5.NBT.: Recognize that in a multi-digit number, a digit in one place represents 0 times as much as it represents in the place to its right and /0 of what it represents in the place to its left. Recognize that in a multi-digit number, a digit in one place represents 0 times as much as it represents in the place to its right and /0 of what it represents in the place to its left. I can recognize that in a multi-digit number, a digit in one place represents 0 times as much as it represents in the place to its right and /0 of what it represents in the place to its left. place value Base Ten System 5.NBT.: Explain patterns in the number of zeros of the product when multiplying a number by powers of 0, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 0. Use wholenumber exponents to denote powers of 0. Represent powers of 0 using whole number exponents Fluently translate between powers of ten written as ten raised to a whole number exponent, the expanded form, and standard notation (0 to the third power = 0 x 0 x 0 = 000) I can represent powers of 0 using whole number exponents I can express a number using powers of ten (i.e. written as ten raised to a whole number exponent). I can represent a number in expanded form. * powers exponents standard form(notation) expanded form I can represent a number in standard notation (0 to the third power = 0 x 0 x 0 = 000) Explain the patterns in the number of zeros of the product when multiplying a number by powers of 0. Explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 0. I can explain the patterns in the number of zeros of the product when multiplying a number by powers of 0. I can explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 0. 5.NBT.3a: Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.39 = 3 00 + 4 0 + 7 + 3 (/0) + 9 (/00) + (/000). Read and write decimal to thousandths using base-ten numerals, number names, and expanded form I can read and write decimal to thousandths using base-ten numerals, word form, and expanded form. tenths hundredths * thousandths * word form
5.NBT.3b: Read, write, and compare decimals to thousandths. b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use >, =, and < symbols to record the results of comparisons between decimals Compare two decimals to the thousandths based on the place value of each digit. I can use >, =, and < symbols to record the results of comparisons between decimals I can compare two decimals to the thousandths based on the place value of each digit. * comparison symbols 5.NBT.4: Use place value understanding to round decimals to any place. Use knowledge of base ten and place value to round decimals to any place I can use knowledge of base ten and place value to round decimals to any place estimation round base ten system 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm. Fluently multiply multi-digit whole numbers using the standard algorithm. I can fluently multiply multi-digit whole numbers using the standard algorithm. regrouping place value holder * algorithm single-digit multi-digit 5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division to solve division problems. Illustrate and explain division calculations by using equations, rectangular arrays, and/or area models. I can find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors I can use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division to solve division problems. I can illustrate and explain division calculations by using equations, rectangular arrays, and/or area models. quotient dividend divisor remainder array area model
3 Add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings and 5.NBT.7: Add, subtract, multiply, and divide decimals to strategies based on place value, properties of hundredths, using concrete models or drawings and strategies operations, and/or the relationship between addition based on place value, properties of operations, and/or the and subtraction. relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Relate the strategy to a written method and explain the reasoning used to solve decimal operation calculations. I can add and subtract decimals to hundredths using concrete models or drawings and strategies based on place value, and properties of operations. I can 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. I can relate the strategy to a written method and explain the reasoning used to solve decimal operation calculations. 4.NF.: Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Recognize and identify equivalent fractions with unlike denominators I can recognize and identify equivalent fractions with unlike denominators. Explain why a/b is equal to (nab)/(nab) by using I can multiply the numerator and denominator fraction models with attention to how the number and by the same number to create equivalent size of the parts differ even though the two fractions fractions. themselves are the same size. (Ex: Use fraction strips to show why ½=/4=3/6=4/8) *equivalent fraction numerator denominator *Simplify (simplest form) Use visual fraction models to show why fractions are equivalent (ex: ¾ = 6/8) Generate equivalent fractions using visual fraction models and explain why they can be called equivalent. I can use models to show equivalent fractions. I can explain why fractions are equivalent using visual models.
4 4.NF.: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as /. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Recognize fractions as being greater than, less than, or equal to other fractions. Record comparison results with symbols: <, >, = Use benchmark fractions such as ½ for comparison purposes. Make comparisons based on parts of the same whole. Compare two fractions with different numerators, e.g. by comparing to a benchmark fraction such as ½. I can compare fractions. I can use symbols such as >, <, =. I can use benchmark fractions to compare fractions. I can make comparisons based on parts of the same whole. I can compare fractions with different numerators using benchmark fractions. Benchmark *Common denominator Compare two fractions with different denominators, e.g. by creating common denominators, or by comparing to a benchmark fraction such as ½. Justify the results of a comparison of two fractions, e.g. by using a visual fraction model. I can compare fractions with different denominators using benchmark fractions. I can use visual fraction models to show fraction comparisons. 4.NF.3b: Understand a fraction a/b with a > as a sum of fractions /b. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = /8 + /8 + /8 ; 3/8 = /8 + /8 ; /8 = + + /8 = 8/8 + 8/8 + /8. Add and subtract fractions with like denominators. Recognize multiple representations of one whole using fractions with the same denominator. Using visual fraction models, decompose a fraction into the sum of fractions with the same denominator in more than one way. Record decompositions of fractions as an equation and explain the equation using visual fraction models. I can add and subtract fractions with like denominators. I can identify many ways to make one whole using fractions with the same denominator. I can use models to decompose a fraction with the same denominator. I can record and demonstrate decompositions of fractions as equation and explain the equation using visual fraction models.
5 5.NF.: 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, /3 + 5/4 = 8/ + 5/ = 3/. (In general, a/b + c/d = (ad + bc)/bd.) Generate equivalent fractions to find the like denominator Solve addition and subtraction problems involving fractions (including mixed numbers) with like and unlike denominators using an equivalent fraction strategy I can generate equivalent fractions to find the like denominator I can solve addition and subtraction problems involving fractions (including mixed numbers) with like and unlike denominators using an equivalent fraction strategy equivalent equivalent fractions denominator numerator mixed-number improper fraction * unlike denominator * Least common multiple (LCM) * Greatest common factor (GCF) 5.NF.: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result /5 + / = 3/7, by observing that 3/7 < /. Solve word problems involving addition and subtraction of fractions with unlike denominators referring to the same whole (e.g. by using visual fraction models or equations to represent the problem) Evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction. I can solve word problems involving addition and subtraction of fractions with unlike denominators referring to the same whole (e.g. by using visual fraction models or equations to represent the problem) I can evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction. * reasonable unlike denominators benchmark fraction equation * evaluate 5.NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (e.g. using visual fraction models or equations to represent the problem.) Interpret the remainder as a fractional part of the problem. I can interpret a fraction as division of the numerator by the denominator (a/b = a b). I can solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (e.g. using visual fraction models or equations to represent the problem.) I can interpret the remainder as a fractional part of the problem. interpret remainder fractional part numerator denominator
6 Multiply fractions by whole numbers. I can multiply fractions by whole numbers. whole number 5.NF.4a: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show (/3) 4 = 8/3, and create a story context for this equation. Do the same with (/3) (4/5) = 8/5. (In general, (a/b) (c/d) = ac/bd.) Multiply fractions by fractions Interpret the product of a fraction times a whole number as total number of parts of the whole. (for example ¾ x 3 = ¾ + ¾ + ¾ = 9/4) Determine the sequence of operations that result in the total number of parts of the whole. (for example ¾ x 3 = (3 x 3)/4 = 9/4) Interpret the product of a fraction times a fraction as the total number of parts of the whole I can multiply fractions by fractions I can Interpret the product of a fraction times a whole number as total number of parts of the whole. (for example ¾ x 3 = ¾ + ¾ + ¾ = 9/4) I can determine the sequence of operations that result in the total number of parts of the whole. (for example ¾ x 3 = (3 x 3)/4 = 9/4) I can interpret the product of a fraction times a fraction as the total number of parts of the whole product operations 5.NF.4b: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Find area of a rectangle with fractional side lengths using different strategies. (e.g., tiling with unit squares of the appropriate unit fraction side lengths, multiplying side lengths) Represent fraction products as rectangular areas. Justify multiplying fractional side lengths to find the area is the same as tiling a rectangle with unit squares of the appropriate unit fraction side lengths. I can find area of a rectangle with fractional side lengths using different strategies. (e.g., tiling with unit squares of the appropriate unit fraction side lengths, multiplying side lengths) I can represent fraction products as rectangular areas. I can justify multiplying fractional side lengths to find the area is the same as tiling a rectangle with unit squares of the appropriate unit fraction side lengths. area length width tiling square units Model the area of rectangles with fractional side lengths with unit squares to show the area of rectangles (Performance) I can model the area of rectangles with fractional side lengths with unit squares to show the area of rectangles
7 5.NF.5a: Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Know that scaling (resizing) involves multiplication. Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. For example, a x3 rectangle would have an area twice the length of 3. I understand that scaling (resizing) involves multiplication. I can compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. For example, a x3 rectangle would have an area twice the length of 3. * scaling/ resizing factor 5.NF.5b: Interpret multiplication as scaling (resizing), by: b. Explaining why multiplying a given number by a fraction greater than results in a product greater than the given number (recognizing multiplication by whole numbers greater than as a familiar case); explaining why multiplying a given number by a fraction less than results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (nab)/(nab) to the effect of multiplying a/b by. Know that multiplying whole numbers and fractions result in products greater than or less than one depending upon the factors. Draw a conclusion multiplying a fraction greater than one will result in a product greater than the given number. Draw a conclusion that when you multiply a fraction by one (which can be written as various fractions, ex /, 3/3, etc.) the resulting fraction is equivalent. Draw a conclusion that when you multiply a fraction by a fraction, the product will be smaller than the given number. I understand that multiplying whole numbers and fractions result in products greater than or less than one depending upon the factors. I can draw a conclusion multiplying a fraction greater than one will result in a product greater than the given number. I can draw a conclusion that when you multiply a fraction by one (which can be written as various fractions, ex /, 3/3, etc.) the resulting fraction is equivalent. I can draw a conclusion that when you multiply a fraction by a fraction, the product will be smaller than the given number. equivalent product whole numbers fractions
8 5.NF.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Represent word problems involving multiplication of fractions and mixed numbers ( e.g., by using visual fraction models or equations to represent the problem.) Solve real world problems involving multiplication of fractions and mixed numbers. I can represent word problems involving multiplication of fractions and mixed numbers ( e.g., by using visual fraction models or equations to represent the problem.) I can solve real world problems involving multiplication of fractions and mixed numbers. mixed number equations fractions 5.NF.7abc: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (/3) 4 = / because (/) 4 = /3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 (/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (/5) = 0 because 0 (/5) = 4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share / lb of chocolate equally? How many /3-cup servings are in cups of raisins? Know the relationship between multiplication and division Interpret division of a unit fraction by a whole number and justify your answer using the relationship between multiplication and division, and by creating story problems, using visual models, and relationship to multiplication, etc. Interpret division of a whole number by a unit fraction and justify your answer using the relationship between multiplication and division, and by representing the quotient with a visual fraction model. Solve real world problems involving division of unit fractions by whole numbers other than 0 and division of whole numbers by unit fractions using strategies such as visual fractions models and equations. I understand the relationship between multiplication and division I can interpret division of a unit fraction by a whole number and justify your answer using the relationship between multiplication and division, and by creating story problems, using visual models, and relationship to multiplication, etc. I can interpret division of a whole number by a unit fraction and justify the answer using the relationship between multiplication and division, and by representing the quotient with a visual fraction model. I can solve real world problems involving division of unit fractions by whole numbers other than 0 and division of whole numbers by unit fractions using strategies such as visual fractions models and equations. * inverse * multiplicative inverse/reciprocal unit fraction
9 Early 3 OPERATIONS AND ALGEBRAIC THINKING 4.OA.4: Find all factor pairs for a whole number in the range 00. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 00 is a multiple of a given one-digit number. Determine whether a given whole number in the range 00 is prime or composite. Define prime and composite numbers. Know strategies to determine whether a whole number is prime or composite. Identify all factor pairs for any given number -00. Recognize that a whole number is a multiple of each of its factors. Determine if a given whole number (-00) is a multiple of a given one-digit number. I can define prime and composite numbers. I can determine whether a whole number is prime or composite. I can identify all factors of a given number from -00. I can recognize that a whole number is a multiple of each of its factor given one-digit number. I can determine if a number is a multiple of a given number. *Prime *Composite Factor Multiple OPERATIONAS AND ALGEBRAIC THINKING Multiply and divide within 00. I can multiply and divide within 00. *Commutative Property Early 3 3.OA.5: Apply properties of operations as strategies to multiply and divide. (Note: Students need not use formal terms for these properties.) Examples: If 6 4 = 4 is known, then 4 6 = 4 is also known. (Commutative property of multiplication.) 3 5 can be found by 3 5 = 5, then 5 = 30, or by 5 = 0, then 3 0 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 = 6, one can find 8 7 as 8 (5 + ) = (8 5) + (8 ) = 40 + 6 = 56. (Distributive property.) Explain how the properties of operations work. Apply properties of operations as strategies to multiply and divide. I can explain the properties of multiplication and division. I can apply properties of multiplication and division as strategies to solve problems. * Associative Property * Distributive Property Strategies Early 3 OPERATIONS AND ALGEBRAIC THINKINIG 5.OA.: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Use order of operations including parenthesis, brackets, or braces. Evaluate expressions using the order of operations (including using parenthesis, brackets, or braces.) I can explain the order of operations. I can evaluate expressions using order of operations. * order of operations * expressions * exponent
0 OPERATIONS AND ALGEBRAIC THINKINIG Write numerical expressions for given numbers with operation words. I can write numerical expressions for given numbers with operation words. variable Early 3 5.OA.: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by as (8 + 7). Recognize that 3 (893 + 9) is three times as large as 893 + 9, without having to calculate the indicated sum or product. Write operation words to describe a given numerical expression. Interpret numerical expressions without evaluating them. I can write operation words to describe a given numerical expression. I can interpret numerical expressions without evaluating them. Early 3 OPERATIONS AND ALGEBRAIC THINKINIG 5.OA.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Generate two numerical patterns using two given rules. Form ordered pairs consisting of corresponding terms for the two patterns Graph generated ordered pairs on a coordinate plane Analyze and explain the relationships between corresponding terms in the two numerical patterns. Given two rules and two inputs, I can create two outcomes and explain the relationship between the two. I can plot an ordered pair on a coordinate grid. I can analyze and explain the relationships between corresponding terms in the two numerical patterns. * ordered pairs/ coordinates * coordinate plane * axis x and y 5.MD.: 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. Recognize units of measurement within the same system Divide and multiply to change units Convert units of measurement within the same system I recognize units of measurement within the same system I can divide and multiply to change units I can convert units of measurement within the same system conversion multi-step * Customary Units of measurement * Metric Units of measurement Solve multi-step, real world problems that involve converting units I can solve multi-step, real world problems that involve converting units
5.MD.: Make a line plot to display a data set of measurements in fractions of a unit (/, /4, /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. Identify benchmark fractions (/, /4, /8) Make a line plot to display a data set of measurements in fractions of a unit (/, /4, /8). Solve problems involving information presented in line plots which use fractions of a unit (/, /4, /8) by adding, subtracting, multiplying, and dividing fractions. I can identify benchmark fractions (/, /4, /8) I can make a line plot to display a data set of measurements in fractions of a unit (/, /4, /8). I can solve problems involving information presented in line plots which use fractions of a unit (/, /4, /8) by adding, subtracting, multiplying, and dividing fractions. benchmark fractions * line plot 3.MD.: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Note: Excludes compound units such as cm3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Note: Excludes multiplicative comparison problems -- problems involving notions of times as much ; see Glossary, Table.) Explain how to measure liquid volume in liters. Explain how to measure mass in grams and kilograms. Add, subtract, multiply and divide units of liters, grams, and kilograms. Know various strategies to represent a word problem involving liquid volume or mass. Solve one step word problems involving masses given in the same units. Solve one step word problems involving liquid volume given in the same units. Measure liquid volumes using standard units of liters. I can explain how to measure liquid volume in liters. I can explain how to measure mass in grams and kilograms. I can add, subtract, multiply, and divide units of measure. I can use strategies to represent a word problem involving liquid volume or mass. I can solve one step word problems involving masses given in the same units. I can solve one step word problems involving liquid volume given in the same units. I can measure liquid volumes using liters. * Liters * Grams * Kilograms * Mass Measure mass of objects using standard units of grams (g), and kilograms (kg). I can measure mass of objects using grams and kilograms.
Recognize that angles are measured in degrees ( ). I can recognize that angles are measured in degrees. * Protractor * Degrees 4.MD.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Read a protractor. Determine which scale on the protractor to use, based on the direction the angle is open. Determine the kind of angle based on the specified measure to decide reasonableness of the sketch. Measure angles in whole-number degrees using a protractor. (Performance) Sketch angles of specified measure.. (Performance) I can read a protractor. I can determine which scale on the protractor to use, based on the direction the angle is open. I can determine the kind of angle based on the specified measure to describe reasonableness of a sketch. I can measure angles in whole-number degrees using a protractor. I can sketch angles of specified measure. 5.MD.3ab: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. b. 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. Recognize that volume is the measurement of the space inside a solid three-dimensional figure. Recognize a unit cube has cubic unit of volume and is used to measure volume of three-dimensional shapes. Recognize any solid figure packed without gaps or overlaps and filled with (n) unit cubes indicates the total cubic units or volume. I recognize that volume is the measurement of the space inside a solid three-dimensional figure. I recognize a unit cube has cubic unit of volume and is used to measure volume of three-dimensional shapes. I recognize any solid figure packed without gaps or overlaps and filled with (n) unit cubes indicates the total cubic units or volume. * volume 3- Dimensional figures * cubic units * solid figure 5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Measure volume by counting unit cubes, cubic cm, cubic in., cubic ft., and improvised units. I can measure volume by counting unit cubes, cubic cm, cubic in., cubic ft., and improvised units. * volume 3- Dimensional figures * cubic units * improvised units(nonstandard)
3 Identify a right rectangular prism. I can identify a right rectangular prism. * rectangular prism 5.MD.5a: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. 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. Multiply the three dimensions in any order to calculate volume (Commutative and associative properties) Develop volume formula for a rectangle prism by comparing volume when filled with cubes to volume by multiplying the height by the area of the base, or when multiplying the edge lengths (LxWxH) I can multiply the three dimensions in any order to calculate volume (Commutative and associative properties) I can develop volume formula for a rectangular prism by comparing volume when filled with cubes to volume by multiplying the height by the area of the base, or when multiplying the edge lengths (LxWxH) length width height volume Find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes. I can find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes. Know that B is the area of the base I know that B is the area of the base area of base (LxW) 5.MD.5b: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. b. Apply the formulas V = l w h and V = b h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Apply the following formulas to right rectangular prisms having whole number edge lengths in the context of real world mathematical problems: Volume = length x width x height Volume = area of base x height I can apply the following formulas to right rectangular prisms having whole number edge lengths in the context of real world mathematical problems: Volume = length x width x height Volume = area of base x height height Recognize volume as additive. I recognize volume as additive. * volume 5.MD.5c: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. c. 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. Solve real world problems by decomposing a solid figure into two non-overlapping right rectangular prisms and adding their volumes. I can solve real world problems by decomposing a solid figure into two nonoverlapping right rectangular prisms and adding their volumes. overlapping non-overlapping
4 GEOMETRY.G.: Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Note: Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Identify the attributes of triangles, quadrilaterals, pentagons, hexagons, and cubes (e.g. faces, angles, sides, vertices, etc). Identify triangles, quadrilaterals, pentagons, hexagons, and cubes based on the given attributes. I can identify the attributes of triangles, quadrilaterals, pentagons, hexagons, and cubes. I can identify triangles, quadrilaterals, pentagons, hexagons, and cubes based on the given attributes. * Quadrilaterals * Pentagon * Faces * Angles Attribute Blocks Geoboards Pattern Blocks Tangrams www.whizz.us www.vmath.com www.funbrain.com www.primarygames.com 4 Describe and analyze shapes by examining their sides and angles, not by measuring. Compare shapes by their attributes (e.g. faces, angles). I can describe and analyze shapes by examining their sides and angles. I can compare shapes by their attributes. Tessellations www.carstenstudios.com www.coolmath4kids.com www.mathplayground.com Draw shapes with specified attributes. (Product) I can draw shapes with specified attributes. www.a+math.com www.cte.jhu.edu www.aaamath.com GEOMETRY Define the coordinate system I can define the coordinate system * coordinate system 4 5.G.: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Identify the x- and y-axis Locate the origin on the coordinate system Identify coordinates of a point on a coordinate system Recognize and describe the connection between the ordered pair and the x- and y-axis (from the origin) I can identify the x- and y-axis I can locate the origin on the coordinate system I can identify coordinates of a point on a coordinate system I recognize and describe the connection between the ordered pair and the x- and y-axis (from the origin) * ordered pair * X axis * Y axis
5 GEOMETRY Graph points in the first quadrant I can graph points in the first quadrant quadrant 4 5.G.: 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. Represent real world and mathematical problems by graphing points in the first quadrant Interpret coordinate values of points in real world context and mathematical problems I can represent real world and mathematical problems by graphing points in the first quadrant I can interpret coordinate values of points in real world context and mathematical problems 4 GEOMETRY 5.G.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Recognize that some two-dimensional shapes can be classified into more than one category based on their attributes. Recognize if a two-dimensional shape is classified into a category, that it belongs to all subcategories of that category.. I can recognize that some two-dimensional shapes can be classified into more than one category based on their attributes. I can recognize if a two-dimensional shape is classified into a category, that it belongs to all subcategories of that category.. * attributes two-dimensional GEOMETRY 5.G.4: Classify two-dimensional figures in a hierarchy based on properties. Recognize the hierarchy of two-dimensional shapes based on their attributes. Analyze properties of two-dimensional figures in order to place into a hierarchy. I can recognize the hierarchy of twodimensional shapes based on their attributes. I can analyze properties of two-dimensional figures in order to place into a hierarchy. 4 Classify two-dimensional figures into categories and/or sub-categories based on their attributes. I can classify two-dimensional figures into categories and/or sub-categories based on their attributes.