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Unit: Number Puzzles and Multiple Towers Standard Description Number "Big Idea" Standards 5.N.8 Apply the number theory concepts of common factor, common multiple, and divisibility rules for 2, 3, 5, and 10 to the solution of problems. Demonstrate an understanding of the concepts of prime and composite numbers. 5.N.9 Solve problems involving multiplication and division of whole numbers, and multiplication of positive fractions with whole numbers. 5.N.12 Accurately and efficiently add and subtract whole numbers and positive decimals. Multiply and divide (using double-digit divisors) whole numbers. Multiply positive decimals with whole numbers. Supported Standards 5.N.1 Demonstrate an understanding of (positive integer) powers of ten. 5.N.2 Demonstrate an understanding of place value through millions and thousandths. 5.N.3 Represent and compare large (millions) and small (thousandths) positive numbers in various forms, such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4. 5.N.7 Compare and order whole numbers, positive fractions, positive mixed numbers, positive decimals, and percents. 5.N.14 Estimate sums and differences of whole numbers, positive fractions, and positive decimals. Estimate products of whole numbers and products of positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer. 5.M.1 Apply the concepts of perimeter and area to the solution of problems involving triangles and rectangles. Apply formulas where appropriate. Additional Ten Minute Math Standards 5.P.3 Number Puzzles and Multiple Towers -- September - beginning of October Inv. Title & MA Stan. Content Objectives Key Vocabulary Sample Language Pacing Pages Objectives Inv. 1: 5.N.8 Students will use arrays to model multiplication. multiplication, Listening/Speaking: 7 one-hour sessions 5.N.12 division, factor, Students will understand and Finding 5.M.1 Students will determine whether one number is a factor array, product, use key vocabulary during Factors and 5.N.1 or multiple of another. multiple, discussion. Prime 5.N.2 dimensions, Factors 5.P.3 Students will identify prime, square, even, and odd even number, Students will ask and numbers. odd number, respond to questions to TE 24-64 prime number, clarify information. Students will use multiplication facts to find equivalent composite multiplication combinations. number, Writing: square number, Students will write short Students will use multiplication facts for numbers square root, accounts about classroom related by place value. prime topics. factorization Students will find all the ways to multiply whole common factor, Students will write about numbers for a given product. common steps to solve a problem, multiple, placing events in a logical Students will use properties and relationships of divisible, solution order. numbers to solve problems. Students will determine the prime factorization of a number. Teachers' Notes: --Ten-Minute Math is Quick Images: Seeing Numbers. Students should write as many multiplication equations to describe the dot arrangements as they can, using two or more factors. This activity supports standards 5.N.8, 5.N.12, and 5.P.3. --During Session 1.1, Activity 3, have students generalize for all numbers that would fit the "10 tiles wide" clue. This will reinforce divisibility rules for multiples of 10, part of standard 5.N.8. --At the end of Session 1.2, allow struggling learners to build or draw arrays for further practice while advanced learners find additional prime numbers greater than 50. -- Homework for Session 1.3 involves practice with basic multiplication facts. For students who continue to exhibit difficulty with memorizing these facts, try a daily five-minute flash card warm-up and personalized flash cards for daily studying at home. --When students finish solving number puzzles quickly, they can write their own puzzles to give to classmates to solve. --Numbers factored by students can also vary, giving simpler numbers to struggling students, and asking for longer multiplication combinations from advanced learners. Prime factorization addressed in Session 1.7 goes beyond fifth grade standard, addressing the sixth grade number theory standard. This activity could be reserved for students demonstrating mastery of other factoring activities. --Common multiples, common factors, and divisibility rules from standard 5.N.8 not addressed directly as part of investigation. Please use complimentary materials to address these concepts. Inv. Title & MA Stan. Content Objectives Key Vocabulary Sample Language Pacing Pages Objectives Inv. 2: 5.N.12 Students will solve 2-digit by 2-digit multiplication distributive Listening/Speaking: 7 one-hour sessions 5.N.9 problems. property, Students will retell steps of a Multiplicatio 5.M.1 expanded process in logical order. n Strategies 5.N.14 Students will create story problems represented by a notation, 5.N.7 multiplication and division expressions. standard Students will compare and TE 66-107 5.N.2 notation, contrast strategies used to 5.N.3 Students will represent multiplication and division parenthesis, solve multiplication problems 5.N.8 problems with pictures or diagrams. associative orally. property, less Students will use arrays to model multiplication. than, greater Writing: than, value, Students will draw and label Students will multiply fluently by multiples of 10. estimate, or write story problems which approximate, describe multiplication and Students will compare multiplication problems to rounding division situations. determine which product is greater. Students will write short Students will estimate the product of two numbers. explanations of how a problems was solved. Students will decompose multiplication problems efficiently. Students will organize work and use clear and concise notation to show how multiplication problems have been solved. Teachers' Notes: --Ten-Minute Math becomes Number Puzzles, which continues to reinforce 5.N.8. --To get a feel for the fluency students are developing for solving multiplication problems, meet with small groups of students to observe them. Discuss misconceptions and provide specific feedback about progress/mistakes students in each group make. --If students refer to multiplying by 10, or by multiples of 10, as adding a zero, please correct their phraseology so they address this as attaching a zero. When you add a zero to any number, the value of the original number is unchanged. --During 2.3-2.6, adjust numbers as necessary so that students are challenged at appropriate level of understanding. --For students struggling with cluster problems, model an appropriate first step, to start them in the right direction. If students are efficiently finding answers, challenge them to find another way to solve each problem, using other strategies such as doubling and halving. During sessions 2.4 -2.6, it is not necessary for all students to study cluster problems and starter problems. In addition to repeated addition, it is essential that students have at least one other strategy (i.e., area model, lattice method, partial products, cluster problems, U.S. standard algorithm) to be able to multiply 2- digit numbers efficiently and with understanding (make a connection between the two strategies). Inv. Title & MA Stan. Content Objectives Key Vocabulary Sample Language Pacing Pages Objectives Inv. 3: 5.N.9 Students will represent multiplication and division dividend, divisor, Listening/Speaking: 8 one-hour sessions 5.N.12 problems with pictures or diagrams. quotient, Students will compare and Division 5.P.3 remainder contrast strategies used to Strategies 5.N.2 Students will create story problems represented by a solve division problems 5.N.8 multiplication and division expressions. orally. TE 110-152 Students will use knowledge of multiples of 10 to solve Writing: division problems. Students will organize work and use clear and concise Students will use and interpret notation that represents notation to show how division division. problems have been solved. Students will relate division and multiplication Students will choose a notations. division problem and record their strategy for solving that Students will solve division problems with 2-digit problem in a short paragraph. divisors. Students will make sense of remainders when solving division problems. Students will solve a division problem by breaking the dividend into parts. Students will compare division problems to determine which quotient is greater. Teacher Notes: --Ten Minute Math during Investigation 3 will consist of some Quick Images: Seeing Numbers and some Number Puzzles. During Seeing Numbers, students should write multiplication and division equations that represent the dot arrangements they see. For the Number Puzzles, the Random Clue variation can be played, in which clues are combined and drawn randomly. This will lead to a greater number of inconclusive results for which students can modify clues and generate a result. --If students experience difficulty connecting the multiple towers in session 3.2 to multiplication and division, they can write corresponding expressions next to each multiple. In session 3.4, it is not necessary for students to know all suggested strategies, as long as they are efficient with one of the strategies and can connect division to multiplication. During class discussions, be sure to emphasize the partial quotients (big seven) strategy as this will reinforce the U.S. standard algorithm when we reach Unit 7 (How Many People How Many Teams?). --During Session 3.6, Division Compare can be differentiated, so that struggling students practice division of 2-digit numbers by 1-digit numbers, and proficient students can practice playing without multiples of ten. Unit: Thousands of Miles, Thousands of Seats Standard Number Description "Big Idea" Standards 5.N.2 Demonstrate an understanding of place value through millions and thousandths 5.N.3 Represent and compare large (millions) and small (thousandths) positive numbers in various forms, such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4. 5.N.7 Compare and order whole numbers, positive fractions, positive mixed numbers, positive decimals, and percents 5.N.9 Solve problems involving multiplication and division of whole numbers, and multiplication of positive fractions with whole numbers. 5.N.11 Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems. 5.N.12 Accurately and efficiently add and subtract whole numbers and positive decimals. Multiply and divide (using double- digit divisors) whole numbers. Multiply positive decimals with whole numbers. Supported Standards 5.N.1 Demonstrate an understanding of (positive integer) powers of ten 5.N.6 Find and position whole numbers, positive fractions, positive mixed numbers, and positive decimals on a number line Additional Ten Minute Math Standards 5.N.14 Estimate sums and differences of whole numbers, positive fractions, and positive decimals. Estimate products of whole numbers and products of positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer. Thousands of Miles, Thousands of Seats -- November Inv. Title &MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 1: 5.N.1 Students will read, write, and sequence numbers to one, ten, Listening/Speaking: observation of 5 one-hour 5.N.2 10,000 and 100,000. hundred, Students will appropriately student ability to sessions Using Place 5.N.3 thousand, ten name place values though the read, write, and Values 5.N.6 Students will understand the place-value relationships thousand, millions place. order numbers on 5.N.7 between 10, 100, 1,000, and 10,000. hundred 10,000 chart (see TE 24-54 5.N.9 thousand, Students will listen to and checklist, M3) 5.N.11 Students will add and subtract multiples of 100 and million, billion, understand stories involving 5.N.12 1,000. trillion, period, subtraction in order to find a Related 5.N.14 base, exponent, solution to the problem. Problems, SAB Students will find the difference between a number a power of 13-14 10,000. Writing: Students will write brief journal entries Students will find combinations of 3-digit numbers that accounts of how problems about strategies have a sum of 1,000. were solved. used when playing Close to Students will use visual representations to explain and 1000. justify solutions to subtraction problems. Students will solve addition and subtraction problems with large numbers by focusing on the place value of the digits. Students will find the difference between a number and 10,000. Students will identify place values through one trillion. Teacher Notes: --Ten Minute math for this investigation is Practicing Place Value and Estimation ad Number Sense: Closest Estimate. Practicing Place Value supports standards 5.N.2, 5.N.3, and 5.N.12. Closest Estimate supports 5.N.2, 5.N.12, and 5.N.14. --For students who struggle with subtraction, small group sessions to identify misconceptions would be beneficial. --For students who easily play Close to 1000, introduce a variation with positive and negative numbers, so that all students are challenged. --When doing Related Problems during Session1.4, adjust numbers as necessary so that all students can gain flexibility with the number manipulation. Inv. Title & MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 2: 5.N.9 Students will solve whole-number addition and subtraction, Listening/Speaking: observation of 5 one-hour 5.N.11 subtraction problems efficiently. addition, Students will describe and subtraction sessions Studying 5.N.12 algorithm, compare subtraction strategies used Subtraction 5.N.6 Students will analyze and use different subtraction addend, strategies by focusing on how on SAB 20-21 5.N.2 strategies. difference, each strategy starts. TE 56-84 5.N.3 minus, sum, total Starter Problems, 5.N.14 Students will understand the meaning of the steps and Students will orally defend SAB 31-32 notation of the US algorithm for subtraction. how differences represented by two subtraction Distances from expressions are related. Chicago, SAB 39- 40 Writing: Students will organize work Subtraction and use clear and concise Problems, M15 notation for recording addition and subtraction strategies. Teacher Notes: --Continue both Practicing Place Value and Estimation ad Number Sense: Closest Estimate during Ten Minute Math time throughout this investigation. --Students who are strong in one subtraction strategy should be encouraged to try other strategies. The strength in understanding multiple strategies extends far beyond proficiency in subtraction. It helps to develop strong number sense and deeper understanding of the operation of subtraction. Conversely, if students are struggling with subtraction, allow them to focus on becoming proficient in one strategy. --When teaching the US algorithm for subtraction during Session 2.4, try to refer to place value manipulation as regrouping instead of borrowing. This will help connections between addition and subtraction to be more meaningfully built, as when one "carries" in addition, this too is regrouping. Common language between the operations will help enhance their inverse relationship. Inv. Title & MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 3: 5.N.2 Students will solve addition and subtraction problems Listening/Speaking: observations of 5 one-hour 5.N.7 with large numbers by focusing on the place value of Students will retell steps used students playing sessions Adding and 5.N.9 the digits. to solve a problem in a logical Close to 7,500. Subtracting 5.N.11 order. Large 5.N.12 Students will add and subtract multiples of 100 and Rock On! Numbers 5.N.3 1,000. Reading: Problems, SAB 5.N.14 Students will read and 59-62 TE 86-112 Students will solve multi-step story problems. interpret story problems in order to find its solution. End-of-Unit Students will solve whole-number addition and Assessment, M20 subtraction problems efficiently. Writing: Students will write short Students will read, write, and sequence numbers to stories related to subtraction 10,000 and 100,000. problems which can be solved by classmates. Teacher Notes: --Continue both Practicing Place Value and Estimation ad Number Sense: Closest Estimate during Ten Minute Math time throughout this investigation. --When the division fact assessment in given during session 3.1, allow students to retake until mastery. If students do poorly on the assessment and receive a poor mark, that does not help them build the fluency necessary for proficient computation. Retaking for a better mark (even if the assessment is changed slightly) will promote important practice with the basic facts. --For students who are strong with subtraction, they could find actual stadium capacities through research during session 3.2. This extension would also provide valuable time the teacher could use for small group intervention for student still struggling with subtraction. --If students do not use clear and concise notation on their assessments, ask them to orally explain their work to you. This will enable you to determine if the answer was legitimately found or not. If the answer is incorrect, the mini-conference will help you determine if simple subtraction errors were made or if the student has weak concepts of subtraction. Unit: What's That Portion? Standard Number Description "Big Idea" Standards 5.N.4 Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. 5.N.5 Identify and determine common equivalent fractions (with denominators 2, 4, 5, 10) and mixed numbers (with denominators 2, 4, 5, 10), decimals, and percents (through one hundred percent), e.g., 3/4 = 0.75 = 75%. 5.N.7 Compare and order whole numbers, positive fractions, positive mixed numbers, positive decimals, and percents 5.N.13 Accurately and efficiently add and subtract positive fractions and mixed numbers with like denominators and with unlike denominators (2, 4, 5, 10 only); multiply positive fractions with whole numbers. Simplify fractions in cases when both the numerator and the denominator have 2, 3, 4, 5, or 10 as a common factor. Supported Standards 5.N.6 Find and position whole numbers, positive fractions, positive mixed numbers, and positive decimals on a number line 5.M.1 Apply the concepts of perimeter and area to the solution of problems involving triangles and rectangles. Apply formulas where appropriate. 5.D.2 Construct and interpret line plots, line graphs, and bar graphs. Interpret and label circle graphs. Additional Ten Minute Math Standards 5.N.12 Accurately and efficiently add and subtract whole numbers and positive decimals. Multiply and divide (using double-digit divisors) whole numbers. Multiply positive decimals with whole numbers. 5.N.14 Estimate sums and differences of whole numbers, positive fractions, and positive decimals. Estimate products of whole numbers and products of positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer. What's That Portion? -- December - Mid-January Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 1: 5.N.4 Students will interpret everyday uses of fractions, fraction, Listening/Speaking: observations of 5 one-hour 5.N.5 decimals, and percents. decimal, Students will use appropriate how students sessions Using 5.M.1 percent, pronunciation of fraction color 10 by 10 Percents 5.N.12 Students will find fractional parts of a whole or of a equivalent, names. grids to determine and 5.N.14 group. numerator, equivalency Fractions denominator, Reading: Students will find a percentage of a group. fraction bar, Students will read and School Days, TE 20-52 whole number, recognize fractions in SAB 15-16 (see Students will find a percentage of a rectangular area. ratio numerical and word form. checklist M11) Students will identify fraction and percent equivalents. Students will interpret the meaning of the numerator and denominator of a fraction. Students will use equivalent fractions and percents to solve problems. Teacher Notes: --Ten Minute Math during this investigation is Estimation and Number Sense, which supports standards 5.N.12 and 5.N.14, and Guess My Rule, which supports standard 5.N.4, for parts of a collection. By using fractions in simplest form, one can also supports equivalency in 5.N.5. --Students will need to be shown fractions written as ratios in accordance with 5.N.4. --Decimal equivalency (5.N.5) not addressed at this time. --When solving multiple word problems such as that during Session1.1, try summarizing the lesson by making strategy posters and having students do a carousel to view the work of others. Each group can do one problem and the goal becomes showing as many ways to solve the problem as possible. --During Session 1.3 and 1.4, percent grids go beyond 5.N.5, which requires equivalency of fractions with denominators 2, 4, 5, and 10. Have students do these fractions first and offer denominators 3, 6, and 8 as challenge for students who progress quickly. Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 2: 5.N.4 Students will identify fraction and percent equivalents. simplest form Listening/Speaking: observations of 6 one-hour 5.N.5 Students will connect new strategies used by sessions Comparing 5.N.6 Students will order fractions and justify their order by learning from class students to order and 5.N.7 reasoning about equivalencies. discussions to prior and compare Ordering 5.N.12 knowledge. fractions Fractions 5.N.14 Students will compare fractions and percents to the landmarks of 0, 1/2, and 1. Writing: Fraction and TE 54-87 Students will provide written Percent Students will find and compare fractional parts and proof explaining why a given Problems, SAB percents of a whole or a group. fraction is greater than 27-28 another. Students will compare fractional parts of different-sized Using Fractions wholes. Students will write short and Percents, accounts describing how a M20 Students will use equivalent fractions and percents to given problem was solved. solve problems. Teacher Notes: --Ten Minute Math during this investigation continues to be Estimation and Number Sense and Guess My Rule. --Decimals not addressed at this time. --For students struggling with simplest form, a list of fractions to be placed on the percent equivalent strip can be provided. -- Encourage students to develop more strategies for comparing fractions than just illustrations. When two fractions have values that are close to one another, it becomes increasingly difficult to determine which is greater. Also, as students will explore when working with different-sized wholes, if the drawings aren't perfect, then the size comparison is null. Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 3: 5.N.4 Students will find fractional parts of the rotation around simplify, mixed Listening/Speaking: Adding and 10 one- 5.N.5 a circle. number, fraction Students will explain their Subtracting hour Adding and 5.N.6 greater than one thinking process for adding Fractions, SAB 46 sessions Subtracting 5.N.7 Students will add fractions by using a rotation model. whole fractions with unlike (see checklist, Fractions 5.N.13 denominators. M24) 5.D.2 Students will add and subtract fractions by reasoning TE 90-144 5.N.12 about equivalencies. Fraction 5.N.14 Problems, SAB Students will represent fractions on a number line. 60-62 Students will use equivalencies to place fractions on a End-of-Unit set of number lines. Assessment, M32- M33 Students will compare fractions on a number line. Students will order mixed numbers and fractions greater than 1. Students will find combinations of fractions with sums between 0 and 2. Students will add and subtract fractions by using a number line. Teacher Notes: --Ten Minute Math during this investigation continues to be Estimation and Number Sense and Guess My Rule. --Although some problems address multiplication of whole numbers and fractions, i.e.: 3/8 of 64, this portion of 5.N.13 is not explicitly taught. When students solve such problems, summarizing various strategies will be important so that this part of the standard is more directly addressed. --Meet with small groups to observe how students go about adding fractions. As they gain familiarity with the clock face, remove that scaffold and have students who are ready find ways to add fractions without the clock face. These students can also play variations, i.e., continuing to a sum of 2, subtraction from 2, using a whole number cube too and going for a goal of 5, etc. For students struggling with the concept of adding fractions, allow them more time to play Roll Around the Clock before introducing them to Fraction Tracks. Unit: Measuring Polygons Standard Number Description "Big Idea" Standards 5.G.1 Identify, describe, and compare special types of triangles (isosceles, equilateral, right) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezoid), e.g., recognize that all equilateral triangles are isosceles, but not all isosceles triangles are equilateral. 5.G.3 Identify relationships among points and lines, e.g., intersecting, parallel, perpendicular. 5.M.1 Apply the concepts of perimeter and area to the solution of problems involving triangles and rectangles. Apply formulas where appropriate. 5.M.2 Identify, measure, describe, classify, and draw various angles. Draw triangles given two sides and the angle between them, or given two angles and the side between them, e.g., draw a triangle with one right angle and two sides congruent. 5.M.5 Find the sum of the measures of the interior angles in triangles by measuring the angles, and without measuring the angles. Additional Ten Minute Math Standards 5.G.5 Describe and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections 5.G.6 Identify and describe line symmetry in two-dimensional shapes, including shapes that have multiple lines of symmetry. 5.P.1 Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions, e.g., ABBCCC; 1, 5, 9, 13…; 3, 9, 27… 5.D.2 Construct and interpret line plots, line graphs, and bar graphs. Interpret and label circle graphs. Measuring Polygons -- Mid-January - Mid-February Inv. Title & MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 1: 5.G.1 Students will identify the attributes of polygon, right angle, acute Listening/Speaking: observe how 7 one-hour 5.G.3 polygons. angle, obtuse angle, Students will classify comfortable sessions Polygons: 5.M.5 degree, equilateral, descriptive geometry terms students are with Names, 5.M.2 Students will describe triangles by the sizes scalene triangle, isosceles into groupings of their choice. quadrilaterals Angles, and 5.G.6 of their angles and the lengths of their sides. triangle, attribute, property having many Properties 5.P.1 quadrilateral, parallel, Students will orally justify why names Students will use attributes to describe and trapezoid, parallelogram, they have grouped the TE 20-64 compare quadrilaterals. rectangle, rhombus, vocabulary words in the way Some Figures square, perpendicular, they have chosen. Have Many Students will define a regular polygon as a intersect, congruent, Names, SAB 8-10 polygon with all sides and all angles equal. regular, hexagon, Writing: heptagon, octagon, Students will briefly justify in Angles in the Students will use known angles to find the pentagon, nonagon, writing how the measure of a Power Polygons, measures of other angles. decagon, dodecagon, polygon's angles was SAB 17-19 interior angle, exterior determined. angle, complimentary Quadrilaterals angles, supplementary and Angles, M17 angles, kite, protractor, straight angle, reflexive angle, chevron Teacher Notes: --Ten Minute Math is Quick Images: 2-D, which supports 5.G.1, 5.G.3, 5.G.5, 5.G.6, and 5.P.1, depending on strategy used to visualize images. --Introduce students to the protractor as a tool to check angle estimates. --Once students are comfortable with angle measures, try a warm up activity in which students are given an angles and two side measurements. Have them draw the resulting triangle. Did everyone draw the same triangle? This activity addresses the remaining parts of 5.M.2. Inv. Title & MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 2: 5.M.1 Students will compare the perimeters and perimeter, area, one- Reading: journal entries 6 one-hour 5.G.1 areas of rectangles when the dimensions dimensional, two- Students will read and about area- sessions Finding 5.G.3 are changed. dimensional, square units, understand previously-learned perimeter Perimeter 5.G.5 geometry vocabulary. relationships and Area of 5.G.6 Students will use numerical and geometric Related 5.P.1 patterns to describe how the perimeters and Writing: A Sequence of Rectangles 5.D.2 areas of rectangles change when the Students will appropriately Rectangles, SAB dimensions change. group ideas for a brief 35-36 TE 66-104 comparison writing Students will create different rectangles with assignment. Open response the same area but different perimeters. about changing area, but not Students will understand square units as a perimeter (a unit of measure. former MCAS question) Students will create rectangles with the same perimeter but different areas. Perimeter and Area of Rectangles, M19 Teacher Notes: --Ten Minute Math continues with Quick Images: 2-D, but Quick Survey is also introduced. Quick Survey supports bar graphs and line plots from 5.D.2, but not line graphs or pie charts. --Although this investigation deals with area and perimeter, it does not address finding the area of a triangle. Please use complimentary materials to teach this important area formula. --Once students understand perimeter and area conceptually it is appropriate to show them the standard formulas, as they will be seen on standardized test fact sheets. --During Session 2.4, allow students to use color tiles or grid paper to help them visualize changing perimeter but not area. --During Session 2.5, students who are ready for a challenge can be asked to determine under what conditions the area will be the greatest, when the perimeter is constant. Inv. Title & MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 3: 5.G.1 Students will recognize and build similar similar 5 one-hour 5.G.3 figures. sessions Similarity 5.M.1 5.M.2 Students will examine the relationship TE 106-135 5.P.5 among angles, lines lengths, and areas of 5.G.5 similar polygons. 5.G.6 5.P.1 5.D.2 Teacher Notes: -- During investigation 3, both Quick Images: 2-D and Quick Survey are the Ten Minute Math activities. --Similarity goes beyond the fifth grade geometry standards. This time could be used for working with geometry standards not addressed in the fifth grade curriculum (symmetry, translations, coordinate plane, etc.). Complimentary materials would be necessary in this case. Completing this investigation could be beneficial though, since it provides further practice with angles, line length, and area. It also brings in proportional relationships, an important topic in algebra. If the similarity investigation is omitted, then only questions 1 and 2 should be used on the End-of-Unit assessment. Unit: Prisms and Pyramids Standard Number Description "Big Idea" Standards 5.M.4 Find volumes and surface areas of rectangular prisms. 5.G.2 Identify, describe, and compare special types of three-dimensional shapes (cubes, prisms, spheres, pyramids) based on their properties, such as edges and faces. Supported Standards 5.N.8 Apply the number theory concepts of common factor, common multiple, and divisibility rules for 2, 3, 5, and 10 to the solution of problems. Demonstrate an understanding of the concepts of prime and composite numbers. 5.M.3 Solve problems involving simple unit conversions within a system of measurement Additional Ten Minute Math Standards 5.N.2 Demonstrate an understanding of place value through millions and thousandths Represent and compare large (millions) and small (thousandths) positive numbers in various forms, such as expanded notation 5.N.3 without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4. Accurately and efficiently add and subtract whole numbers and positive decimals. Multiply and divide (using double-digit divisors) 5.N.12 whole numbers. Multiply positive decimals with whole numbers. Estimate sums and differences of whole numbers, positive fractions, and positive decimals. Estimate products of whole numbers 5.N.14 and products of positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer. Prisms and Pyramids -- October Inv. Title & MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 1: 5.M.4 Students will determine the number of cubes that will fit volume, cube, Listening/Speaking: Student Activity 7 one-hour 5.N.8 into a box made by a given pattern. rectangular prism, Students will rephrase Book p.3 sessions Finding the 5.N.14 cubic units, three- thoughts and ideas stated by Volume of 5.N.12 Students will develop a strategy for determining the dimensional, solid classmates. observations of Boxes 5.N.2 volume of rectangular prisms. student ability to 5.N.3 Students will use key apply strategy for TE 20 - 60 Students will design boxes that hold a given number of vocabulary appropriately finding volume of cubes. during discussions. any prism Students will find the volume of rectangular prisms. Reading/Writing: Student Activity Students will record their Book, p.19 Students will consider how the dimensions of a box strategy for determining the change when the volume is changed. volume of any box in writing. Finding the Volume of rectangular Students will organize packages to fit in rectangular Students will read and answer Prisms M19- boxes. measurement questions, M20 using knowledge of volume to Students will design boxes that can be completely filled support their answers. with several different-shaped rectangular packages. Teacher Notes: --Both Quick Images: 3-D and Estimation and Number Sense are introduced as Ten Minute Math during this first Investigation. Quick Images supports 5.M.4, as students must realize the number of cubic units in the 3-D shape in order to rebuild it. Estimation and Number Sense support 5.N.14, 5.N.12, 5.N.2, and 5.N.3 as students can use a variety of strategies to determine their estimate. Place value rounding, number decomposition, and calculation are methods which could be shared by students with the rest of the class in order to reinforce all these standards. --During Session 1.1, as students fill boxes with the unit cubes, have them label their answers with cubic units, since the exact measurement is 3/4-inch cubed. Not requiring a label now, may yield a lack of volume labels later. --Once volume strategies are solidified, after Session 1.2, it is appropriate to introduce the standard volume formulas, in full words and with letters only, i.e.: L x W x H =V. Students should see these formulas, as they will see them later on assessment fact sheets. --Differently-Sized packages in Session 1.4 goes beyond the 5.M.4 standard. This could be reserved for students demonstrating proficiency with determining volume, while other students continue to build their understanding about volume. Students demonstrating proficiency could also investigate why doubling all dimensions results in a volume that increases eight-fold. Inv. Title & MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 2: 5.M.4 Students will determine the volume, in cubic length, width, Listening/Speaking: observation of 4 one-hour 5.M.3 centimeters, of a small prism. height Students will summarize student strategies sessions Using 5.N.14 measurement strategies and for measuring Standard 5.N.12 Students will construct units of volume. defend their outcomes. volume of Cubic Units 5.N.2 unmarked box (fill 5.N.3 Students will choose an appropriate unit of volume to Writing: or measure sides) TE 62 - 86 measure a large space. Students will write clear and concise plans they will follow Measuring Volume Students will find the volume of a large space using to measure the volume of the in Cubic cubic meters. classroom. Centimeters, M24 (see rubric M25) Teacher Notes: --Continue Estimation and Number Sense as the Ten-Minute Math during Investigation 2. Since the fifth grade estimation standard addresses all operations but division, you may choose to try another operation when division estimation is introduced. --During Session, 2.1, encourage multiple strategies such as filling or measuring dimensions. Have students share these strategies aloud and verify their accuracy. --When assessing student ability to calculate volume, be sure ask for strategies or clear and concise work, as students could make errors in using a ruler or multiplying when they have a clear understanding of volume. Inv. Title & MA Content Objectives Key Vocabulary Sample Language Assessment Pacing Pages Stan. Objectives Suggestions Inv. 3: 5.G.2 Students will compare volumes of different-shaped pyramid, cylinder, Listening/Speaking: Student Activity 5 one-hour 5.M.4 containers. cone, base, Students will orally compare Book p.45 sessions Volume 5.N.14 height, apex, attributes of 3-D geometric Relationshi 5.N.12 Students will build geometric solids. sphere, face, shapes, using content End of Unit ps Among 5.N.2 edge, vertex or vocabulary when appropriate. Assessment, M35- Solids 5.N.3 Students will find volume relationships between solids vertices, net, M36 with the same base and height. surface area Writing: TE 88 - 111 Students will write about a Students will build a prism with three times the volume method they could use to of a given pyramid. compare the volume of two solids. Students will demonstrate the 3:1 relationship between rectangular prisms and pyramids with the same base and height. Students will find the volume, in cubic centimeters, of prisms, pyramids, cylinders, and cones. Teacher Notes: --Continue both Quick Images: 3-D and Estimation and Number Sense as Ten Minute Math during Investigation 3. --Although this unit addresses standards 5.G.2 and 5.M.4, these standards are not addressed entirely. It will be important to find complimentary materials in order to address the standards completely. For 5.G.2, students will need to work with spheres in addition to the other 3-D shapes. They will also need to spend time during Session 3.1, after the shapes are made from the net designs, to describe and talk about similarities and differences between the shapes made (such as faces, edges, and vertices). For 5.M.4, students will need experience with surface area. Unit: Decimal Grids and Number Lines Standard Number Description "Big Idea" Standards 5.N.2 Demonstrate an understanding of place value through millions and thousandths 5.N.3 Represent and compare large (millions) and small (thousandths) positive numbers in various forms, such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4. 5.N.5 Identify and determine common equivalent fractions (with denominators 2, 4, 5, 10) and mixed numbers (with denominators 2, 4, 5, 10), decimals, and percents (through one hundred percent), e.g., 3/4 = 0.75 = 75%. 5.N.7 Compare and order whole numbers, positive fractions, positive mixed numbers, positive decimals, and percents 5.N.12 Accurately and efficiently add and subtract whole numbers and positive decimals. Multiply and divide (using double- digit divisors) whole numbers. Multiply positive decimals with whole numbers. Supported Standards 5.N.4 Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. 5.N.6 Find and position whole numbers, positive fractions, positive mixed numbers, and positive decimals on a number line 5.M.1 Apply the concepts of perimeter and area to the solution of problems involving triangles and rectangles. Apply formulas where appropriate. Additional Ten Minute Math Standards 5.N.14 Estimate sums and differences of whole numbers, positive fractions, and positive decimals. Estimate products of whole numbers and products of positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer. Decimals on Grids and Number Lines -- Mid-February - Mid-March Inv. Title & MA Stan. Content Objectives Key Sample Language Assessment Pacing Pages Vocabulary Objectives Suggestions Inv. 1: 5.N.2 Students will identify everyday uses of fractions and decimals. decimal point, Listening/Speaking: Decimals on 10 one-hour 5.N.3 tenths, Students will properly Hundredths and sessions Understand 5.N.5 Students will represent decimal fractions as part of an area. hundredths, pronounce place value terms Thousandths ing and 5.N.6 thousandths, in order to maintain meaning. Grids, SAB 9-14 Comparing 5.N.7 Students will read and write decimals in the tenths, hundredths, and thousandths. ten-thousandths Decimals 5.N.4 Reading: Ordering 5.N.12 Students will identify decimal, fraction, and percent equivalencies. Students will identify the Decimals, SAB 17 TE 20-80 5.N.14 morpheme -th, which gives 5.M.1 Students will represent decimals by using a number line. some place value words their meaning. Decimal Problems, Students will order decimals and justify their reasoning by connecting to work done in SAB 23-25 (see class. Writing: checklist, M18) Students will record patterns Students will compare decimals to the landmarks 0, 1/2, and 1. noticed on the division table Comparing and in their journals. Ordering Students will interpret fractions as division. Decimals, M20 Teacher Notes: --Ten Minute Math during this investigation is Practicing Place Value, which supports standards 5.N.2, 5.N.3, and 5.N.12, and Estimation and Number Sense, which supports 5.N.12 and 5.N.14. --During Session 1.1, using a context for shading the grids may help provide meaning to the activity. On SAB 2-4, students will have the context that a garden is shaded. Using this context to introduce the shading would be beneficial. Students can even color vegetation according to color described, i.e.: tomatoes would be red. This can then be carried over to adding the decimal in investigation 2. --Session 1.3 brings students to work involving ten-thousandths, which reaches beyond the 5.N.2 standard. If students need additional practice with simpler decimals, allow only those students who are ready to work with ten-thousandths and their equivalencies. --Students who are having trouble ordering the decimals, can continue to use decimal grids for shading, and could place a smaller amount of decimals onto the number lines. It will also be important to present students with some whole numbers and mixed whole number-decimals. Ordering such a set of numbers will require students look for and understand the decimal point. --On SAB p.31, students should record the total number of games played for each team so that the winning percentage can be calculated as a fraction with total number of games played as the denominator. --During Session 1.8, students can fill in the Fraction-to-Decimal Division Table where the denominator is 2, 4, 5, or 10, first in accordance with 5.N.5. By looking at descending patterns, students can then predict what the rest of the table will look like filled in. Inv. Title & MA Stan. Content Objectives Key Sample Language Assessment Pacing Pages Vocabulary Objectives Suggestions Inv. 2: 5.N.2 Students will estimate sums of decimal numbers. Listening/Speaking: Adding Decimals, 8 one-hour 5.N.3 Students will restate the SAB 49-50 sessions Adding 5.N.12 Students will visual representations to add tenths, hundredths, and thousandths. strategies classmates use to Decimals 5.N.14 add decimals. End-of-Unit Students will add decimals to the thousandths through reasoning about place value. Assessment, M27- TE 82-119 Reading: 28 Students will read and comprehend story problems in order to find appropriate solutions. Teacher Notes: --Practicing Place Value is the Ten Minute Math to be used during this investigation. Although Estimation and Number Sense is not recommended as the Ten Minute Math during this session, 5.N.14 does require estimation involving decimal computation. This could be used as a few Ten Minute Math sessions during the investigation or as a warm-up activity. -- Although the purpose of this investigation is not computational fluency, standard 5.N.12 requires fluency for addition, subtraction, and multiplication of decimals (with whole numbers). It will be important to extend practice as necessary and to complement activities in the investigation with those involving other operations. Division of decimals is not an expectation in fifth grade. -- Students who easily play Fill Two, can be encouraged to play with the with thousandths cards on thousandths grids, or play Fill to a higher number. Unit: How Many People? How Many Teams? Standard Number Description "Big Idea" Standards 5.N.8 Apply the number theory concepts of common factor, common multiple, and divisibility rules for 2, 3, 5, and 10 to the solution of problems. Demonstrate an understanding of the concepts of prime and composite numbers. 5.N.9 Solve problems involving multiplication and division of whole numbers, and multiplication of positive fractions with whole numbers. 5.N.12 Accurately and efficiently add and subtract whole numbers and positive decimals. Multiply and divide (using double- digit divisors) whole numbers. Multiply positive decimals with whole numbers. Supported Standards 5.P.3 5.N.14 Estimate sums and differences of whole numbers, positive fractions, and positive decimals. Estimate products of whole numbers and products of positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer. Additional Ten Minute Math Standards 5.N.13 Accurately and efficiently add and subtract positive fractions and mixed numbers with like denominators and with unlike denominators (2, 4, 5, 10 only); multiply positive fractions with whole numbers. Simplify fractions in cases when both the numerator and the denominator have 2, 3, 4, 5, or 10 as a common factor. How Many People? How Many Teams? -- Mid-March - End of April Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 1: 5.N.9 Students will generate equivalent multiplication double, halve, Reading: Finding 4 one-hour 5.N.12 expressions by multiplying one factor and dividing the triple, Students will read and Equivalent sessions Equivalenc 5.P.3 other by the same number. expression, understand story problems in Expressions for e in 5.N.13 equation, twice order to generate equivalent 40 x 32, SAB 7 Multiplicatio 5.N.14 Students will create visual representations that support expressions related to the (see checklist n and explanations about equivalent expressions. problem. M15) Division Students will compare equivalent multiplication Writing: TE 24-44 expressions to equivalent division expressions. Students will write short explanations of how two Students will create visual representations of equivalent multiplication expressions are division expressions. related, using evidence from the classwork to support their Students will generate equivalent division expressions. answer. Students will write short stories about equivalent expressions. Teacher Notes: --Ten Minute Math for this Investigation is Estimation and Number Sense: Closest Estimate. The estimation problems in this investigation support 5.N.13 and 5.N.14. --During Session 1.3, students who are comfortable with doubling, halving, tripling, and thirding can work with larger numbers. They could also be encouraged to work with numbers that once divided into parts are no longer whole numbers. This would help support multiplication of whole numbers and decimals (5.N.12). Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 2: 5.N.9 Students will solve multi-digit multiplication problems Listening/Speaking: observations 4 one-hour 5.N.12 fluently. Students will orally share from small group sessions Reviewing 5.N.14 strategies used for solving conferences of Multiplicatio 5.N.8 Students will compare strategies used to solve multi- multiplication problems. strategies used to n Strategies digit multiplication problems. multiply multi- Writing: digit numbers TE 46-64 Students will estimate answers to multiplication and Students will order work division problems. appropriately and use clear Solving and concise notation to show Multiplication Students will understand the US algorithm for how a problem was solved. Problems, SAB multiplication. 25 253 x 46, M25 Teacher Notes: --Ten Minute Math for this Investigation is Number Puzzles, which supports 5.N.8, and Estimation and Number Sense: Closest Estimate, which supports 5.N.12 and 5.N.14. --During investigations where computation is taught, try meeting with like-ability groups, where strategies can be discussed and numbers used can be similar. Struggling students can continue to work with strategies such as clustering or partial product, while more proficient students should be encouraged to use the US standard algorithm. Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 3: 5.N.9 Students will represent a division problem with a picture Listening/Speaking: Division: How Did 7 one-hour 5.N.12 or diagram. Students will use appropriate I Solve It?, SAB sessions Division 5.N.8 language structures for 47-48 Strategies 5.N.14 Students will compare strategies used to solve division comparing division strategies. and problems. 701 divided by Notation Reading/Writing: 27, M29 Students will solve division problems with a 2-digit Students will read and write TE 66-98 divisor fluently. story problems which can be solved using division. Students will solve multi-step word problems. Students will use clear and concise notation when solving division problems. Teacher Notes: --For Ten Minute Math, continue Number Puzzles and Estimation and Number Sense: Closest Estimate. --As with multiplication, meet with small groups to work on computation strategies. Allow struggling students to use a method such as clustering or partial quotient ("the big 7") while encouraging more proficient students to learn the US standard algorithm for division. Struggling students can learn one strategy really well, while more proficient students explore more strategies and look for more comparisons. Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 4: 5.N.9 Students will solve multi-step word problems. operation Listening/Speaking: Multiplying and 5 one-hour 5.N.12 Students will share answers to Dividing Large sessions Using the Students will solve multi-digit multiplication problems problems solved and justify Numbers, SAB Operations fluently. how that answer was found. 64-65 TE 100-119 Students will solve division problems with a 2-digit End-of-Unit divisor fluently. Assessment, M31-32 Students will use all operations fluently in order to solve problems. Students will compare strategies used to solve problems. Teacher Notes: --For Ten Minute Math, continue Number Puzzles and Estimation and Number Sense: Closest Estimate. Unit: Growth Patterns Standard Number Description "Big Idea" Standards 5.P.2 5.P.4 Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols, e.g., input-output tables. 5.P.5 Solve problems involving proportional relationships using concrete models, tables, graphs, and paper-pencil methods. 5.P.6 Interpret graphs that represent the relationship between two variables in everyday situations. Supported Standards 5.G.4 Using ordered pairs of whole numbers (including zero), graph, locate, and identify points, and describe paths on the Cartesian coordinate plane 5.D.2 Construct and interpret line plots, line graphs, and bar graphs. Interpret and label circle graphs. 5.M.1 Apply the concepts of perimeter and area to the solution of problems involving triangles and rectangles. Apply formulas where appropriate. 5.M.3 Solve problems involving simple unit conversions within a system of measurement Additional Ten Minute Math Standards 5.N.2 Demonstrate an understanding of place value through millions and thousandths 5.N.3 Represent and compare large (millions) and small (thousandths) positive numbers in various forms, such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4. 5.N.12 Accurately and efficiently add and subtract whole numbers and positive decimals. Multiply and divide (using double-digit divisors) whole numbers. Multiply positive decimals with whole numbers. 5.N.14 Estimate sums and differences of whole numbers, positive fractions, and positive decimals. Estimate products of whole numbers and products of positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer. Growth Patterns -- End of April - Mid-May Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 1: 5.G.4 Students will plot points on coordinate grids to rate of change, Listening/Speaking: The Krink, the 5 one-hour 5.D.2 represent situations in which one quantity is changing growth, steady, Students will communicate Trifoot, and the sessions Height and 5.P.4 in relation to another. rapid, constant, about the shape of graphs Water Weasel, Growth 5.P.5 slope, graph, using common vocabulary Saab 15-16 5.P.6 Students will use tables to represent the relationship axis, table, generated onto a class list. TE 24-60 5.M.3 between two quantities. function, Comparing 5.N.2 increase, Writing: Animals' Growth, 5.N.3 Students will identify points in a graph with decrease, Students will write brief M17 5.N.12 corresponding values in a table and interpret the coordinates, stories that describe changes 5.N.14 information in terms of the situation represented. origin, point, x- in rate of growth for a person. Fastwalker, SAB axis, y-axis, x- 18-20 Students will describe the slope of graphs or parts of coordinate, y- graphs in terms of different rates of change. coordinate Students will describe the relationship of quantities in a situation with a constant rate of change. Students will find the value of one quantity in a situation with a constant rate of change, given the value of the other. Students will compare situations by describing differences in their graphs. Students will describe a situation in which the rate of change is not constant. Students will compare tables, graphs, and situations with constant rates of change with those in which the change is not constant. Teacher Notes: --Ten Minute Math during this investigation is Estimation and Number Sense, which supports 5.N.12 and 5.N.14, and Practicing Place Value, which supports 5.N.2, 5.N.3, and 5.N.12. --Although the investigation refers to the slope of lines as steepness, students can still be encouraged to discuss slope of lines. The steeper the line, the more change between points. This would mean it has a greater slope. Inv. Title & MA Content Objectives Key Sample Language Assessment Pacing Pages Stan. Vocabulary Objectives Suggestions Inv. 2: 5.P.2 Students will write expressions for finding the value of rule, variable, Listening/Speaking: observation of 8 one-hour 5.P.4 one quantity in terms of the other in a situation with a coefficient Students will orally describe student ability to sessions Growing 5.P.5 constant rate of change. similarities and differences make Patterns 5.P.6 between graphs they create. connections 5.G.4 Students will make rules that relate one variable to the between hands- TE 62-114 5.D.2 other in situations with a constant rate of change. on materials, 5.M.1 graphs, tables, 5.N.2 Students will use symbolic letter notation to represent and rules (2.3) 5.N.3 the value of one variable in terms of another variable. 5.N.12 oral explanations 5.N.14 Students will find the value of one quantity in a of graph situation with a constant rate of change, given the comparisons value of the other. The Doubling Students will describe the relationship between two Penny Jar, SAB quantities in situations with or without constant rates of 50-51 change. Staircase Students will identify points in a graph with Towers: Jumps corresponding values in a table and interpret the of 2, SAB 60-62 information in terms of the situation represented. End of Unit Students will compare situations by describing Assessment, differences in their graphs. M22-25 Students will describe the slope of graphs or parts of graphs in terms of different rates of change. Students will describe and compare tables, graphs, and situations with constant rates of change with those in which the rate of change is not constant. Teacher Notes: --Continue Estimation and Number Sense and Practicing Place Value as the Ten Minute Math during this investigation. --Students should be challenged to write rules with variables that would work for any number in these situations. Unit: Data About Us 5.D.1 Given a set of data, find the median, mean, mode, maximum, minimum, and range, and apply to solutions of problems. 5.D.2 Construct and interpret line plots, line graphs, and bar graphs. Interpret and label circle graphs. 5.N.12 Accurately and efficiently add and subtract whole numbers and positive decimals. Multiply and divide (using double-digit divisors) whole numbers. Multiply positive decimals with whole numbers. Invest Title & MA Std Content Objective Key Vocabulary Language Resources Assessment Suggestions Pacing Page No. Language objectives for this investigation should include reading, writing, speaking and listening. A sample for this investigation might be: Invest 1 5.D.1 Students will be able to identify data set, Students will be able to elaborate on and extend Mathematical Reflection, p. 29 5 days Looking at Data 5.D.2 maximum, minimum, range, numerical data, other students descriptions about data mode, and median (5.D.1) range, represented in a line plot (S.3.60) District Formative available on Problems Galileo: maximum, 1.1 Students will be able to describe how to find the 5.D.1 Median, Mode, and Students will be able to minimum, 1.2 median of a set of numerical data using Range interpret line plots (5.D.2) mode, median, appropriate math vocabulary (S.1.28) 1.4 table, line plot, bar graph, pp. 6-29 typical Teacher's Notes: Problem 1.3 is not recommended here but may be used for enrichment. In order to align Problem 1.4 with standard 6.D.2, students should create line plots for the data that is represented in the tables and bar graphs. Problem 1.5 is not recommended since bar graphs have been addressed in earlier grades. However, teachers may use Problem 1.5 with students who demonstrate a need for review of bar graphs. Invest Title & MA Std Content Objective Key Vocabulary Language Resources Assessment Suggestions Pacing Page No. Language objectives for this investigation should include reading, writing, speaking and listening. A sample for this investigation might be: Invest 2 Using 5.D.1 Students will be able to stem, leaves, Students will be able to use appropriate Mathematical Reflection, p. 48 3 days Graphs to 5.D.2 construct stem and leaf plots stem-and-leaf mathematical vocabulary and concepts to #1 Explore Data for data sets with a large range plot, key, describe data represented in a stem and leaf interval, modal plot (S.1.28) (5.D.2) Problem interval 2.1 pp 30-48 Teacher's Notes: Students will need practice constructing and interpreting stem-and-leaf plots. Teachers should extend this problem identifying the mode, median, maximum, minimum, and range of data sets represented in stem-and-leaf plots. You can find additional items in the ACE questions for Investigation 2 on pp.40-44 and in the CMP2 Additional Practice and Skills workbook, p. 120. Problem 2.2 is not recommended since it deals with "back-to-back stem and leaf plots" which are not part of the state standard. This problem may be appropriate for enrichment. Problems 2.3 and 2.4 are not recommended in this guide because sufficient work with relationships between two variables and the first quadrant of the Cartesian coordinate plane is included in the unit "Variables and Patterns". Invest Title & MA Std Content Objective Key Vocabulary Language Resources Assessment Suggestions Pacing Page No. Language objectives for this investigation should include reading, writing, speaking and listening. A sample for this investigation might be: Invest 3 5.D.1 Students will be able to mean Students will be able to describe the steps in the District formative available on 4 days 5.N.12 calculate the mean for a set of algorithm for calculating mean using appropriate Galileo: Problems data (5.D.1) math vocabulary. (S.1.28) 5.D.1 Mean 3.1 3.3 End-of-Unit Assessment pp. 49-63 Teacher's Notes: Calculating the mean provides a chance for teachers to review division algorithms with students who need some reteaching of this skill. Students who are ready for enrichment can work on problem 3.2. Additional notes about this unit: Standard 5.D.2 is only partially covered in this unit since circle graphs are not included in any of these investigations. However, teachers can use ACE item #12 from page 44 to give students the chance to interpret a circle graph.