The four basic arithmetic operations are interrelated, and the properties of each may be used to understand the others. Analyzing patterns increases mathematical understanding of whole numbers. Flexible methods of computation involve grouping numbers in strategic ways. The distributive property is connected to the area model and/or partial products method of multiplication. Multiplication and division are inverse operations. There are three different structures for multiplication and division problems: area/arrays, equal groups, and comparison, and the unknown quantity in multiplication and division situations is represented in three ways: unknown products, group size unknown, and number of groups unknown. Unit: Operations and Algebraic Thinking Topic: Represent and Solve Problems How do the four operations relationships help to solve problems? How can patterns and properties be used to find some multiplication facts? How are multiplication and division related? What are different models for multiplication and division? How can unknown multiplication facts be found by breaking them apart into known facts? How can unknown division facts be found by thinking about a related multiplication fact? What are efficient methods for finding products and quotients, and how can place value properties aid computation? In addition to, in-depth inferences or applications that go beyond level. For generalize the importance of the multiplication properties (commutative, zero property, identity property, distributive) in solving mathematical problems. develop and explain strategies to show how arithmetic operations are related (inverse operations). represent a mathematical situation (multiplication or division) as an expression or number sentence using a letter or symbol, and explain which multiplication property can help you solve it and why. 3.5 In addition to performance, in-depth inferences and applications with partial success. interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. (4.OA.1) solve word problems involving multiplicative comparison using drawings or equations. (4.OA.2) solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (4.OA.3) use mathematical language to justify your reasoning 1
2.5 No major errors or gaps in content and partial knowledge in content. recognize or recalls accurate statements about multiplication and division. recognize multiplication problems represented by an array. recognize or recall specific terminology: o array o quotient o product 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 2
Unit: Operations and Algebraic Thinking Topic: Arithmetic Patterns Analyzing patterns increases mathematical Why do number patterns repeat? understanding of whole numbers. What strategies can be used to find rules Patterns are generated by following a specific rule. for patterns and what predictions can the pattern support? How can patterns be used to describe how quantities are related? How can a relationship between two quantities be shown using a table? In addition to, in-depth inferences or applications that go beyond level. For draw a shape pattern and explain the rule for the pattern. chart a number pattern that contains at least two steps, e.g. ( x3, -1 ) and explain the rule. 3.5 In addition to performance, in-depth inferences and applications with partial success. generate a number or shape pattern that follows a given rule. (4.OA.5) use mathematical language to describe the features of a number or shape pattern, including those that were not explicit in the rule itself. (4.OA.5) 2.5 No major errors or gaps in content and partial knowledge in content. identify and complete given patterns. recognize or recall specific terminology: o geometric pattern o numeric pattern 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 3
Unit: Operations and Algebraic Thinking Topic: Factors and Multiples A whole number is a multiple of each of its factors. How do I determine the factors of a number? What is the difference between a prime and composite number? How are factors and multiples related? In addition to, in-depth inferences or applications that go beyond level. For develop a strategy to determine factors of numbers above 100. explain the relationship between factors and division (Topic 1) and factors and fractions (Topic 11). 3.5 In addition to performance, in-depth inferences and applications with partial success. determine whether a given whole number in the range 1-100 is prime or composite. (4.OA.4) find all factor pairs for a whole number in the range 1-100. (4.OA.4) recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. (4.OA.4) 2.5 No major errors or gaps in content and partial knowledge in content. recognize or recall specific terminology: o multiples o factors classify numbers by their characteristics, including prime, composite and square. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 4
Unit: Numbers and Operations- Base 10 Topic: Place Value As digits progress from right to left, their individual value increases ten times. Understanding place value aids in reading, writing, rounding, and comparing multi-digit How does the value of a digit change within a number? numbers. How can place value understanding help Place value is based on groups of ten and the value of a number is determined by the place us with comparing, ordering, and rounding whole numbers? of its digits. How can the value of digits be used to Whole numbers are read from right to left using compare two numbers? the name of the period; commas are used to separate periods. In what ways can numbers be composed and decomposed? A number can be written using its name, standard, or expanded form. How are greater numbers read and written? Rounding numbers can be used when estimating answers to real-world problems. In addition to, in-depth inferences or applications that go beyond level. For identify reasons that whole numbers get larger as they move to the left in the Place Value System, and smaller as they move to the right. given a problem that includes errors, students must develop an argument for how to correct the problem or explain the errors the student made. 3.5 In addition to performance, in-depth inferences and applications with partial success. read and write multi-digit whole numbers using base-ten numerals, number names and expanded form. (4.NBT.2) compare multi-digit numbers based on meanings of the digits in each place, using <,>,= symbols to record results of the comparison. (4.NBT.2) round whole numbers up to 1,000,000 to the nearest ten, hundred, thousand, ten thousand, hundred thousand, million using place value understanding. (4.NBT.3) 2.5 No major errors or gaps in content and partial knowledge in content. 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.2) read and write multi-digit whole numbers using base ten numerals, number names, and expanded form. (4.NBT.2) 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.1) generalize place value understanding for multi-digit whole numbers in the millions. (4.NBT.1) 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 5
0.5 With help, a partial understanding of the content and none of the content. 6
Unit: Numbers and Operations- Base 10 Topic: Place Value Strategies to Add and Subtract Place value understanding and properties of operations are necessary to solve multidigit arithmetic. subtraction? The standard algorithm for addition and subtraction relies on adding or subtracting like base-ten units. How can my understanding of place value explain the process of addition and How are addition and subtraction related to one another? How does understanding place value help you solve multi-digit addition and subtraction problems, and how can rounding be used to estimate answers to problems? What are standard procedures for adding and subtracting numbers? In addition to, in-depth inferences or applications that go beyond level. For create an alternate model to add and subtract multi-digit whole numbers and explain the strategies used. 3.5 In addition to performance, in-depth inferences and applications with partial success. fluently add and subtract multi-digit whole numbers using the standard algorithm. (4.NBT.4) describe and justify the processes used to add and subtract. (4.NBT.4) 2.5 No major errors or gaps in content and partial knowledge in content. solve an addition or subtraction multi-digit whole number. (4.NBT.4) 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 7
Unit: Numbers and Operations- Base 10 Topic: Multiply Whole Numbers How can my understanding of place value Place value understanding and properties of operations are necessary to solve multi-digit explain the process of multiplication? arithmetic. How can products be found mentally? Understanding place value and properties of How can products be estimated? operations is necessary to perform multi-digit What is a standard procedure for multiplication. multiplying multi-digit numbers, and how do There are three different structures for place value properties aid computation? multiplication and division problems: area/arrays, equal groups, and comparison, What real-life situations require the use of and the unknown quantity in multiplication and multiplication? division situations is represented in three What are different models for multiplication ways: unknown products, group size (arrays) and division? unknown, and number of groups unknown. How are multiplication and division related? In addition to, in-depth inferences or applications that go beyond level. For multiply a whole number of up to three digits by a two-digit whole number. given a problem with errors, the student can identify errors and explain how to correct it. illustrate and explain two different ways of how to solve any multi digit multiplication problem. 3.5 In addition to performance, in-depth inferences and applications with partial success. multiply two 2-digit numbers using strategies based on place value and properties of operations. (4.NBT.5) illustrate and use mathematical language to explain the calculations using equations, rectangular array and area models. (4.NBT.5) estimate and reason when multiplying whole numbers. 2.5 No major errors or gaps in content and partial knowledge in content. multiply a whole number of up to four digits by a one-digit number. (4.NBT.5) recognize multiplication problems represented by models. illustrate a multiplication problem of two digits by a one digit number with an array. solve a multiplication problem of a two digit number by a one digit whole number. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 8
Place value understanding and properties of operations are necessary to solve multidigit arithmetic. Understanding place value and properties of operations is necessary to perform multidigit division. There are three different structures for multiplication and division problems: area/arrays, equal groups, and comparison, and the unknown quantity in multiplication and division situations is represented in three ways: unknown products, group size unknown, and number of groups unknown. Some division situations will produce a reminder, but the remainder should always be less than the divisor. If the remainder is greater that the divisor, that means at least one more can be given to each group or at least one more group of the given size may be created. When suing division to solve word problems, how the remainder is interpreted depends on the problem situation. Unit: Numbers and Operations Base 10 Topic: Divide Whole Numbers How can my understanding of place value explain the process of multiplication? How are multiplication and division related? What real-life situations require the use of division? What are different models for multiplication and division (repeated subtraction)? How are dividends, divisors, quotients, and remainders related? How can a remainder affect the answer in a division word problem? What are the different meanings of division? How can mental math and estimation be used to divide? What is the standard procedure for dividing multi-digit numbers? In addition to, in-depth inferences or applications that go beyond level. For divide a whole number of up to four digits by a two-digit whole number. given a problem with errors, the student can identify errors and explain how to correct it. illustrate and explain two different ways of how to solve any multi digit division problem. 3.5 In addition to performance, in-depth inferences and applications with partial success. demonstrate how to solve whole-number quotients and remainders with up to fourdigit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. (4.NBT.6) illustrate and use mathematical language to explain the calculation by using equations, rectangular arrays, and/or area models. (4.NBT.6) estimate and reason when dividing whole numbers 2.5 No major errors or gaps in content and partial knowledge in content. 9
recognize an array model can be used to solve a division problem. demonstrate how to solve whole-number quotients and remainders with up to two-digit dividends and one-digit divisors with remainders. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 10
Unit: Numbers and Operations- Fractions Topic: Compare and Order Fractions Use comparing, ordering, and equivalent fractions to extend understanding of How does finding equivalent fractions help you compare? fractions. How are fractions used in problem-solving Fractions can be represented visually and situations? in written form. How are fractions composed, decomposed, Comparisons are only valid when the two compared and represented? fractions refer to the same whole. Why is it important to identify, label, and Fractions and mixed numbers are composed of unit fractions and can be compare fractions as representations of equal parts of a whole or of a set? decomposed as a sum of unit fractions. How can the same fractional amount be Improper fractions and mixed numbers named in different ways using symbols? express the same value. How can fractions be compared and ordered? In addition to, in-depth inferences or applications that go beyond level. For make a model and defend how two fractions with unlike denominators are equivalent, i.e 1/3 and 3/9. order fractions with unlike denominators by explaining their relationship to benchmark fractions. (They should not find common denominators, but use their reasoning about benchmark fractions in conjunction with the ones provided.) 3.5 In addition to performance, in-depth inferences and applications with partial success. explain and compare using mathematical language how two fractions, e.g., 2/8 and 4/16 are equivalent fractions through the use of a visual model or through multiplying by 1 whole (which can be represented whenever the numerator and denominator are the same). Show 2/8 x (2/2) = 4/16 or 2/8 x (3/3) = 6/24. (4.NF.1) compare two fractions through comparing both to a benchmark fraction such as 1/2. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (4.NF.2) use models, benchmarks (0, 1/2 and 1) and equivalent forms to judge the size of fractions. (4.NF.2) 2.5 No major errors or gaps in content and partial knowledge in content. draw and identify fractional pieces. recognize or recall specific terminology: o equivalent fractions 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 11
Using students previous knowledge of the properties of whole numbers in addition and subtraction will aid in teaching of addition and subtractions of fractions. Improper fractions and mixed numbers express the same value. Addition and subtraction of fractions involves joining and separating parts referring to the same whole. Unit: Numbers and Operations- Fractions Topic: Add and Subtract Fractions Why does the numerator change, but the denominator stay the same when adding and subtracting fractions with like denominators? What does it mean to add and subtract fractions and mixed numbers with like denominators? What is a standard procedure for adding and subtracting mixed numbers with like denominators? How can fractions and mixed numbers be added and subtracted on a number line? In addition to, in-depth inferences or applications that go beyond level. For students should apply their understanding of equivalent fractions and their ability to rewrite fractions in an equivalent form to help them add and subtract with unlike denominators. given the fraction ¾ and 7/8, students must develop an argument to make those two equivalent. (Add 1/8 to ¾ to make 7/8) 3.5 In addition to performance, in-depth inferences and applications with partial success. understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (4.NF.3a) add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. (4.NF.3c) decompose a fraction into a sum of fractions with the same denominator in more than one way, such as an equation or a fraction model. Example: 3/8 = 1/8 + 1/8 + 1/8 or 3/8 = 1/8 + 2/8. (4.NF.3b) solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. (4.NF.3d) 2.5 No major errors or gaps in content and partial knowledge in content. add and subtract fractions using like denominators. decompose a fraction into a sum of fractions in only one way. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 12
Multiplying a fraction by a whole number is a logical step after multiplication of whole numbers. Unit: Numbers and Operations- Fractions Topic: Multiply Fractions How/why does the whole number become smaller when you multiply a whole number by a fraction? Improper fractions and mixed numbers represent the same value. How can multiplying a whole number by a fraction be displayed as repeated addition A product of a fractions times a whole number (as a multiple of a unit fraction)? can be written as a multiple of a unit fraction. In addition to, in-depth inferences or applications that go beyond level. For example compare and contrast the effects of multiplying fractions in relationship to multiplying whole numbers. apply what you know about multiplying fractions by a whole number to multiplying fractions by a fraction. 3.5 In addition to performance, in-depth inferences and applications with partial success. apply and extend previous understandings of multiplication to multiply a fraction by a whole number: o understand a fraction a/b as a multiple of 1/b, e.g. ¾ = ¼ +1/4 +1/4 or 3 x (1/4) = ¾ (4.NF.4a) o understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5). (4.NF.4b) solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction by using models and equations to represent the problem. (4.NF.4c) 2.5 No major errors or gaps in content and partial knowledge in content. solve word problems involving multiplication of fractions by a whole number without using a model to represent the problem. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 13
Unit: Numbers and Operations- Fractions Topic: Compare Decimals and Fractions Decimal notation is another way to represent a fraction. How can a fraction be represented by a decimal? Fractions with denominators of 10 can be expressed as an equivalent fraction with a denominator of 100. How can visual models be used to help with understanding decimals? How can visual models be used to determine Fractions with denominators of 10 and 100 may be expressed when using decimal notation. and compare equivalent fractions and decimals? How would you compare and order decimals When comparing two decimals to hundredths, the comparisons are only valid if they refer to the same whole. through hundredths? How is decimal numeration related to whole number numeration? In addition to, in-depth inferences or applications that go beyond level. For create a generalization about the process to turn any fraction into a decimal. given a benchmark decimal, students can produce two benchmark fractions. 3.5 In addition to performance, in-depth inferences and applications with partial success. express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this technique to add two fractions. (4.NF.5) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. use decimal notation for fractions with denominators 10 to 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (4.NF.6) compare two decimals to hundredths by reasoning by their size by recording the comparisons with the symbols >, <, =, and justify conclusions using a visual model with mathematical language. (4.NF.7) 2.5 No major errors or gaps in content and partial knowledge in content. compare two decimals to the hundredths using comparison symbols. match a fraction with a denominator 10 with the denominator 100. write decimal notations as a fraction with a denominator of 10 or 100. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 14
Unit: Geometry Topic: Classify Shapes Lines, rays, and angles are used to identify two-dimensional figures. What are examples of two-dimensional figures in everyday life? Two-dimensional figures are classified based on type of lines (parallel/perpendicular) and size of angles. How/why are geometric shapes constructed from different types of lines and angles? How are parallel and perpendicular lines used in classifying two-dimensional shapes? How can lines, angles, and shapes be described, analyzed, and classified? In addition to, in-depth inferences or applications that go beyond level. For defend the attributes of various shapes. given a misclassified shape, develop an argument for the correct classification. 3.5 In addition to performance, in-depth inferences and applications with partial success. construct and classify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular/parallel lines in two-dimensional figures (4.G.1) 2.5 No major errors or gaps in content and partial knowledge in content. identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular/parallel lines in two-dimensional figures 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 15
Unit: Geometry Topic: Measurement of Angles Angles can be measured and these measurements are additive. How can angles be composed or decomposed to form larger or smaller angles? Angles are measured in the context of a central angle of a circle. How are angles measured, added, or subtracted? Angles are composed of smaller angles. What are the types of angles and the relationships? How are angles applied to the context of a circle? How are protractors used to measure and aid in drawing angles and triangles? How can an addition or subtraction equation be used to solve a missing angle measure when the whole angle has been divided into two angles and only one measurement is given? In addition to, in-depth inferences or applications that go beyond level. For investigate why the angles of a triangle total 180 degrees, and a quadrilateral s angles total 360 degrees, and explain your reasoning. 3.5 In addition to performance, in-depth inferences and applications with partial success. classify two-dimensional figures based on the absence or presence of their parallel or perpendicular lines. (4.G.2) classify two-dimensional figures based on the absence or presence of angles and their specific size. (4.G.2) recognize angles as geometric shapes that are formed where two rays share a common endpoint, and understand concepts of angle measurement. (4.MD.5) measure angles in whole-number degrees using a protractor and sketch angles of a specific measure, realizing that a circle contains 360 1- degree angles and that all angles are measured with reference to a circle. (4.MD.6) understand the angle measure of the whole is the sum of the angle measures of the parts and solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems,. E.g. by using an equation with a symbol for the unknown angle measure. (4.MD.7) 2.5 No major errors or gaps in content and partial knowledge in content. identify two dimensional figures based on their parallel or perpendicular lines. Identify two-dimensional figures based on the types of angles in the figures. match and identify right triangles. identify the number of degrees of an angle. recognize that the number of degrees between the two rays of an angle is the measurement of that angle. recognize angles as geometric shapes that are formed whenever two rays share a common endpoint, and understand concepts of angle measurement, i.e. An angle is 16
measured with reference to a circle with its center at the common endpoint of the rays. 4.MD.5) recognize right triangles as a category and identify right triangles. (4.G.2) 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content.. 17
Unit: Geometry Topic: Lines of Symmetry A line of symmetry for a two-dimensional figure can be found by folding the shape Why do some shapes have more than one line of symmetry? into two congruent parts. How do the measurement of angles and sides relate to the number of lines of symmetry a shape has? In addition to, in-depth inferences or applications that go beyond level. For generalize why some shapes have 0, 1, or multiple lines of symmetry. given a specific number of lines of symmetry, the student will create a shape that meets those qualifications. 3.5 In addition to performance, in-depth inferences and applications with partial success. identify line-symmetric figures and draw lines of symmetry. (4.G.3) represent 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. (4.G.3) The student exhibits no major errors or gaps in the learning goal (complex ideas and 2.5 No major errors or gaps in content and partial knowledge in content. identify figures that are symmetrical. recognize a line of symmetry for a two dimensional figure as a line across the figure such that a figure can be folded along the line into matching parts. The student exhibits no major errors or gaps in the simpler details and processes. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 18
Unit: Measurement and Data Topic: Area & Perimeter The area and perimeter of objects can be found in the real world and mathematical Why would you need to find the area and perimeter of something? problems. What do area and perimeter mean and Perimeter is a real life application of how can each be found? addition and subtraction. How can the formulas for area and Area is a real life application of multiplication and division. perimeter help you solve real-world problems? distinguish between area and perimeter. apply the area and perimeter formulas when not given all dimensions of the shape. 3.5 In addition to performance, in-depth inferences and applications with partial success. apply the area and perimeter formulas for rectangles in real world and mathematical problems. (4.MD.3) (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.) 2.5 No major errors or gaps in content and partial knowledge in content. identify the correct area and perimeter of a rectangle given a list of answers. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 19
Unit: Measurement and Data Topic: Customary Measurement and Conversions Measurement units can be converted within a How can you estimate, measure, and change single system of measurement. customary units of length, volume, and mass? Use the four operations aids in solving word How can use the four operations to help solve problems involving measurement. word problems in measurement? When converting measurements within one Why does the size, length, mass, volume of an system, the size, length, mass, volume, of the object remain the same when converted to object remains the same. another unit of measurement? What are the customary units for measuring length, capacity, and weight/mass, and how are they related? In addition to, in-depth inferences or applications that go beyond level. For describe the patterns that you see among the different types of measurement in the Customary System. construct a problem using one of the four operations involving distance, intervals of time, liquid volumes, masses of objects, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit (e.g., feet to inches, dollars to cents). 3.5 In addition to performance, in-depth inferences and applications with partial success. know relative sizes of measurement units within one system of units including lb., oz.; in.; ft.; h, min, sec. (4.MD.1) express (convert) measurements in a larger unit in terms of a smaller unit within a single system of measurements. (4.MD.1) construct and record measurement equivalents in a two column table. (MD.4.1) represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. (4.MD.2) use the four operations to solve word problems involving distance, intervals of time, liquid volumes, masses of objects, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit (e.g., feet to inches, dollars to cents). (MD.4.2) 2.5 No major errors or gaps in content and partial knowledge in content. recognize equivalent measurements, i.e. 12 inches = 1 foot identify the appropriate measurement system to use in different situations. complete a table showing equivalent measurements. identify the operation to use to solve word problems involving distance, intervals of time, liquid volumes, masses of objects, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit (e.g., feet to inches, dollars to cents). 1.5 Partial understanding of the content with major errors or gaps in content. 20
With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 21
Unit: Measurement and Data Topic: Metric Measurement and Conversions Measurement units can be converted within a How can you estimate, measure, and single system of measurement. change metric units of length, volume, and Use the four operations aids in solving word mass? problems involving measurement. How can use the four operations to help When converting measurements within one solve word problems in measurement? system, the size, length, mass, volume, of the Why does the size, length, mass, volume object remains the same. of an object remain the same when Converting from larger to smaller units of converted to another unit of measurement? measurement in the metric system is done by What are the metric units for measuring multiplying by powers of ten. length, capacity, and weight/mass, and how are they related? In addition to, in-depth inferences or applications that go beyond level. For describe the patterns that you see among the different types of measurement in the Metric System. construct a problem using one of the four operations involving distance, intervals of time, liquid volumes, masses of objects, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit (e.g., centimeters to meters, milliliters to liters, grams to kilograms). 3.5 In addition to performance, in-depth inferences and applications with partial success. know relative sizes of measurement units within one system of units including km, m, cm. (4.MD.1) express (convert) measurements in a larger unit in terms of a smaller unit within a single system of measurements. (4.MD.1) construct and record measurement equivalents in a two column table. (MD.4.1) represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. (4.MD.2) use the four operations to solve word problems involving distance, intervals of time, liquid volumes, masses of objects, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit (e.g., milliliters to liters, grams to kilograms, meters to centimeters). (4.MD.2) 2.5 No major errors or gaps in content and partial knowledge in content. recognize that equivalent measurements can be written in more than one way, i.e. 100 cm= 1,000 mm = 1 meter. identify the appropriate measurement system to use in different situations. complete a table showing equivalent measurements. 22
identify the operation to use to solve word problems involving distance, intervals of time, liquid volumes, masses of objects, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit (meters to centimeter). 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 23
Unit: Measurement and Data Topic: Represent and Interpret Data Using addition and subtraction aids in solving word problems involving measurement. measurement? Data sets can be organized in a variety of ways, including line plots. How can you use addition and subtraction to help solve world problems in How can line plots and other tools help to solve measurement problems? In addition to, in-depth inferences or applications that go beyond level. For analyze the best way to display the data set.(pie chart, line graph, bar graph, pictograph, etc.) based on a line plot, provide 2 3 different interpretations/conclusions that you can reach from the data set. 3.5 In addition to performance, in-depth inferences and applications with partial success. make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). (4.MD.4) solve problems involving addition and subtraction of fractions by using information presented in line plots. (4.MD.4) 2.5 No major errors or gaps in content and partial knowledge in content. make a line plot to display a data set of measurements with whole numbers. 1.5 Partial understanding of the content with major errors or gaps in content. With help, a partial understanding of the content and some of the content. 0.5 With help, a partial understanding of the content and none of the content. 24