ussell County Schools Pacing Guide Overview Operations and Algebraic hinking [OA] Write and interpret numerical expressions. Analyze patterns and relationships. Number and Operations in Base en [NB] 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. epresent 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. Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. eason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Key for New Column ntroduce Skill each Skill eview Skill May, 2016 1
ussell County Schools Pacing Guide aught esources Vocabulary Students Can ested Operations and Algebraic hinking 5.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5-OA1] Ch. 1: Les. 1.11, 1.12 Ch. 3: Les. 3. 1 braces brackets evaluate order of operations parentheses --use algebraic expressions. --evaluate algebraic expressions using symbols 5.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5-OA2] 5.4. ecognize 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-NB1] Ch. 1: Les. 1.10 evaluate numerical expressions Numbers and Operations in Base 10 Ch.1: Les. 1.1, 1..2 Ch. 3: Les. 3.1 multiply place value period --write simple numerical expressions. --explain simple numerical expressions without finding the answer --determine that a digit represents ten times what it would be in the place to its right and one-tenth to its left. May, 2016 2
Grading ussell County Schools Pacing Guide esources Vocabulary Students Can ested Numbers and Operations in Base 10 (continued) 5.5 Explain patterns in the number of zeros of the base --explain the powers of ten. when multiplying a number by powers of Ch. 1: Les.1.4, 1.5 exponent 10, and explain patterns in the placement of the pattern --explain the pattern in the decimal point when a decimal is multiplied or Ch. 4: Les. 4.1, 4.8 place value placement of a decimal point divided by a power of 10. Use whole-number using a power of ten. exponents to denote powers of 10. [5-NB2] 5.6. ead, write, and compare decimals to thousandths. [NB3] 5.6a. ead 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-NB3a] Ch. 3: Les. 3.3 Ch. 3: Les. 3.2 decimal estimate round hundredth place value thousandth tenth --read decimals to thousandths using numerals, number names, and expanded form. --write decimals to thousandths using numerals, number names, and expanded form. 5.6b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [5-NB3b] Ch. 3: Les. 3.3 decimal place value --compare two decimals to thousandths using,, and =. May, 2016 3
Grading 5.7. Use place value understanding to round decimals to any place. [5-NB4] ussell County Schools Pacing Guide esources Vocabulary Students Can ested Numbers and Operations in Base 10 (continued) Ch. 3: Les. 3.4 estimate place value round --multiply multi-digit of whole numbers 5.8. Fluently multiply multi-digit whole numbers using the standard algorithm. [5-NB5] 5.9. Find whole-number quotients of whole numbers with up to four-digit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. llustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5-NB6] Ch. 1: Les. 1.6, 1.7 Ch. 1: Les. 1.3, 1.8, 1.9 Ch. 2: Les. 2.1, 2.9 estimate factor multiply place value associative property commutative property distributive property factor identity property inverse operation quotient --multiply multi-digit of whole numbers. --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. May, 2016 4
Grading 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-NB7] ussell County Schools Pacing Guide esources Vocabulary Students Can ested Numbers and Operations in Base 10 (continued) Chapters 3-5 (Choose appropriate lessons.) decimal place value properties of operations (addition, subtraction, multiplication, division) --add, subtract, multiply, and divide decimals to the hundredths using various methods. --explain how the answer was found 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] 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] Numbers and Operations - Fractions Chapters 3-5 (Choose appropriate lessons.) Chapter 6 denominator equivalent fraction mixed numbers benchmark fraction denominator estimate --use equivalent fractions to add fractions with unlike denominators. --use equivalent fractions to subtract fractions with unlike denominators. --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. May, 2016 5
ussell County Schools Pacing Guide Grading 5.14. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5-NF4] esources Vocabulary Students Can ested Numbers and Operations - Fractions denominator Chapter 7 equivalent fractions improper fraction mixed number numerator simplest form 5.14a. nterpret the (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] 5.14b. 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 s as rectangular areas. [5-NF4b] Chapter 7 Chapter 7: Les. 7.7 denominator equivalent fractions factor mixed number numerator simplest form area denominator equivalent fractions factor mixed number numerator simplest form --number and a fraction using a visual fraction model. --explain the of two fractions using a visual fraction model. --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 s as rectangular areas. May, 2016 6
ussell County Schools Pacing Guide Grading 5.20. ecognize volume as an attribute of solid figures and understand concepts of volume measurement. [5-MD3] esources Vocabulary Students Can ested Measurement and Data Chapter 11: Les. 11.5 base decagonal prism hexagonal prism lateral face octagonal prism pentagonal pyramid polyhedron prism pyramid 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] Chapter 11: Les.11.6 Chapter 11: Les. 11.7 unit cube volume cubic unit volume --use a unit cube to measure volume. --identify the volume of a solid figure in cubic units. --use a unit cube to measure volume. 5.21.Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5-MD4] Chapter 11: Les. 11.8 cube cubic unit volume --measure volume by counting unit cubes. May, 2016 7
ussell County Schools Pacing Guide Grading 5.22 elate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume. [5-MD5] esources Vocabulary Students Can ested Measurement and Data (continued) Chapter 11: Les. 11.9-11.12 5.22a. 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. epresent threefold wholenumber s as volumes, e.g., to represent the associative property of multiplication. [5-MD5a] 5.22b. 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] Chapter 11: Les. 9 Chapter 11: Les. 11.10-11.11 base cubic unit rectangular prism volume base cubic unit rectangular prism volume --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. ---use l x w x h and b x h to find volume for right rectangluar prisms in real world problems. May, 2016 8
ussell County Schools Pacing Guide Grading esources Vocabulary Students Can ested Measurement and Data (continued) 5.22c. ecognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. [5-MD5c] Chapter 11: Les. 11.12 base cubic unit rectangular prism volume --can find the volume of a solid figure made of two nonoverlapping parts by adding the volumes of the two right rectangular prisms in real world problems. 25. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. [5-G3] Example: All rectangles have four right angles, and squares are rectangles, so all squares have four right angles. 5.26. Classify two-dimensional figures in a hierarchy based on properties. [5-G4] Chapter 11: Les. 11.1, 11.2, 11.4 Chapter 11: Les. 11.2-11.3 congruent decagon heptagon hexagon nonagon octagon pentagon polygon quadrilateral regular polygon acute triangle classify equilateral triangle isosceles triangle obtuse triangle right triangle scalene triangle --classify two-dimensional figures in a hierarchy according to their attributes. --classify two-dimensional figures in a hierarchy according to their attributes. May, 2016 9
ussell County Schools Pacing Guide Grading 5.3. Generate two numerical patterns using two given rules. dentify 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] esources Vocabulary Students Can ested Operations and Algebraic hinking Function table Ch. 9: Les. 9.5-9.6 Ordered pairs --create a function table (input/output). --explain the rule. --graph the ordered pairs. 5.13. nterpret 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] 5.15 nterpret multiplication as scaling (resizing), by: [5-NF5] Numbers and Operations - Fractions Chapter 8: Les. 8.3 Chapter 7: Les. 7.5, 7.8 denominator dividend divisor equation equivalent fractions fraction numerator quotient denominator equivalent fractions factor mixed number numerator simplest form --explain my graph. --explain a fraction as division of the numerator by the denominator. --solve word problems involving division and write the remainder as a fraction. 5.15a. Comparing the size of a to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. [5-NF5a] Chapter 7: Les. 7.5-7.10 denominator equivalent fractions factor mixed number numerator simplest form --compare the size of a to the size of one factor based on the size of the other factor without multiplying. May, 2016 10
Grading ussell County Schools Pacing Guide esources Vocabulary Students Can ested Numbers and Operations Fractions (continued) 15b. Explaining why multiplying a given number equal --compare the size of a by a fraction greater than 1 results in a Chapter 7: factor to the size of one factor based on greater than the given number (recognizing Les. 7.8-7.9 greater than the size of the other factor multiplication by whole numbers greater than 1 as improper fraction without multiplying. a familiar case); explaining why multiplying a less than --explain why multiplying a given number by a fraction less than 1 results in a mixed number number by a fraction greater than smaller than the given number; and 1 results in a greater relating the principle of fraction equivalence a/b = than the number. (n a)/(n b) to the effect of multiplying a/b by 1. --explain why multiplying a [5-NF5b] number by a fraction less than 1 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] 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. However, division of a fraction by a fraction is not a requirement at this grade.) [5-NF7] Chapter 7: Les. 7.10 Chapter 8: Les. 8.1-8.5 equal factor greater than improper fraction less than mixed number dividend equation fraction quotient whole number --solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models. May, 2016 11
Grading ussell County Schools Pacing Guide esources Vocabulary Students Can ested Numbers and Operations Fractions (continued) 5.17a. nterpret division of a unit fraction by a --explain division of a unit fraction non-zero whole number, and compute such Ch. 8: Les. 8.1 by a whole number. quotients. [5-NF7a] dividend equation fraction quotient whole number --find the quotient of a division problem for a unit fraction and whole number. 5.17b. nterpret division of a whole number by a unit fraction, and compute such quotients. [5-NF7b] 5.17c. 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] Chapter 8: Les. 8.1-8.2 Chapter 8: Les. 8.4-8.5 dividend equation fraction quotient whole number dividend equation fraction quotient whole 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. May, 2016 12
ussell County Schools Pacing Guide Grading 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] esources Vocabulary Students Can ested Measurement and Data Customary units Chapter 10: of length (foot, Les. 10.1-10.7 inch, mile yard) Capacity Customary units of capacity (cup, fluid ounce, gallon, pint, quart, tablespoon, teaspoon) Customary units of weight (ounce, pound, tone, weight) Metric units (dekameter, centimeter, decimeter, gram, kilogram, kilometer, liter, mass, meter, milligram, milliliter, millimeter) --do measurement conversions within the same system. --use these conversions to solve multi-step, real world problems. Elapsed time May, 2016 13
ussell County Schools Pacing Guide Grading 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] esources Vocabulary Students Can ested Measurement and Data (continued) data Chapter 9: Les. 9.1 line plot --make a line plot to display a set of measurements in fractions of a unit. --solve problems with the information on the line plot. 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] Geometry Chapter 9: Les. 9.2 ordered pair origin x-axis x-coordinate y-axis y-coordinate --identify the parts of a coordinate plane. --plot a given point on the plane using ordered pairs. 5.24. epresent 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] Chapter 9: Les. 9.3.- 9.4 interval line graph scale --represent and interpret real world and math problems by graphing points on the coordinate plane. May, 2016 14
ussell County Schools Pacing Guide Grading esources Vocabulary Students Can ested (No New Covered) 4 th Grading Practice fluency with basic facts in addition, subtraction, and multiplication. eteach skills in which students are weak. Provide remediation/intervention if needed. Enrichment Activities. ntroduce students to Grade 6 skills. Supplemental Materials Digital esources 4 th Nine May, 2016 15
ussell County Schools Pacing Guide Assessment Schedule Formative 1 Formative 2 Formative 3 Formative 4 4 th Nine Chalkable/Unit ests/eachercreated ests Chalkable/Unit ests/eachercreated ests Chalkable/Unit ests/eachercreated ests eacher-created ests 1 2 4 5 6 6a 6b 7 8 9 10 11 12 14 14a 14b 20 20a 20b 21 22 22a 22b 22c 25 26 3 13 15 15a 15b 16 17 17a 17b 17c 18 19 23 24 Any standards/skills taught during this grading period. May, 2016 16