4th Grade Common Core Math Standards Guide
4th Grade Standards Guide
Table of Contents
Content Overview to the Math Standards Guide Geometry Measurement & Data Number & Operations - Fractions Number & Operations in Base Ten Operations & Algebraic Thinking
Page Number 2-3 4 4-5 5-7 7-8 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
4th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Draw and identify line segments Draw and identify lines
4.G.A.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Procedural, Conceptual
Draw and identify parallel and perpendicular lines Draw and identify points Draw and identify rays
4.G.A
o
Draw and identify right, acute, and obtuse angles
Additional Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Recognize and identify right triangles
4.G.A.2
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Classify 2-D figures based on the presence or absence of perpendicular lines Conceptual Classify 2-D figures based on the presence or absence of parallel lines Classify 2-D figures based on the presence or absence of angles of a specified size
4.G.A.3
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
Understand that a line of symmetry in a 2-D figure represents the line across the figure such that the figure can be folded along the line into matching parts Conceptual
Recognize lines of symmetry in 2-D figures Draw lines of symmetry in 2-D figures
4.MD.A.1
4.MD.A
p Supporting Measurement & Data
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
4.MD.A.2
4.MD.A.3
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Know relative sizes of measurement units within one system of units (including: feet, inches, km, m, cm, kg, g, lb, oz, l, ml, hr, min, sec) Conceptual, Procedural
Convert a measurement from a larger unit to a smaller unit within 1 system of measurement
Record equivalent measurements in a two-column table Use the four operations to solve word problems involving measurement, including simple fractions or decimals
Application
Use the four operations to solve word problems involving measurement, including conversion from a larger unit to a smaller unit Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, or money Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale Apply the area formula for rectangles in real-world and mathematical problems
Procedural, Application Apply the perimeter formula for rectangles in real-world and mathematical problems
4th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
4.MD.B.4
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
4.MD.B
p Supporting Represent and interpret data.
4.MD.C.5
Measurement & Data
4.MD.C
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a) An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. b) An angle that turns through n onedegree angles is said to have an angle measure of n degrees.
Aspect(s) of Rigor
Parts of the Standard
Make a line plot with measurements in fractions of a unit Application Use the information in a line plot to solve problems involving the addition and subtraction of fractions Understand that an angle is measured with reference to a circle by considering the fraction of the circular arc between the points where the two rays intersect the circle Understand that an angle that turns through 1/360 of a circle is called a "one degree angle" Conceptual Understand that an angle that turns through n one-degree angles has an angle measure of n degrees Understand that angles are formed when two rays share an endpoint
o Additional Geometric measurement: understand concepts of angle and measure angles.
4.MD.C.6
Procedural Measure angles in whole number degrees using a protractor
4.MD.C.7
4.NF.A.1 4.NF.A Number & Operations Fractions
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Sketch angles of a specified measure using a protractor
, =, or ,
Table of Contents
Content Overview to the Math Standards Guide Geometry Measurement & Data Number & Operations - Fractions Number & Operations in Base Ten Operations & Algebraic Thinking
Page Number 2-3 4 4-5 5-7 7-8 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
4th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
Aspect(s) of Rigor
Parts of the Standard Draw and identify line segments Draw and identify lines
4.G.A.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Procedural, Conceptual
Draw and identify parallel and perpendicular lines Draw and identify points Draw and identify rays
4.G.A
o
Draw and identify right, acute, and obtuse angles
Additional Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Recognize and identify right triangles
4.G.A.2
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
Classify 2-D figures based on the presence or absence of perpendicular lines Conceptual Classify 2-D figures based on the presence or absence of parallel lines Classify 2-D figures based on the presence or absence of angles of a specified size
4.G.A.3
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
Understand that a line of symmetry in a 2-D figure represents the line across the figure such that the figure can be folded along the line into matching parts Conceptual
Recognize lines of symmetry in 2-D figures Draw lines of symmetry in 2-D figures
4.MD.A.1
4.MD.A
p Supporting Measurement & Data
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
4.MD.A.2
4.MD.A.3
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Know relative sizes of measurement units within one system of units (including: feet, inches, km, m, cm, kg, g, lb, oz, l, ml, hr, min, sec) Conceptual, Procedural
Convert a measurement from a larger unit to a smaller unit within 1 system of measurement
Record equivalent measurements in a two-column table Use the four operations to solve word problems involving measurement, including simple fractions or decimals
Application
Use the four operations to solve word problems involving measurement, including conversion from a larger unit to a smaller unit Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, or money Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale Apply the area formula for rectangles in real-world and mathematical problems
Procedural, Application Apply the perimeter formula for rectangles in real-world and mathematical problems
4th Grade Common Core Math Standards Guide Domain
Cluster
CC Standard
CC Standard Language
4.MD.B.4
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
4.MD.B
p Supporting Represent and interpret data.
4.MD.C.5
Measurement & Data
4.MD.C
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a) An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. b) An angle that turns through n onedegree angles is said to have an angle measure of n degrees.
Aspect(s) of Rigor
Parts of the Standard
Make a line plot with measurements in fractions of a unit Application Use the information in a line plot to solve problems involving the addition and subtraction of fractions Understand that an angle is measured with reference to a circle by considering the fraction of the circular arc between the points where the two rays intersect the circle Understand that an angle that turns through 1/360 of a circle is called a "one degree angle" Conceptual Understand that an angle that turns through n one-degree angles has an angle measure of n degrees Understand that angles are formed when two rays share an endpoint
o Additional Geometric measurement: understand concepts of angle and measure angles.
4.MD.C.6
Procedural Measure angles in whole number degrees using a protractor
4.MD.C.7
4.NF.A.1 4.NF.A Number & Operations Fractions
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
Sketch angles of a specified measure using a protractor
, =, or ,
