Georgia Department of Education

Transcription

1 Fifth Grade 5.NBT.1 Dividing whole numbers in base ten; Compute quotients of two-, three-, and four-digit whole numbers and two-digit whole numbers using strategies based on place value, the properties of operations, and/or the inverse relationship between multiplication and division; explain the reasoning used. 5.NBT.2 Dividing whole numbers in base ten; Explain why division strategies and algorithms work, using place value and the properties of operations. Include explanations supported by drawings, equations, or both. A range of reasonably efficient algorithms may be covered, not only the standard algorithm. 5.NBT.3 Dividing whole numbers in base ten; Use the standard algorithm to compute quotients of two-, three- and four-digit whole numbers and twodigit whole numbers, expressing the results as an equation (e.g., 145 = or = 17 1/7). 5.NBT.4 Decimal concepts; Read, write, and compare numbers expressed as decimals. Understand that a digit in one place represents ten times what it represents in the place to its right. For example, 7 in the hundredths place represents 10 times as many as 7 in the thousandths place. M4N4.bc. Students will further develop their understanding of division of whole numbers and divide in problem solving situations without calculators. b. Solve problems involving division by 1 or 2-digit numbers (including those that generate a remainder). c. Understand the relationship between dividend, divisor, quotient, and remainder. M4N4.bc. Students will further develop their understanding of division of whole numbers and divide in problem solving situations without calculators. b. Solve problems involving division by 1 or 2-digit numbers (including those that generate a remainder). c. Understand the relationship between dividend, divisor, quotient, and remainder. M4N4.bc. Students will further develop their understanding of division of whole numbers and divide in problem solving situations without calculators. b. Solve problems involving division by 1 or 2-digit numbers (including those that generate a remainder). c. Understand the relationship between dividend, divisor, quotient, and remainder. M5N2.ac. Students will further develop their understanding of decimals as part of the base-ten number system. a. Understand place value. c. Use <, >, or = to compare decimals and justify the comparison. M3N1.b. Students will further develop their understanding of whole numbers and decimals and ways of representing them. b. Understand the relative sizes of digits in place value notation (10 times, 100 times, 1/10 of a single digit whole number) and ways to represent them including word name, standard form, and expanded form. March 15, 2010 Page 47 of 119

2 5.NBT.5 Decimal concepts; Round decimals (to hundredths) to the nearest whole number. 5.NBT.6 Decimal concepts; Write fractions in decimal notation for fractions with denominators 2, 4, 5, 8, 10, and NBT.7 Operations on decimals; Understand that in adding or subtracting finite decimals, one adds or subtracts like units (tenths and tenths, hundredths and hundredths, etc.) and sometimes it is necessary to compose or decompose a higher value unit. 5.NBT.8 Operations on decimals; Fluently find 0.1 more than a number and less than a number; 0.01 more than a number and less than a number; and more than a number and less than a number, for numbers expressed as finite decimals. 5.NBT.9 Operations on decimals; Compute sums and differences of finite decimals by expressing the decimals as fractions and adding the fractions. For example, = 5/ /100 = 96/100 or M4N2.d. Students will understand and apply the concept of rounding numbers. d. Round a decimal to the nearest whole number or tenth. M5N4.h. Students will continue to develop their h. Use fractions (proper and improper) and decimals interchangeably. M3N5.b. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations. b. Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3). M4N5.c. Students will further develop their understanding of the meaning of decimals and use them in computations. c. Add and subtract both one and two digit decimals. M4N5.c. Students will further develop their understanding of the meaning of decimals and use them in computations. c. Add and subtract both one and two digit decimals. M6N1. Students will understand the meaning of the four arithmetic operations as related to positive M4N5.c. Students will further develop their understanding of the meaning of decimals and use them in computations. c. Add and subtract both one and two digit decimals. M3N5.ab. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations. b. Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3). M6N1. Students will understand the meaning of the four arithmetic operations as related to positive March 15, 2010 Page 48 of 119

3 5.NBT.10 Operations on decimals; 3 Compute sums, differences, products, and quotients of finite decimals using strategies based on place value, the properties of operations, and/or the inverse relationships between addition and subtraction and between multiplication and division; explain the reasoning used. For example, transform into 15 3 = 5. 5.NBT.11 Operations on decimals; Explain why strategies and algorithms for computations with finite decimals work. Include explanations supported by drawings, equations, or both. A range of reasonably efficient algorithms may be covered, not only the standard algorithm. M5N2.b. Students will further develop their understanding of decimals as part of the base-ten number system. b. Analyze the effect on the product when a number is multiplied by 10, 100, 1000, 0.1, 0.01, and.001. M5N3. Students will further develop their understanding of the meaning of multiplication and division with decimals and use them. M4N4.a. Students will further develop their understanding of division of whole numbers and divide in problem solving situations without calculators. a. Understand and explain the effect on the quotient of multiplying or dividing both the divisor and dividend by the same number. ( yields the same answer as 205 5). M6N1. Students will understand the meaning of the four arithmetic operations as related to positive M5N2.ab. Students will further develop their understanding of decimals as part of the base-ten number system. a. Understand place value. b. Analyze the effect on the product when a number is multiplied by 10, 100, 1000, 0.1, 0.01, and.001. M5N3.abd. Students will further develop their understanding of the meaning of multiplication and division with decimals and use them. a. Model multiplication and division of decimals. b. Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimals. d. Understand the relationships and rules for multiplication and division of whole numbers also apply to decimals. M4N5.d. Students will further develop their understanding of the meaning of decimals and use them in computations. d. Model multiplication and division of decimals by whole numbers. March 15, 2010 Page 49 of 119

4 5.NBT.12 Operations on decimals; Use the standard algorithm for each of the four operations on decimals (to hundredths). 5.NBT.13 Operations on decimals; Solve word problems involving operations on decimals. 5.NF.1a Fraction equivalence; Understand fraction equivalence: a. Multiplying the numerator and denominator of a fraction by the same nonzero whole number produces an equivalent fraction. For example, 2/3 = (2 4)/(3 4) = 8/12. (1/3 is 4 copies of 1/12, so 2/3 is 8 copies of 1/12.) 5.NF.1b Fraction equivalence; Understand fraction equivalence: b. Equivalent fractions correspond to the same point on a number line. In Grade 5, all numbers lines begin with zero. 5.NF.1c Fraction equivalence; Understand fraction equivalence: c. When the numerators of equivalent fractions are divided by their denominators, the resulting quotients are the same. 5.NF.2 Fraction equivalence; Identify pairs of equivalent fractions; given two fractions with unlike denominators, find two fractions with the same denominator and equivalent to each. M4N5.ce. Students will further develop their understanding of the meaning of decimals and use them in computations. c. Add and subtract both one and two digit decimals. e. Multiply and divide both one and two digit decimals by whole numbers. M5N3.c. Students will further develop their understanding of the meaning of multiplication and division with decimals and use them. c. Multiply and divide with decimals including decimals less than one and greater than one. M6N1g. Students will understand the meaning of the four arithmetic operations as related to positive g. Solve problems involving fractions, decimals, and percents. M5N4.b. Students will continue to develop their b. Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one. M5N4.c. Students will continue to develop their c. Find equivalent fractions and simplify fractions. M5N4.ch.Students will continue to develop their c. Find equivalent fractions and simplify fractions. h. Use fractions (proper and improper) and decimals interchangeably. M5N4.bce. Students will continue to develop their b. Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one. c. Find equivalent fractions and simplify fractions. e. Explore finding common denominators using concrete, pictorial, and computational models. March 15, 2010 Page 50 of 119

5 5.NF.3 Fraction equivalence; Compare and order fractions with like or unlike denominators, e.g., by finding equivalent fractions with the same denominator, and describe the sizes of fractional quantities from a context with reference to the context. Compare using the fractions themselves, tape diagrams or number line representations, and area models. 5.NF.4 Operations on fractions; Understand that sums and differences of fractions with unlike denominators can be computed by replacing each with an equivalent fraction so that the resulting fractions have the same denominator. For example, 2/3 + 5/4 = 8/ /12 = 23/12. 5.NF.5 Operations on fractions; Compute sums and differences of fractions with like or unlike denominators, and solve word problems involving addition and subtraction of fractions. Estimate fraction sums and differences to assess the reasonableness of results. 5.NF.6 Operations on fractions; Understand that multiplying a fraction by a/b means taking a parts of a decomposition of the fraction into b equal parts. For example, to multiply 2/3 4/5 = 8/15, one may decompose a whole of size 4/5 into 3 equal parts; each part has size 4/15. Two of these parts then make 8/15, so 2/3 4/5 = 8/15. (In general, a/b p/q = ap/bq.) This standard includes multiplication of a whole number by a fraction, by writing the whole number as fraction with denominator 1. 5.NF.7 Operations on fractions; Understand that the area of a rectangle with side lengths a/b and c/d is the product a/b p/q. This extends the area formula for rectangles to fractional side lengths, and also allows products of fractions to be represented visually as areas of rectangles. M5N4.cef. Students will continue to develop their c. Find equivalent fractions and simplify fractions. e. Explore finding common denominators using concrete, pictorial, and computational models. f. Use <, >, or = to compare fractions and justify the comparison. M5N4.cef. Students will continue to develop their c. Find equivalent fractions and simplify fractions. e. Explore finding common denominators using concrete, pictorial, and computational models. f. Use <, >, or = to compare fractions and justify the comparison. M5N4.g. Students will continue to develop their g. Add and subtract common fractions and mixed numbers with unlike denominators. M5N4.ad.Students will continue to develop their a. Understand division of whole numbers can be represented as a fraction (a/b= a b). d. Model the multiplication and division of common fractions. M5N4.d.Students will continue to develop their d. Model the multiplication and division of common fractions. March 15, 2010 Page 51 of 119

6 5.NF.8 Operations on fractions; Explain and justify the properties of operations with fractions, e.g., by using equations, number line representations, area models, and story contexts. 5.NF.9a Operations on fractions; Understand division of unit fractions by whole numbers and division of whole numbers by unit fractions: a. Dividing a unit fraction 1/b by a whole number a results in a smaller unit fraction 1/a b. For example, 1/3 2 = 1/6 because when 1/3 is divided into 2 equal parts, the size of each part is 1/6; a third of a pound of cheese shared between two people will give each person a sixth of a pound. (Using the inverse relationship between multiplication and division: 1/3 2 = 1/6 because 1/6 2 = 1/3.) 5.NF.9b Operations on fractions; Understand division of unit fractions by whole numbers and division of whole numbers by unit fractions: Operations on fractions; Dividing a whole number a by a unit fraction 1/b results in a greater whole number a b. For example, 2 1/3 = 6 because 6 is the number of 1/3s in 2; two pounds of cheese will make six portions of a third of a pound each. (Using the inverse relationship between multiplication and division: 2 1/3 = 6 because 6 1/3 = 2.) 5.NF.10 Operations on fractions; Calculate products of fractions, and quotients of unit fractions and nonzero whole numbers (with either as divisor), and solve word problems involving these operations. Represent these operations using equations, area models and length models. M5N4.dg.Students will continue to develop their d. Model the multiplication and division of common fractions. g. Add and subtract common fractions and mixed numbers with unlike denominators. M6N1. Students will understand the meaning of the four arithmetic operations as related to positive M5N4.ad. Students will continue to develop their a. Understand division of whole numbers can be represented as a fraction (a/b= a b). d. Model the multiplication and division of common fractions. M5N4.ad. Students will continue to develop their a. Understand division of whole numbers can be represented as a fraction (a/b= a b). d. Model the multiplication and division of common fractions. M6N1.e. Students will understand the meaning of the four arithmetic operations as related to positive e. Multiply and divide fractions and mixed numbers. M6N1.eg. Students will understand the meaning of the four arithmetic operations as related to positive e. Multiply and divide fractions and mixed numbers. g. Solve problems involving fractions, decimals, and percents. March 15, 2010 Page 52 of 119

7 5.NF.11 Operations on fractions; Understand that a mixed number such as 3 2/5 represents the sum of a whole number and a fraction less than one. Because a whole number can be represented as a fraction (3 = 3/1), and the sum of two fractions is also a fraction, a mixed number also represents a fraction (3 2/5 = 3 + 2/5 = 15/5 + 2/5 = 17/5). Write fractions as equivalent mixed numbers and vice versa. 5.MD.1 Units of measure; Understand that quantities expressed in like units can be added or subtracted giving a sum or difference with the same unit; different quantities may be multiplied to obtain a new kind of quantity (e.g., as when two lengths are multiplied to compute an area, or when an area and a length are multiplied to compute a volume). 5.MD.2 Units of measure; Understand that when measuring a quantity, if a smaller unit is used, more units must be iterated to measure the quantity in those units. 5.MD.3 Units of measure; Convert among differentsized standard measurement units within a given measurement system (e.g., feet to yards, centimeters to meters) and use conversion in solving multi-step word problems. 5.MD.4a Volume; Understand concepts of volume measurement: a. A cube with side length 1 unit (a unit cube) is said to have one cubic unit of volume, and can be used to measure volume. M4N6.c. Students will further develop their understanding of the meaning of decimal fractions and common fractions and use them in computations. c. Use mixed numbers and improper fractions interchangeably. M5M4.a. Students will understand and compute the volume of a simple geometric solid. b. Identify the units used in computing volume as cubic centimeters (cm3), cubic meters (m3), cubic inches (in3), cubic feet (ft3), and cubic yards (yd3). M3M4.ab. Students will understand and measure the area of simple geometric figures (squares and rectangles). a. Understand the meaning of the square unit and measurement in area. b. Model (by tiling) the area of a simple geometric figure using square units (square inch, square foot, etc.). M3M2.d. Students will measure length choosing appropriate units and tools. d. Compare one unit to another within a single system of measurement M6M1. Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships. M5M4.a. Students will understand and compute the volume of a simple geometric solid. a. Understand a cubic unit (u3) is represented by a cube in which each edge has the length of 1 unit. March 15, 2010 Page 53 of 119

8 5.MD.4b Volume; Understand concepts of volume measurement: b. The volume of a right rectangular prism with whole-unit side lengths can be found by packing it with unit cubes and using multiplication to count their number. For example, decomposing a right rectangular prism 3 length units wide by 5 units deep by 2 units tall shows that its volume is cubic units. The base of the prism has area 3 5 square units, so the volume can also be expressed as the height times the area of the base. 5.MD.4c Volume; Understand concepts of volume measurement: c. When measuring a volume, if a smaller unit is used, more units must be iterated to measure the volume in those units. 5.MD.4d Volume; Understand concepts of volume measurement: d. If a solid figure is decomposed into several disjoint pieces, then the volume enclosed by the figure can be found by adding the volumes of the pieces (when these volumes are expressed in the same units). 5.MD.5 Volume; Decompose right rectangular prisms into layers of arrays of cubes; determine and compare volumes of right rectangular prisms, and objects well described as right rectangular prisms, by counting cubic units (using cm 3, m 3, in 3, ft 3, and improvised units). 5.MD.6 Representing and interpreting data; Make a dot 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 dot 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. 5.G.1a Coordinates; Understand that a pair of perpendicular number lines, called axes, defines a coordinate system: a. Their intersection is called the origin, usually arranged to coincide with the 0 on each line. M5M4.bc. Students will understand and compute the volume of a simple geometric solid. b. Identify the units used in computing volume as cubic centimeters (cm3), cubic meters (m3), cubic inches (in3), cubic feet (ft3), and cubic yards (yd3). c. Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives. M5M4. Students will understand and compute the volume of a simple geometric solid. M5M4. Students will understand and compute the volume of a simple geometric solid. M5M4. Students will understand and compute the volume of a simple geometric solid. M5D1.bc. Students will analyze graphs. b. Compare and contrast multiple graphic representations (circle graphs, line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs) for a single set of data and discuss the advantages/disadvantages of each. c. Determine and justify the mean, range, mode, and median of a set of data. M4G3. Students will use the coordinate system. March 15, 2010 Page 54 of 119

9 5.G.1b Coordinates; Understand that a pair of perpendicular number lines, called axes, defines a coordinate system: b. A given point in the plane can be located by using an ordered pair of numbers, called its coordinates. The first number indicates how far to travel from the origin in the direction of one axis, the second number indicates how far to travel in the direction of the second axis. 5.G.1c Coordinates; Understand that a pair of perpendicular number lines, called axes, defines a coordinate system: c. To avoid ambiguity, conventions dictate 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 Coordinates; Graph points in the first quadrant of the coordinate plane, and identify the coordinates of graphed points. Where ordered pairs arise in a problem situation, interpret the coordinate values in the context of the situation. 5.G.3 Plane figures; Understand that properties belonging to a category of plane 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. M4G3.b. Students will use the coordinate system. b. Locate a point in the first quadrant in the coordinate plane and name the ordered pair. M4G3. Students will use the coordinate system. M4G3.ac. Students will use the coordinate system. a. Understand and apply ordered pairs in the first quadrant of the coordinate system. c. Graph ordered pairs in the first quadrant. M4G1.acd. Students will define and identify the characteristics of geometric figures through examination and construction. a. Examine and compare angles in order to classify and identify triangles by their angles. c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi) by their properties. d. Compare and contrast the relationships among quadrilaterals. March 15, 2010 Page 55 of 119

10 5.G.4 Plane figures; Classify plane figures in a hierarchy based on properties. M4G1.acd. Students will define and identify the characteristics of geometric figures through examination and construction. a. Examine and compare angles in order to classify and identify triangles by their angles. c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi) by their properties. d. Compare and contrast the relationships among quadrilaterals. M3G1.abc. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. a. Draw and classify previously learned fundamental geometric figures and scalene, isosceles, and equilateral triangles. b. Identify and compare the properties of fundamental geometric figures. c. Examine and compare angles of fundamental geometric figures. March 15, 2010 Page 56 of 119