5th Grade Standards Guide
5th Grade Standards Guide
Table of Contents
Content Overview to the Math Standards Guide Geometry Measurement & Data Numbers & Operations in Base Ten Numbers & Operations – Fractions Operations & Algebraic Thinking
Page Number 2-3 4 4-5 5-6 7-8 9
1
Overview to the Math Standards Guide What is the Math Standards Guide?1 Teachers know the Common Core standard language is important, yet it can often be dense or confusing. The Math Standards Guide is designed to shed light on each Common Core standard, including the key parts of the standard and the aspect(s) of rigor (Conceptual, Procedural, or Application) to which each standard most appropriately aligns. How should I use the Math Standards Guide? Use the Standards Guide to deeply study the standards. We suggest using this document during annual and unit planning as it is designed to help you better understand the key components of each standard and see how standards fit together within their cluster and domain.
What is different about the Math Standards Guide in 2016-17? We have revised this document, as we do every year, to best reflect our deepening knowledge of the Common Core. We have updated the aspects of rigor for some standards to give you a better understanding of which standards call for conceptual understanding of key concepts, speed and accuracy in calculations (procedural rigor), and/or to use math flexibly for applications in problem-solving contexts. In addition, each standard code is now hyperlinked to their standard page on myANet. The revisions represent feedback from Achievement Network’s assessment and coaching teams, Student Achievement Partners, and our schools. When planning, be sure to consider how the parts fit together, representing the breadth of the standard, as well as how the standards fit within the appropriate cluster and domain. It’s important to note that fragmenting the standards may prevent you from recognizing the full scope and rigor of the standards, so avoid interpreting the parts of the standard as individual or daily objectives.
1
The content in this guide is an interpretation of the standards, and could differ from other sources. However, this guide represents feedback from Achievement Network’s assessment and coaching teams, Student Achievement Partners, and our schools.
For example: Domain
Cluster
4.NBT.A
CC Standard
CC Standard Language
4.NBT.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Major
Number & Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.2
4.NBT.3
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.(4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) Use place value understanding to round multi-digit whole numbers to any place. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Aspect(s) of Rigor
Parts of the Standard
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Conceptual
Recognize that 10 tens is 100, 10 hundreds is 1,000, so forth up to 1,000,000. Apply concepts of place value to recognize quotients and products in multiplication and division problems involving whole numbers and a factor of 10.
Conceptual Procedural
tsbienrdsivuisdin ua lyatsoe-btetnter Read multi-diR gietawdhtohlee pnaurm glb erbsetrandam thees,s& taenxdpaarn d’s rements numerals,unnudm derdeq fourim but avoid treating them as discrete or daily objectives. Instead, consider how Write multit-hdeigpitaw rthsofliet tnougmeb theersr,upslianngnbinagset-ot ensure numeralst,hneuym wbilel ran llabm e easd,d&resxspeadnidneydofuorrm lesson(s). Compare multi-digit numbers based on the meaning of the digits
Standards e ach fit within a cluster and domain. Use the symbols , and = to compare two multiers When planning, read the language odfigeiatcnhum stb an dard within the cluster to see how, together, they achieve the cluster-level requirements. Note that major, supporting, u smtebrelresvteol.any place (with and additional emRpohuansdesmaurletig-d iviegn hleecnlu it awthto Conceptual specific attention to thousands, ten thousands, Are there deeper connections across standards (or Procedural hundred thousands, and millions places as these are clusters) that can be made during in struction? Is there an new in Grade 4.) opportunity for supporting or additional standards to
5th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
5.G.A.1 5.G.A
o Additional Graph points on the coordinate plane to solve real-world and mathematical problems. Geometry
5.G.A.2
CC Standard Language 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 xcoordinate, y-axis and y-coordinate).
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.
Aspect(s) of Rigor
Parts of the Standard 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
Conceptual
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) Plot points on the coordinate plane, given an ordered pair of whole-number coordinates Identify an ordered pair of whole-number coordinates, given a plotted point on a coordinate plane Represent mathematical problems by graphing points in the first quadrant of the coordinate plane
Conceptual, Procedural, Application
Represent real-world problems by graphing points in the first quadrant of the coordinate plane Interpret coordinate values of points in the context of the situation
5.G.B
5.G.B.3
o Additional Classify two-dimensional figures into categories based on their properties.
5.G.B.4
Understand that attributes belonging to a category of twodimensional 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.
Classify two-dimensional figures in a hierarchy based on properties.
Understand that attributes belonging to a category of triangles or quadrilaterals also belong to all subcategories of that category Conceptual
Conceptual
Supporting
Measurement & Data
5.MD.A.1
Convert like measurement units within a given measurement system.
Convert a measurement of length, mass, or volume from a larger unit to a smaller unit within the same system of measurement (customary or metric)
p Represent and interpret data.
Procedural, Application
Convert a measurement of length, mass, or volume from a smaller unit to a larger unit within the same system of measurement (customary or metric) Use conversions to solve multi-step real-world problems
5.MD.B Supporting
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.
Classify quadrilaterals in a hierarchy based on properties: for example, squares belong to the category of rectangles; rectangles belong to the category of parallelograms; parallelograms belong to the category of quadrilaterals Classify triangles in a hierarchy based on properties: for example, equilateral triangles belong to the category of isosceles triangles; isosceles triangles belong to the category of triangles
5.MD.A
p
Create a line of reasoning to explain how attributes of two-dimensional figures propagate through categories. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles
5.MD.B.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 would contain if the total amount in all the beakers were redistributed equally.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8) Application
Use operations on fractions for this grade to solve multi-step problems using information presented in line plots, including problems involving finding the total (weight, distance, etc) of all the measured amounts in the line plot, and problems involving equal redistribution of all the measured amounts in the line plot
5th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Recognize volume as an attribute of solid figures
5.MD.C.3
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.
Conceptual
Know that a cube with side length 1 unit is called a unit cube and can be used to measure volume Know that 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.C.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Conceptual, Procedural
5.MD.C
< Major Measurement & Data
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
5.MD.C.5a
5.MD.C.5b
Find the volume of a right rectangular prism with wholenumber 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. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
Deduce the volume of a specific three-dimensional figure by experiment or by counting unit cubes Understand and visualize "hidden" cubes and layers Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes
Conceptual
Demonstrate that packing a right rectangular prism with cubes, multiplying the dimension lengths, and multiplying the height by the area of the base all produce equivalent measurements of volume Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication
Procedural, Application
Apply the formula V = l x w x h to find volumes or right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems Apply the formula V = b x h to find volumes or right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems Recognize volume as additive
5.MD.C.5c
5.NBT.A.1 5.NBT.A Number & Operations in Base Ten
< Major Understand the place value system.
5.NBT.A.2
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Recognize 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.
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.
Conceptual, Application
Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts Apply the technique of adding the volumes of non-overlapping parts to solve real-world problems
Conceptual
Recognize that the value of a digit changes by a factor of 10 when it moves by one place value, having a value 10 times greater when it moves left and 1/10 of the value when it moves to the right. Students do not need to extend this knowledge to moving multiple places values (e.g. knowing that moving a digit two places values to the left increases its value 100 times) Explain patterns in the number of zeros of a product when multiplying a whole number by a power of 10
Conceptual, Procedural
Explain patterns in the placement of the decimal point when multiplying or dividing a decimal by a power of 10 Use and understand whole-number exponents to denote powers of 10
5th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard
5.NBT.A.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).
Conceptual, Procedural
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) Read and write decimals to the thousandths using base-ten numerals (standard form), number names, and expanded form (including both fraction and decimal format)
5.NBT.A (cont'd)
< Major 5.NBT.A.3b Understand the place value system.
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Convert numbers between forms Conceptual
Compare decimals to the thousandths using place value understanding. Use , and = symbols to record comparisons Convert between number forms in order to compare decimals
5.NBT.A.4
Use place value understanding to round decimals to any place.
Conceptual, Procedural
Use place value understanding to round decimals to any place Fluently multiply 2-digit by 3-digit whole numbers using the standard algorithm
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
Fluently multiply 2-digit by 4-digit whole numbers using the standard algorithm Procedural Fluently multiply 3-digit by 3-digit whole numbers using the standard algorithm
Number & Operations in Base Ten
Fluently multiply 3-digit by 4-digit whole numbers using the standard algorithm Find whole-number quotients of whole numbers with up to four-digit dividends and one-digit divisors using strategies based on place value and/or the distributive property
5.NBT.B
< Major Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.B.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.
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value and/or the distributive property Conceptual, Procedural
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on the relationship between multiplication and division Illustrate and explain division of whole numbers with up to four-digit dividends and two-digit divisors by using equations, rectangular arrays, and/or area models, including solving problems involving finding the missing side length given the area
5.NBT.B.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.
Add and subtract 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 these strategies to a written method Conceptual, Divide decimals to hundredths, using concrete models or drawings and strategies based on Procedural place value and/or properties of operations; relate these strategies to a written method Multiply decimals to hundredths, using concrete models or drawings (such as area models) and strategies based on place value and/or properties of operations; relate these strategies to a written method
5th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Replace 2 fractions with unlike denominators with equivalent fractions with like denominators
5.NF.A.1
5.NF.A
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.)
Add and subtract 2 proper fractions and/or mixed numbers with unlike denominators by converting to like denominators Procedural
Add and subtract 3 proper fractions or mixed numbers with unlike denominators by converting to like denominators Add proper fractions or mixed numbers in problems involving regrouping an additional whole
Table of Contents
Content Overview to the Math Standards Guide Geometry Measurement & Data Numbers & Operations in Base Ten Numbers & Operations – Fractions Operations & Algebraic Thinking
Page Number 2-3 4 4-5 5-6 7-8 9
1
Overview to the Math Standards Guide What is the Math Standards Guide?1 Teachers know the Common Core standard language is important, yet it can often be dense or confusing. The Math Standards Guide is designed to shed light on each Common Core standard, including the key parts of the standard and the aspect(s) of rigor (Conceptual, Procedural, or Application) to which each standard most appropriately aligns. How should I use the Math Standards Guide? Use the Standards Guide to deeply study the standards. We suggest using this document during annual and unit planning as it is designed to help you better understand the key components of each standard and see how standards fit together within their cluster and domain.
What is different about the Math Standards Guide in 2016-17? We have revised this document, as we do every year, to best reflect our deepening knowledge of the Common Core. We have updated the aspects of rigor for some standards to give you a better understanding of which standards call for conceptual understanding of key concepts, speed and accuracy in calculations (procedural rigor), and/or to use math flexibly for applications in problem-solving contexts. In addition, each standard code is now hyperlinked to their standard page on myANet. The revisions represent feedback from Achievement Network’s assessment and coaching teams, Student Achievement Partners, and our schools. When planning, be sure to consider how the parts fit together, representing the breadth of the standard, as well as how the standards fit within the appropriate cluster and domain. It’s important to note that fragmenting the standards may prevent you from recognizing the full scope and rigor of the standards, so avoid interpreting the parts of the standard as individual or daily objectives.
1
The content in this guide is an interpretation of the standards, and could differ from other sources. However, this guide represents feedback from Achievement Network’s assessment and coaching teams, Student Achievement Partners, and our schools.
For example: Domain
Cluster
4.NBT.A
CC Standard
CC Standard Language
4.NBT.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Major
Number & Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
4.NBT.2
4.NBT.3
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.(4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) Use place value understanding to round multi-digit whole numbers to any place. (4.NBT footnote: Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Aspect(s) of Rigor
Parts of the Standard
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Conceptual
Recognize that 10 tens is 100, 10 hundreds is 1,000, so forth up to 1,000,000. Apply concepts of place value to recognize quotients and products in multiplication and division problems involving whole numbers and a factor of 10.
Conceptual Procedural
tsbienrdsivuisdin ua lyatsoe-btetnter Read multi-diR gietawdhtohlee pnaurm glb erbsetrandam thees,s& taenxdpaarn d’s rements numerals,unnudm derdeq fourim but avoid treating them as discrete or daily objectives. Instead, consider how Write multit-hdeigpitaw rthsofliet tnougmeb theersr,upslianngnbinagset-ot ensure numeralst,hneuym wbilel ran llabm e easd,d&resxspeadnidneydofuorrm lesson(s). Compare multi-digit numbers based on the meaning of the digits
Standards e ach fit within a cluster and domain. Use the symbols , and = to compare two multiers When planning, read the language odfigeiatcnhum stb an dard within the cluster to see how, together, they achieve the cluster-level requirements. Note that major, supporting, u smtebrelresvteol.any place (with and additional emRpohuansdesmaurletig-d iviegn hleecnlu it awthto Conceptual specific attention to thousands, ten thousands, Are there deeper connections across standards (or Procedural hundred thousands, and millions places as these are clusters) that can be made during in struction? Is there an new in Grade 4.) opportunity for supporting or additional standards to
5th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
5.G.A.1 5.G.A
o Additional Graph points on the coordinate plane to solve real-world and mathematical problems. Geometry
5.G.A.2
CC Standard Language 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 xcoordinate, y-axis and y-coordinate).
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.
Aspect(s) of Rigor
Parts of the Standard 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
Conceptual
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) Plot points on the coordinate plane, given an ordered pair of whole-number coordinates Identify an ordered pair of whole-number coordinates, given a plotted point on a coordinate plane Represent mathematical problems by graphing points in the first quadrant of the coordinate plane
Conceptual, Procedural, Application
Represent real-world problems by graphing points in the first quadrant of the coordinate plane Interpret coordinate values of points in the context of the situation
5.G.B
5.G.B.3
o Additional Classify two-dimensional figures into categories based on their properties.
5.G.B.4
Understand that attributes belonging to a category of twodimensional 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.
Classify two-dimensional figures in a hierarchy based on properties.
Understand that attributes belonging to a category of triangles or quadrilaterals also belong to all subcategories of that category Conceptual
Conceptual
Supporting
Measurement & Data
5.MD.A.1
Convert like measurement units within a given measurement system.
Convert a measurement of length, mass, or volume from a larger unit to a smaller unit within the same system of measurement (customary or metric)
p Represent and interpret data.
Procedural, Application
Convert a measurement of length, mass, or volume from a smaller unit to a larger unit within the same system of measurement (customary or metric) Use conversions to solve multi-step real-world problems
5.MD.B Supporting
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.
Classify quadrilaterals in a hierarchy based on properties: for example, squares belong to the category of rectangles; rectangles belong to the category of parallelograms; parallelograms belong to the category of quadrilaterals Classify triangles in a hierarchy based on properties: for example, equilateral triangles belong to the category of isosceles triangles; isosceles triangles belong to the category of triangles
5.MD.A
p
Create a line of reasoning to explain how attributes of two-dimensional figures propagate through categories. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles
5.MD.B.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 would contain if the total amount in all the beakers were redistributed equally.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8) Application
Use operations on fractions for this grade to solve multi-step problems using information presented in line plots, including problems involving finding the total (weight, distance, etc) of all the measured amounts in the line plot, and problems involving equal redistribution of all the measured amounts in the line plot
5th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Recognize volume as an attribute of solid figures
5.MD.C.3
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.
Conceptual
Know that a cube with side length 1 unit is called a unit cube and can be used to measure volume Know that 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.C.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Conceptual, Procedural
5.MD.C
< Major Measurement & Data
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
5.MD.C.5a
5.MD.C.5b
Find the volume of a right rectangular prism with wholenumber 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. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
Deduce the volume of a specific three-dimensional figure by experiment or by counting unit cubes Understand and visualize "hidden" cubes and layers Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes
Conceptual
Demonstrate that packing a right rectangular prism with cubes, multiplying the dimension lengths, and multiplying the height by the area of the base all produce equivalent measurements of volume Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication
Procedural, Application
Apply the formula V = l x w x h to find volumes or right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems Apply the formula V = b x h to find volumes or right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems Recognize volume as additive
5.MD.C.5c
5.NBT.A.1 5.NBT.A Number & Operations in Base Ten
< Major Understand the place value system.
5.NBT.A.2
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Recognize 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.
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.
Conceptual, Application
Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts Apply the technique of adding the volumes of non-overlapping parts to solve real-world problems
Conceptual
Recognize that the value of a digit changes by a factor of 10 when it moves by one place value, having a value 10 times greater when it moves left and 1/10 of the value when it moves to the right. Students do not need to extend this knowledge to moving multiple places values (e.g. knowing that moving a digit two places values to the left increases its value 100 times) Explain patterns in the number of zeros of a product when multiplying a whole number by a power of 10
Conceptual, Procedural
Explain patterns in the placement of the decimal point when multiplying or dividing a decimal by a power of 10 Use and understand whole-number exponents to denote powers of 10
5th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard
5.NBT.A.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).
Conceptual, Procedural
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) Read and write decimals to the thousandths using base-ten numerals (standard form), number names, and expanded form (including both fraction and decimal format)
5.NBT.A (cont'd)
< Major 5.NBT.A.3b Understand the place value system.
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Convert numbers between forms Conceptual
Compare decimals to the thousandths using place value understanding. Use , and = symbols to record comparisons Convert between number forms in order to compare decimals
5.NBT.A.4
Use place value understanding to round decimals to any place.
Conceptual, Procedural
Use place value understanding to round decimals to any place Fluently multiply 2-digit by 3-digit whole numbers using the standard algorithm
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
Fluently multiply 2-digit by 4-digit whole numbers using the standard algorithm Procedural Fluently multiply 3-digit by 3-digit whole numbers using the standard algorithm
Number & Operations in Base Ten
Fluently multiply 3-digit by 4-digit whole numbers using the standard algorithm Find whole-number quotients of whole numbers with up to four-digit dividends and one-digit divisors using strategies based on place value and/or the distributive property
5.NBT.B
< Major Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.B.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.
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value and/or the distributive property Conceptual, Procedural
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on the relationship between multiplication and division Illustrate and explain division of whole numbers with up to four-digit dividends and two-digit divisors by using equations, rectangular arrays, and/or area models, including solving problems involving finding the missing side length given the area
5.NBT.B.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.
Add and subtract 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 these strategies to a written method Conceptual, Divide decimals to hundredths, using concrete models or drawings and strategies based on Procedural place value and/or properties of operations; relate these strategies to a written method Multiply decimals to hundredths, using concrete models or drawings (such as area models) and strategies based on place value and/or properties of operations; relate these strategies to a written method
5th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Replace 2 fractions with unlike denominators with equivalent fractions with like denominators
5.NF.A.1
5.NF.A
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.)
Add and subtract 2 proper fractions and/or mixed numbers with unlike denominators by converting to like denominators Procedural
Add and subtract 3 proper fractions or mixed numbers with unlike denominators by converting to like denominators Add proper fractions or mixed numbers in problems involving regrouping an additional whole
