Web viewStudents should come to 5th grade with automaticity in addition/subtraction facts within 20 and multiplication/division facts 0-12 and the standard algorithm concept

Biloxi Public Schools 5th Grade Math Pacing Guide 2015 - 2016

Term 1: Module 1

Place Value and Decimal Fractions5.NBT.1 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.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 whole-number exponents to denote powers of 10.5.NBT.3 Read, write, and compare decimals to thousandths.3a. 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).3b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.5.NBT.4 Use place value understanding to round decimals to any place.5.NBT.7 Add, subtract, and multiply 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.MD.1 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.

Suggested Modifications for Module 1: Combine Lessons 9 and 10


Term 1: Module 2

2 Multi-Digit Whole Number and Decimal Fraction Operations5.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.5.NBT.1 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.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 whole-number exponents to denote powers of 10.5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.5.NBT.7 Add, subtract and multiply 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.MD.1 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.

Suggested Modifications for Module 2:

Combine Lessons 5 and 6 Combine Lessons 7 and 8 Combine Lessons 11 and 12


5 th Grade 1st Term Accelerated Math Objectives / Ready Alignment

Standard AM Objectives Ready CC Lessons

5.NBT.1 This standard involves teacher evaluation of the student’s approach and justifications.

Lesson 1

5.NBT.2 45 Lesson 2

5.NBT.3 12, 13, 14, 15, 16, 17 Lesson 3Lesson 4

5.NBT.4 18 Lesson4

5.NBT.5 1, 2, 3, 4 Lesson 5

5.NBT.7 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 Lesson 7Lesson 8

5.MD.1 88, 89, 90, 91, 92, 93, 94, 95 Lesson 21Lesson 22

5.OA.1 40, 41, 42 Lesson 19

5.OA.2 43, 44 Lesson 19

Biloxi Public Schools 5th Grade Math Pacing Guide 2015 - 2016Term 1 Vocabulary:

Centimeter (cm) = a unit of measure equal to one hundredth of a meter.

Conversion Factor = the factor in a multiplication sentence that renames one measurement unit as another equivalent unit, e.g., 14 X (1 in) = 14 X (1/12 ft); 14/12 ft or 1 1/6 ft

Decimal = a fraction whose denominator is a power of ten and whose numerator is expressed by figures placed to the right of a decimal point.

Decimal Fraction = a proper fraction whose denominator is a power of 10.

Equation = a statement that two expressions are equal, e.g., 3 X _____ = 12 (5 X b ) = 20

Exponent = how many times a number is to be used in a multiplication sentence. 102= 10 X 10 = 100.

103 = 10 X 10 X 10 = 1,000

Millimeter = a metric unit of length equal to one-thousandth of a meter.

Multiplier = a product by which a given number – a multiplicand – is to be multiplied.

Number Sentence = an equation or inequality for which both expressions are numerical and can be evaluated to a single number. Number sentences are either true or false and contain no unknowns. (21 > 7 X 2) True (21 ÷ 7 = 4) False

Parentheses = the symbols ( ) used to relate order of operations.

Rounding = approximating the value of a given number.

Thousandths = the place value three to the right of the decimal, each unit is worth .001 or 1/1,000.

Unit Form = place value counting e.g., 943 stated as 9 hundreds 4 tens 3 ones

Biloxi Public Schools 5th Grade Math Pacing Guide 2015 - 2016Students should come to 5th grade with automaticity in addition/subtraction facts within 20 and multiplication/division facts 0-12 and the standard algorithm concept for all four operations. 5th Graders will be expected to fluently multiply multi-digit numbers (2X2, 3X2, 4X2, and 3X3). (5.NBT.5) 5 th graders should also work on becoming fluent with 2 digit division. (5.NBT.6)

Each test will be given as a timed test. The results are interpreted as follows:

*We want students entering the 6th grade to have fluency of the 4 operations (+, -, X, and ÷)

Multi-Digit Multiplication (2X2 (4) , 3X2 (4) 1st nine weeks 8 problems in 16 minutes

Rubric

7 – 8 Correct Exceeds Standards 45 – 6 Correct Proficient 33 – 4 Correct Almost Proficient 2

2 or less Correct Not Proficient 1Multi-Digit Multiplication (2X2 (2), 3X2 (2),

and 4X2 (4)2nd nine weeks 8 problems in 16

minutes7 – 8 Correct Exceeds Standards 45 – 6 Correct Proficient 33 – 4 Correct Almost Proficient 2

2 or less Correct Not Proficient 1Multi-Digit Multiplication 2 X 2 (1), 3 X 2 (1),

4 X 2 (3), and 3 X 3 (3)3rd nine weeks 8 problems in 16

minutes7 – 8 Correct Exceeds Standard 45 – 6 Correct Proficient 33 – 4 Correct Almost Proficient 2

2 or less Not Proficient 1Double Digit Division

(4 digit dividend divided by a 2 digit divisor) with or without fractional remainders

4th nine weeks 8 problems in 20 minutes

7 – 8 Correct Exceeds Standard 45 -6 Correct Proficient 33 – 4 Correct Almost Proficient 2

2 or less Not Proficient 1


Term 1 Module 1: Focus Standards for Mathematical PracticeMP.6 Attend to precision. Students express the units of the base ten system as they work with decimal operations,

expressing decompositions and compositions with understanding, e.g., “9 hundredths + 4 hundredths = 13 hundredths. I can change 10 hundredths to make 1 tenth.”

MP.7 Look for and make use of structure. Students explore the multiplicative patterns of the base ten system when they use place value charts and disks to highlight the relationships between adjacent places. Students also use patterns to name decimal fraction numbers in expanded, unit, and word forms.

MP.8 Look for and express regularity in repeated reasoning. Students express regularity in repeated reasoning when they look for and use whole number general methods to add and subtract decimals and when they multiply and divide decimals by whole numbers. Students also use powers of ten to explain patterns in the placement of the decimal point and generalize their knowledge of rounding whole numbers to round decimal numbers.

Term 1 Module 2: Focus Standards for Mathematical PracticeMP.1 Make sense of problems and persevere in solving them. Students make sense of problems when they use

number disks and area models to conceptualize and solve multiplication and division problems.MP.2 Reason abstractly and quantitatively. Students make sense of quantities and their relationships when they use

both mental strategies and the standard algorithms to multiply and divide multi-digit whole numbers. Student also “decontextualize” when they represent problems symbolically and “contextualize” when they consider the value of the units used and understand the meaning of the quantities as they compute.

MP.7 Look for and make use of structure. Students apply the times 10, 100, 1,000 and the divide by 10 patterns of the base ten system to mental strategies and the multiplication and division algorithms as they multiply and divide whole numbers and decimals

MP.8 Look for and express regularity in repeated reasoning. Students express the regularity they notice in repeated reasoning when they apply the partial quotients algorithm to divide two-, three-, and four-digit dividends by two-digit divisors. Students also check the reasonableness of the intermediate results of their division algorithms as they solve multi-digit division word problems.


Term 2: Module 2

2 Multi-Digit Whole Number and Decimal Fraction Operations5.NBT.6 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.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.


Term 2: Module 3

Adding and Subtracting of FractionsUse equivalent fractions as a strategy to add and subtract fractions.5.NF.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.)5.NF.2 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 < 1/2.


Omit Lesson 2

Omit Lesson 16 early finishers (Center Activity)


Term 2 Module 4:

Multiplication and Division of Fractions and Decimal Fractions5.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 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?5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.4a. 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.)5.MD.2 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.


Omit Lesson 4


5 th Grade 2nd Term Accelerated Math Objectives / Ready Alignment


5.NBT.6 5, 6, 7, 8, 9, 10, 11 Lesson 6

5.NBT.7 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39

Lesson 7Lesson 8 Lesson 9

5.MD.2 87 Lesson 23

5.NF.1 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59 Lesson 10

5.NF.2 58, 59, 60, 61, 62, 63, 64 Lesson 11

5.NF.3 65, 66 Lesson 12

5.NF.4A 67, 68, 69, 70, 71, 76 Lesson 13Lesson 14


Term 2 Vocabulary:

Benchmark Fraction = ½ is a benchmark fraction when comparing 1/3 and 3/5.

Between = bigger than the smaller number and smaller than the bigger number, e.g., ½ is between 1/3 and 3/5.

Commutative Property = e.g., 4 X ½ = ½ X 4

Decimal Divisor = the number that divides the whole and has units of tenths, hundredths, thousandths, etc.

Denominator = names the fractional unit; fifths in 3 fifths, 5 is the denominator in 3/5

Distribute = e.g., 1 2/5 X 15 = (1 X 15) + (2/5 X 15)

Divide = partitioning a total into equal groups to show how many units in a whole, e.g., 5 ÷ 1/5 = 25.

Equivalent Fractions = fractions that are equal, e.g., 3/5 = 6/10

Factors = numbers that are multiplied to obtain a product e.g., 3 and 8 are factors of 24 because 3 X 8 = 24.

Hundredth = 1/100 or 0.01

Like Denominators = the fractions 1/8 and 5/8 have like or the same parts (denominators)

Numerator = the count of fractional units, 3 in 3 fifths or 3 in 3/5

One tenth of a number = e.g., 1/10 X 250 = 25 1/10 X 470 = 47

Simplify = using the largest fractional unit possible to expression an equivalent fraction. (3/6 = ½)

Unlike Denominators = the fractions 2/9 and 3/7 have unlike or different parts (denominators)

Whole Unit = any unit that is partitioned into smaller, equally sized fractional units.


Term 2: Module 3: Focus Standards for Mathematical PracticeMP.2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear

on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

MP.3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in

constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grade levels can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

MP.4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might

be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts, and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

MP. 5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

MP.6 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

MP.7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.


Term 2: Module 4: Focus Standards for Mathematical Practice

MP.2 Reason abstractly and quantitatively. Students reason abstractly and quantitatively as they interpret the size of a product in relation to the size of a factor, interpret terms in a multiplication sentence as a quantity and a scaling factor and then create a coherent representation of the problem at hand while attending to the meaning of the quantities.

MP.4 Model with mathematics. Students model with mathematics as they solve word problems involving multiplication and division of fractions and decimals and identify important quantities in a practical situation and map their relationships using diagrams. Students use a line plot to model measurement data and interpret their results in the context of the situation, reflect on whether results make sense, and possibly improve the model if it has not served its purpose.

MP.5 Use appropriate tools strategically. Students use rulers to measure objects to the 1/2, 1/4 and 1/8 inch increments recognizing both the insight to be gained and the limitations of this tool as they learn that the actual object may not match the mathematical model precisely.


Term 3 Module 4:

Multiplication and Division of Fractions and Decimal Fractions5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.4b. 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.NF.5 Interpret multiplication as scaling (resizing), by:5a. 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.5b. 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.NF.6 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.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.7a. 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 = 1/3.7b. 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) = 4.7c. 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?


Omit Lessons 11 and 28


Term 3 Module 5:

Addition and Multiplication with Volume and Area5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.4b. 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.NF.6 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.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.3a. 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.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.5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.5a. 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.5b. 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.5c. 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.


Omit Lessons 9 and 10


5 th

Grade 3rd Term Accelerated Math Objectives / Ready Alignment


5.MD.3 The Accelerated Math Glossary terms address skills in this standard.

Lesson 24

5.MD.4 102 Lesson 25

5.MD.5 102, 103, 104, 105, 106, 107, 108 Lesson 26 Lesson 27

5.NF.4B 70, 71, 76 Lesson 14

5.NF.5A This standard involves teacher evaluation of the student’s approach and evaluation and justifications.

Lesson 15

5.NF.5B This standard involves teacher evaluation of the student’s approach and evaluation and justifications.

Lesson 15

5.NF.6 72, 73, 74, 75, 78, 79 Lesson 16

5.NF.7 80, 81, 82, 83, 84, 85, 86 Lesson 17Lesson 18


Term 3 Vocabulary:

Angle = the union of two different rays sharing a common vertex.

Area = the number of square units that covers a two-dimensional shape.

Attribute = a given quality or characteristic, e.g., the rectangle has two sets of parallel sides.

Axis = fixed reference line for the measurement of coordinates.


Base = one face of a three dimensional solid often thought of as the surface on which the solid rests.

Bisect = divide into two equal parts.

Cube = a 3-dimensional figure with six square sides.

Cubic Units = cubes of the same size used for measuring volume.

Face = any flat surface of a three dimensional figure, e.g., a cube has 6 square faces.

Height = adjacent layers of the base that form a rectangular prism.

Hierarchy = series of ordered groupings of shapes.

Kite = quadrilateral with two pairs of two equal sides that are adjacent; a kite can be a rhombus if all sides are equal.

Ordered pair = two quantities written in a given fixed order, written as (x, y) (5, 3) 5 over and 3 up

Origin = the starting point of the coordinate plane, fixed point from which coordinates are measured; the point at which the x-axis and y-axis intersect, labeled (0,0) on the coordinate plane.

Parallel Lines = two lines in a plane that never cross or intersect they stay the same distance apart.

Perpendicular = two lines are perpendicular if they intersect, and any of the angles formed between the lines are 90 degree right angles.

Plane = flat surface that extends infinitely in all directions.

Polygon = closed figure made of line segments that are straight.

Quadrilateral = closed figure that has four sides and four angles.

Rectangle = a parallelogram with four 90 degree right angles.


Rectangular Prism = a 3- dimensional figure with six rectangular sides.

Trapezoid = quadrilateral with at least one set of parallel sides.

Unit Cube = cube whose sides all measure one unit; cubes of the same size used for measuring volume.

Volume of a solid = measurement of space or capacity of a 3-dimensional object. Algorithm Volume = Length X Width X Height or Volume = Base Area X Height

Term 3: Module 5: Focus Standards for Mathematical PracticeMP.1 Make sense of problems and persevere in solving them. Students work toward a solid understanding of volume through the design

and construction of a three-dimensional sculpture within given parameters.

MP.2 Reason abstractly and quantitatively. Students make sense of quantities and their relationships when they analyze a geometric shape or real life scenario and identify, represent, and manipulate the relevant measurements. Students decontextualize when they represent geometric figures symbolically and apply formulas.

Biloxi Public Schools 5th Grade Math Pacing Guide 2015 - 2016MP.3 Construct viable arguments and critique the reasoning of others. Students analyze shapes, draw conclusions, and recognize and

use counterexamples as they classify two-dimensional figures in a hierarchy based on properties.

MP.4 Model with mathematics. Students model with mathematics as they make connections between addition and multiplication as applied to volume and area. They represent the area and volume of geometric figures with equations (and vice versa), and represent fraction products with rectangular areas. Students apply concepts of volume and area and their knowledge of fractions to design a sculpture based on given mathematical parameters. Through their work analyzing and classifying two-dimensional shapes, students draw conclusions about their relationships and continuously see how mathematical concepts can be modeled geometrically.

MP.6 Attend to precision. Mathematically proficient students try to communicate precisely with others. They endeavor to use clear definitions in discussion with others and their own reasoning. Students state the meaning of the symbols they choose, including using the equal sign (consistently and appropriately). They are careful about specifying units of measure and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school, students have learned to examine claims and make explicit use of definitions.

MP.7 Look for and make use of structure. Students discern patterns and structures as they apply additive and multiplicative reasoning to determine volumes. They relate multiplying two of the dimensions of a rectangular prism to determining how many cubic units would be in each layer of the prism, as well as relate the third dimension to determining how many layers there are in the prism. This understanding supports students in seeing why volume can be computed as the product of three length measurements or as the product of one area by one length measurement. Additionally, recognizing that volume is additive allows students to find the total volume of solid figures composed of more than one non-overlapping right rectangular prism.

Term 4 Module 5:

Addition and Multiplication with Volume and Area5.G.3 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.5.G.4 Classify two-dimensional figures in a hierarchy based on properties.

Term 4 Module 6:

Problem Solving with the Coordinate PlaneAnalyze patterns and relationships.5.OA.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. 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.5.G.1 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.G.2 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.


Omit Lessons 21-34

5 th Grade 4th Term Accelerated Math Objectives / Ready Alignment


5.G.1 96, 97, 98, 99 Lesson 28

5.G.2 96, 100 Lesson 29

5.G.3 This standard involves teacher evaluation of the student’s approach and justifications.

Lesson 31

5.G.4 101 Lesson 30

5.OA.3 46, 47 Lesson 20


Term 4 Vocabulary:

Angle = union of two different rays sharing a common vertex. Angle measure = number of degrees in an angle. Axis = fixed reference line for the measurement of coordinates.

Biloxi Public Schools 5th Grade Math Pacing Guide 2015 - 2016 Coordinate pair = two numbers that are used to identify a point on a plane; written (x, y) where x

represents a distance from 0 on the x-axis and y represents a distance from 0 on the y-axis. Coordinate plane = plane spanned by the x-axis and y-axis in which the coordinates of a point are

distances from the two perpendicular axes. Degree = unit used to measure angles. Horizontal = parallel to the x-axis. Line= two dimensional object that has no endpoints and continues on forever in a plane. Ordered pair = two quantities written in a given fixed order, usually written as (x, y) Origin = fixed point from which coordinates are measured; the point at which the x-axis and y-axis

intersect, labeled (0,0) on the coordinate plane. Parallel = two lines in a plane that do not intersect they stay the same distance apart. Perpendicular = two lines are perpendicular if they intersect, and any of the angles formed between the

lines are 90 degree right angles. Point = zero dimensional figure that satisfies the location of an ordered pair. Quadrant = any of the four equal areas created by dividing a plane by an x-axis and y-axis. Rule = procedure or operation(s) that affects the value of an ordered pair. Vertical = parallel to the y-axis.

Term 4: Module 6: Focus Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them. Students make sense of problems as they use tape diagrams and other models, persevering to solve complex, multi-step word problems. Students check their work and monitor

Biloxi Public Schools 5th Grade Math Pacing Guide 2015 - 2016their own progress, assessing their approach and its validity within the given context and altering their method when necessary.

MP.2 Reason abstractly and quantitatively. Students reason abstractly and quantitatively as they interpret the steepness of orientation of a line given by the points of a number pattern. Students attend to the meaning of the values in an ordered pair and reason about how they can be manipulated in order to create parallel, perpendicular, or intersecting lines.

MP.3 Construct viable arguments and critique the reasoning of others. As students construct a coordinate system on a plane, they generate explanations about the best place to create a second line of coordinates. They analyze lines and the coordinate pairs that comprise them, then draw conclusions and construct arguments about their positioning on the coordinate plane. Students also critique the reasoning of others and construct viable arguments as they analyze classmates’ solutions to lengthy, multi-step word problems.

MP.6 Attend to precision. Mathematically proficient students try to communicate precisely with others. They endeavor to use clear definitions in discussion with others and their own reasoning. Students state the meaning of the symbols they choose, including using the equal sign (consistently and appropriately). They are careful about specifying units of measure and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school, students have learned to examine claims and make explicit use of definitions.

MP.7 Look for and make use of structure. Students identify and create patterns in coordinate pairs and make predictions about their effect on the lines that connect them. Students also recognize patterns in the sets of coordinate pairs and use those patterns to explain why a line is parallel or perpendicular to an axis. They use operational rules to generate coordinate pairs and, conversely, generalize observed patterns within coordinate pairs as rules.

Standards for Mathematical Practice#1 Make sense of problems and persevere in solving them.


#2 Reason 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.

Web viewStudents should come to 5th grade with automaticity in addition/subtraction facts within 20 and multiplication/division facts 0-12 and the standard algorithm concept

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