fractions and mixed numbers using visual fraction models

compare the size of a product to the size of one factor based onthe size of the other factor withoutmultiplying.

explain why multiplying a number by a fraction greater than 1results in a product greater than thenumber.

explain why multiplying a number by a fraction less than 1results in a product smaller than thenumber

Date / MP / Resource / CCRS / Student Can / Vocabulary

3rd 9 Weeks

Jan 3 – Mar 11

(Ch 8 - 8 days)

Jan 9 – Jan 21 / 2

4 / Lessons: 8.1

Lessons: 8.1, 8.2

Lessons: 8.4, 8.5

Lesson: 8.3 / 5.17 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (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.) [5-NF7]

5.17a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. [5-NF7a]

5.17.b Interpret division of a whole number by a unit fraction, and compute such quotients. [5-NF7b

5.17.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. [5-NF7c ]

5.13 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. [5-NF3] / solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models.

find the quotient of a division problem for a unit fraction and whole number.

explain division of a unit fraction by a whole number.

find the quotient of a division problem for a unit fraction andwhole number.

explain division of a whole number by unit fraction.

find the quotient of a division problem for a whole number and a unit fraction.

solve real world problems involving division of unit fractions by whole numbers.

solve real world problems involving division of whole numbers by unit fractions.

explain a fraction as division of the numerator by the denominator.

solve word problems involving division and write the remainder as a fraction. / 8.1 dividend, fraction, quotient, whole number

8.5 equation

Date / MP / Resource / CCRS / Student Can / Vocabulary

3rd 9 Weeks

Jan 3 – Mar 11

Ch 9 - 10 days

Jan 22 – Feb 4 / 4

8 / Lesson: 9.1

Lesson: 9.2

Lessons: 9.3, 9.4

Lessons: 9. 5- 9.7 / 5.19 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. [5-MD2]

5.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.[5-OA1]

5.17a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. [5-NF7a]

5.23 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). [5-G1]

5.24 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. [5-G2]

5.3 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. [5-OA3] / make a line plot to display a set of measurements in fractions of a unit.

solve problems with the information on the line plot.

plot a given point on the plane using ordered pairs.

represent and interpret real world and math problems by graphing points on the coordinate plane.

create a function table (input/output).

explain the rule.

graph the ordered pairs.

explain my graph. / 9.1 data, line plot

9.2 ordered pair, origin, x-axis, x-coordinate, y-axis, y-coordinate

9.3 degree Fahrenheit (°F)

9.4 interval, line graph, scale

Date / MP / Resource / CCRS / Student Can / Vocabulary

3rd 9 Weeks

Jan 3 – Mar 11

(Ch 10 - 10 days)

Feb 5 – Feb 18 / 1

7 / Lessons: 10.1 -10.7 / 5.18 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. [5-MD1] / do measurement conversions within the same system.

use these conversions to solve multi-step, real world problems. / 10.1 foot, inch, mile, yard

10.2 capacity, cup, fluid, ounce, gallon, pint, quart, tablespoon, teaspoon

10.3 ounce, pound, ton, weight

10.5 dekameter, centimeter, decimeter, gram, kilogram, kilometer, liter, mass, meter, milligram, millimeter

10.7 elapsed time

Date / MP / Resource / CCRS / Student Can / Vocabulary

3rd 9 Weeks

Jan 3 – Mar 11

AMSTI

15 days

Feb 19 – Mar 11 / AMSTI

Fractions

Date / MP / Resource / CCRS / Student Can / Vocabulary

4th 9 Weeks

Mar 12 – May 23

Ch 11 - 15 days

Mar 12 – Apr 19 / 4

5

6 / Lessons: 11.1,11.2, 11.4

Lessons:11.2, 11.3

Lesson: 11.5

(After ARMT+)

Lesson: 11.6

(After ARMT+)

Lesson: 11.7

(After ARMT+)

Lessons: 11.7, 11.8

(After ARMT+)

Lesson: 11.9

(After ARMT+) / 5.25 Understand that attributes belonging to a category of two–dimensional figures also belong to all subcategories of that category. [5-G3]

5.26 Classify two-dimensional figures in a hierarchy based on properties. [5-G4]

5.20 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. [5-MD3]

5.20.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. [5-MD3a]

5.20.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. [5-MD3b]

5.21 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5-MD4]

5.22.a Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. [5-MD5]

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. [5-MD5a] / identify attributes and categories of two-dimensional figures.

classify two-dimensional figures in a hierarchy according to their attributes.

use a unit cube to measure volume.

identify the volume of a solid figure in cubic units.

measure volume by counting

unit cubes.

find the volume of a right

rectangular prism using unit cubes.

show volume of a right rectangular prism by multiplying the edge lengths.

show volume of a right rectangular prism by multiplying the height by the area of the base. / 11.1 congruent, heptagon, nonagon, polygon, regular polygon, decagon, hexagon, octagon, pentagon, quadrilateral

11.2 equilateral triangle, isosceles triangle, scalene triangle, acute triangle, obtuse triangle, right triangle

11.3 parallel lines, parallelogram, perpendicular lines, rectangle, rhombus, trapezoid

11.5 base, decagonal prism, hexagonal prism, lateral face, octagonal prim, pentagonal prism, pentagonal pyramid, polyhedron, prism, pyramid

11.6 unit cube

11.7 cubic unit, volume

Date / MP / Resource / CCRS / Student Can / Vocabulary

Ch 11 (continued) / Lessons: 11.10, 11.11

Lesson: 11.12 / 5.22.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. [5-MD5b ]

5.2.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. [5-MD5c] / use l x w x h and b x h to find volume for right rectangluar prisms in real world problems.

find the volume of a solid

figure made of two non-overlapping

parts by adding the volumes of the two right rectangular prisms in real world problems.

Date / MP / Resource / CCRS/ARMT* / Students Can / Vocabulary

4th 9 Weeks

Mar 12 – May 23

Apr 19

ASPIRE

Admin. / ASPIRE

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