Greenup County School District 5th Grade Curriculum Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: August Unit #1 Critical Area #2 Standard # 5.NBT.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to I can recognize that each place to the left is 10 times larger in a multi-digit number (e.g., 2, 20, 200). I can recognize that each place to the right is 1/10 as much as in a number (e.g., 2, 2/10, 2/100). I can read and write decimals to the thousandths in word form, base-ten numerals, and expanded form. Decimal Decimal place thousandth Cluster: Understand the place value system. Target Type: Knowledge Cluster: Understand the place value system. 10 days MP- Look for and express regularity in repeated reasoning Comments: 5.NBT.1 is ongoing. Will be formally assessed at the end of Unit 4. MP-Construct viable arguments and critique the reasoning of Go Math Lessons 1.1 and 1.2 and Lessons 3.1-3.4. Base ten blocks Calendar Math Counting Tape Vonda Stamm’s Go Fish Game KET videos: Math Mansions: The Deciworms, Decimals,and The Rounding Machine Place Value charts Number lines Hundred charts Websites:
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: August and September Unit #2 Critical Area #2 Standard # 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. I can express powers of 10 using exponents (e.g., 10=101, 100 = 102, 1000 = 103). (K) I can illustrate and explain a pattern for how the number of zeros of a product-when multiplying a whole number by a power of 10-relates to the power of 10 (e.g., 500-which is 5 x 100, or 5 x 102-has two zeros in its product). (R) I can explain the standard algorithm for multi-digit whole number multiplication. (R) I can use the Powers of ten Exponent Decimal base Cluster: Understand the place value system. Target type: Knowledge Reasoning/Understanding 15 days MP- Look for and express regularity in repeated reasoning Go Math lessons in Chapter 1. Websites: KET Video: Math Mansions 14 Vonda Stamm’s Property Card Game Calendar Math: Counting Tape
5.NBT.5: Fluently multiply whole numbers using the standard algorithm. 5.OA.2: 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 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. standard algorithm to multiply whole numbers with ease. (S) I can represent a calculation expressed verbally with a numerical expression. (S) I can analyze expressions without solving. (R) I can use parentheses, brackets, or braces to group an expression within a numerical expression. (S) I can evaluate numerical expressions with parentheses, brackets, or Standard algorithm Cluster: Perform operations with multi-digit whole numbers and with decimals to hundredths. Target Type: Reasoning/Understanding Skill Cluster: Write and interpret numerical expressions MP-Attend to precision. MP-Look for and make use of
5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. braces. (S) Expression Numerical expressions Numerical expressions Evaluate Target Type: Skill Reasoning/Understanding Cluster: Write and interpret numerical expressions. Target Type: Skill structure. MP-Reason abstractly and quantitatively.
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: September and October Unit #3 Critical Area #2 Standard # 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. I can demonstrate division of whole numbers with four-digit dividends and two-digit divisors using place value, rectangular arrays, area models, and other strategies. (S) I can solve division of whole numbers with four-digit dividends and two-digit divisors using properties of operations and skills. (S) I can explain my chosen strategy. (R) Rectangular arrays Area model Cluster: Perform operations with whole numbers and with decimals to hundredths. Target Type: Skill Reasoning/ Understanding 14 days MP- Make sense of problems and persevere in solving them. Go Math Chapter 2 Websites: Calendar Math: Counting Tape Base Ten Blocks KET Videos: Math Mansions 15, The Remainder In Division,
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: October and November Unit #4 Critical Area #2 Standard # 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. I can add and subtract decimals to hundredths using strategies based on place value, properties of operations, or other strategies. (S) I can explain and illustrate strategies using concrete models or drawings when adding or subtracting decimals to hundredths. (R) Decimal Thousandth Cluster: Perform operations with whole numbers and with decimals to hundredths. Target Type: Skill Reasoning/ Understanding 10 days MP- Construct viable arguments and critique the reasoning of others. Go Math Chapter 3. Websites: Calendar Math: counting tape; partner game “Go for One” and “Go for Zero” Base Ten Blocks KET videos: Math Mansions 29
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: November Unit #5 Critical Area #2 Standard # 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use exponents to denote powers of 10. 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship I can illustrate and explain a pattern for how multiplying any decimal by a power of 10 relates to the placement of the decimal point (e.g., dividing 15.3 by 100, or 15.3 ÷ 102, results in 0.153—where the decimal point in the quotient is 2 places to the left of where is was in the dividend). (R) I can multiply decimals to hundredths using strategies based on place value, properties of operations, or other strategies. (S) I can explain and illustrate strategies using concrete Powers of 10 Exponent Decimal Cluster: Understand the place value system. Target Type: Reasoning/ Understanding 12 days MP- Look for and express regularity in repeated reasoning. Go Math Chapter 4 Websites: Decimal models Calendar Math: counting tape
between addition and subtraction; relate the strategy to a written method and explain the reasoning used. models or drawings when multiplying decimals to hundredths. (R) Decimal Cluster: Perform operations with whole numbers and with decimals to hundredths. Target Type: Skill Reasoning/ Understanding MP-Construct viable arguments and critique the reasoning of others.
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: December Unit #6 Critical Area #2 Standard # 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use exponents to denote powers of 10. 5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship I can illustrate and explain a pattern for how dividing any decimal by a power of 10 relates to the placement of the decimal point (e.g., dividing 15.3 by 100, or 15.3 ÷ 102, results in 0.153—where the decimal point in the quotient is 2 places to the left of where is was in the dividend). (R) I can divide decimals to hundredths using strategies based on place value, properties of operations, or other strategies. (S) I can explain and illustrate strategies using concrete models or drawings when dividing decimals to hundredths. (R) Powers of 10 Exponent Decimal decimal Cluster: Understand the place value system. Target Type: Reasoning/ Understanding Cluster: Perform operations with whole numbers and with decimals to hundredths. Target Type: Skill Reasoning/ Understanding 15 days MP- Look for and express regularity in repeated reasoning. MP-Construct viable arguments and critique the reasoning of others. Go Math-Chapter 5 Websites: Calendar Math Counting Tape KET Videos: Math Mansions 2
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: January Unit #7 Critical Area #1 Standard # 5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, I can determine common multiples of unlike denominators. (S) I can create equivalent fractions using common multiples. (S) I can add and subtract fractions with unlike denominators (including mixed numbers) using equivalent fractions. I can solve addition and subtraction word problems involving fractions using visual models or equations. (S) Mixed numbers Equivalent fractions Common denominator Common multiples Simplest form Cluster: Use equivalent fractions as a strategy to add and subtract fractions. Target Type: Skill Cluster: Use equivalent 12 days MP- Look for and make use of structure. Go Math Chapter 6 Websites: Calendar Math Counting Tape KET Videos: Math Mansions 25; The Cartoon Encyclopedia of Math: Addition with Mixed Numbers; The Cartoon Encyclopedia of Math: Subtraction with Mixed Numbers; Number lines Fraction Models; fraction strips Fraction Dice
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: January and February Unit #8 Critical Area #1 Standard # 5.NF.4: 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 (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) I can create story contexts for problems involving multiplication of a fraction and a whole number ((a/b ) x q) or multiplication of two fractions ((a/b) x (c/d)) by interpreting multiplication with fractions in the same way that I would interpret multiplication with whole numbers (e.g., 2/3 x 4 can be interpreted as, “If I need 2/3 cups of sugar for 1 batch of cookies, how much sugar do I need to make 4 batches of cookies?”). I can explain why (a/b) x q = (a x q)/b by using visual models to show that q is partitioned into b equal parts, and a parts of each partition results in (a x q) /b (e.g., in 2/3 x 4, there are Cluster: Apply and extend previous understanding of multiplication and division to multiply and divide fractions. Target Type: Product Reasoning Skill 20 days MP- Model with mathematics. Go Math Chapter 7 Calendar Math Counting Tape Counters Fraction Strips Fraction Circles Cuisenaire Rods Fraction blocks Number lines Dice Graph paper Grab and Go Centers Kit: Fraction Fix Up (Activity Card 6) and Fraction Factors Game KET videos: Math Mansions: Get Some Fraction Action; The Cartoon Encyclopedia of Math: Multiplying Fractions Websites:
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. 5.NF.5: 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. b. Explaining why multiplying a given number by a fraction greater multiplying the side lengths. I can interpret the relationship between the size of the factors to the size of the product. I can explain why multiplying a given number by a number of fraction greater than 1 results in a product greater than the given number (e.g., if ¾ is the given number and it is multiplied by 5, the product results in a fraction that is larger than ¾). I can explain why multiplying a given number by a fraction less than 1 results in a product less than the given number (e.g., if 5 is the given number and it is multiplied by ¾, the product Scaling Factor Cluster: Apply and extend previous understanding of multiplication and division to multiply and divide fractions. Target Type: Reasoning Skill MP-Look for and make use of structure.
than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. 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 results in a fraction that is less than 5). I can explain multiplication as scaling (to enlarge or reduce) using a visual model. I can multiply a given fraction by 1 (e.g., 2/2, 5/5) to find an equivalent fraction (e.g., ¾ x 2/2 = 6/8). I can solve real world problems involving multiplication of fractions and mixed numbers and interpret the product in the context of the problem. I can explain or illustrate my solution strategy using visual fractions models or equations that represent the problem. Mixed numbers Cluster: Apply and extend previous understanding of multiplication and division to multiply and divide fractions. Target Type: Skill Reasoning MP-Make sense of problems and persevere in solving them.
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: February and March Unit #9 Critical Area # Standard # 5.NF.7: 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 I can create story contexts for problems involving division of a unit fraction by a whole number (1/b ÷ n) or division of a whole number by a unit fraction (n ÷ 1/b) by interpreting division with fractions in the same way that I would interpret division with whole numbers (e.g., 1/3 ÷ 4 can be interpreted as, “How big would each piece be if I had to share a 1/3 slice of pizza with 4 people?”). I can solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, and interpret the quotient in the context of the problem. I can explain or Unit fraction Cluster: Apply and extend previous understanding of multiplication and division to multiply and divide fractions. Target Type: Product Skill Reasoning 20 days MP- Model with mathematics. Comment: Division of a fraction by a fraction is not a requirement at this grade. Go Math Chapter 8 Fraction Strips Number lines Calendar Math Counting Tape Fraction Circles Cuisenaire Rods Fraction blocks Graph paper Websites:
division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. c. Solve real world problems involving division of unit fractions by 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 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? 5.NF.3: Interpret a fraction as division of the numerator by the denominator I can explain that fractions (a/b) can be represented as a division of the numerator by the denominator (a ÷ b) and illustrate why a ÷ b can be represented by the fraction a/b. I can solve word problems involving the division of whole numbers and interpret the quotient – which could be a whole number, mixed number, or fraction – in the Mixed number Cluster: Apply and extend previous understanding of multiplication and division to multiply and divide fractions. Target Type: MP- Reason abstractly and quantitatively.
(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 context of the problem. I can explain or illustrate my solution strategy using visual fraction models or equations that represent the problem. Reasoning Skill
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: March Unit #10 Critical Area #3 Standard # 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 I can generate two numerical patterns with the same starting number for two given rules. I can explain the relationship between the two numerical patterns by comparing how each pattern grows or by comparing the relationship between each of the corresponding terms from each pattern. I can form ordered pairs out of corresponding terms from each pattern and graph them on a coordinate plane. Numerical pattern Corresponding terms Ordered pair Coordinate plane Cluster: Analyze patterns and relationships. Target Type: Skill Reasoning Skill 8 days MP- Look for and make use of structure. Go Math Chapter 9 Calendar Math Counting Tape Paper cups, water, Fahrenheit thermometer, ice cubes, and stopwatch for Investigation 9.3 Graph paper Smartboard Lessons “Number Patterns” and “Ordered Pairs” Websites:
observe that the terms in one sequence. Explain informally why this is so. 5.MD.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed I can create a line plot with a given set of unit fraction measurements. I can solve problems using data on line plots. I can construct a coordinate Line plot Unit fraction Cluster: Represent and interpret data. Target type: Skill Skill Cluster: Graph points on the MP-Use appropriate tools strategically. MP- Look for and make use of
Unit & Critical Area KCAS Standard Learning Target Statement Vocabulary Cluster & Target Type Days, Mathematical Practices, & Comments Resources Time Frame: April and May Unit #12 Critical Area #3 Standard # 5.G.3: Understand that attributes belonging to a category of 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. 5.G.4: Classify figures in a hierarchy based on properties. I can classify figures by their attributes. I can explain attributes can belong to several two-dimensional figures. I can identify subcategories using attributes. I can group together all shapes that share a single property, and then among these shapes, group together Cluster: Classify figures into categories based on their properties. Target Type: Skill Reasoning Reasoning Cluster: Classify 15 days MP- Look for and make use of structure. Comment: This is a large chapter with a lot of standards to teach. You may want to break this into 2 unit of study: One that focuses on geometry and one that focuses on volume. Go Math Chapter 11 Grab and Go Centers Kit Pattern blocks Vocabulary Word wall Venn Diagrams Centimeter Ruler Protractor Scissors Quadrilaterals Tracing Paper Solid figures Paper nets Unit cubes Empty rectangular prisms Volume formulas The Greedy Triangle by Marilyn Burns Geoboards Triangle song Spaghetti and marshmallows Geometry memory game Quadrilateral dance KET video: Math Mansions 33: A very fine pet is a polyhedron Websites:
5.MD.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. 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. those that share a second property, and then among these, group together those that share a third property, etc. I can identify volume as an attribute of a solid figure. I can recognize that a cube with 1 unit side length is “one cubic unit” of volume. I can explain a process for finding the volume of a solid figure by filling it with unit cubes without gaps and overlaps. Volume Unit cube Cubic unit figures into categories based on their properties. Target Type: Skill Cluster: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Target Type: Knowledge Knowledge Reasoning MP- Construct viable arguments and critique the reasoning of others. MP- Construct viable arguments and critique the reasoning of others.
5.MD.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5.MD.5: 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 whole-number side lengths by packing it with unit cubes, and show I can measure the volume of a hollow figure by filling it with unit cubes without gaps and counting the number of unit squares. I can use unit cubes to determine the volume of a rectangular prism. I can explain multiplication of the area of the base ( l x w = b) by the height ( b x h = V) will result in the volume. I can relate finding the product of three numbers to finding volume and relate both to the associative property of multiplication. I can use the formulas to Volume Unit cube Cluster: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Target Type: Skill MP- Use appropriate tools strategically. MP- Look for and express regularity in repeated reasoning.
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 products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with edge lengths in the context of solving real world and mathematical problems. c. Recognize determine the volume of rectangular prisms. I can decompose an irregular figure into rectangular prisms and find the volume of the irregular figure by finding the sum of the volumes of each of the decomposed prisms. I can solve real world problems involving volume. Volume Right rectangular prism Additive Cluster: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Target Type: Skill Reasoning Reasoning Skill Skill Skill