5th Grade Quick Sheet

Transcription

1 5th Grade Quick Sheet State Test Specification information. The primary purpose of test specifications is to help test developers build a test that is consistent over time. The MCA-III DRAFT Test Specifications for Mathematics, Grades 3 8 are also meant to serve as a source of information about the test design for teachers and the general public. Test specifications do not indicate what should be taught; the Minnesota academic standards do. Test specifications do not indicate how students should be taught; the classroom teacher does. Test specifications indicate which strands, standards and benchmarks will be assessed on the test and in what proportions. In addition, test specifications provide the types of items to be included, number of items and distribution of cognitive levels. Test specifications also clarify, define and/or limit how test items will be written. The purpose of the MCA-III Quick Sheet is to give teachers a quick glimpse of the above information. Each strand page outlines what is expected of all students at each grade level. Possible teaching strategies have been included with each strand to familiarize teachers with the strategies and vocabulary that is mentioned in the test spec document. Item Samplers are included with some of the standards to show possible question types. Since the item samplers have not been created by the state it is a best education guess to the question types. A variety of item types will be used on the Mathematics MCA-III, including multiple choice (MC) items and open-ended (OE) items. MC - Multiple Choice OE - Open Ended Response Consists of: Type in - Type in numerical answer in a box, Graphing - Plot data to complete various mathematical displays Drag and Drop- Student will formulate a response using drag and drop Hot Spot - Select multiple correct responses or mark locations on displays and graphics Palette- Student will formulate a response using drag and drop If you see the terms using common algorithms. It is a non calculator item Strands Include Number and Operation Algebra Geometry and Measurement Data Analysis Vocabulary: Every word from a previous grade is available to be tested in the next grade. Words written under vocabulary in this document are added in current grade. See last page to see a full listing of words students are responsible for.

2 Number and Operation MCA-III MCA-M th Grade Quick Sheet MCA-III 5-7 Items MCA-M 4-6 items Divide multi-digit numbers using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number or a decimal. Limits Dividends may not be more than 4 digits Divisors may not be more than 2 digits Fractional remainders are not required to be given in lowest terms Allowable division notation:, fraction bar No Calculator Vocabulary remainder Pull Janet has 1,780 marbles. She wants to put them into bags, each of which holds 32 marbles. How many full bags of marbles will she have? Multiplying groups Subtracting groups Partial Quotient Mixed Number Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Vocabulary remainder Limits Dividends may not be more than 4 digits Divisors may not be more than 2 digits Fractional remainders are not required to be given in lowest terms Items may require interpretation of when decimals should be rounded

3 Number and Operation _ MCA-III MCA-M th Grade Quick Sheet Cont. MCA-III 5-7 Items MCA-M 4-6 items Estimate solutions to arithmetic problems in order to assess the reasonableness of results. Assessed within Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology and the context of the problem to assess the reasonableness of results. Limits Solutions are less than 1,000,000 Multiplication is limited to no more than three-digit numbers by no more than threedigit numbers Division is limited to no more than four-digit numbers by no more than two-digit numbers Fractional remainders are not required to be given in lowest terms strategies based on understanding the inverse relationship between multiplication and division Sharing: Divide 35 pennies among 5 people equally. How many pennies are in each share? Grouping: How many groups of 5 pennies can I make if I have 35 pennies? 3+ 7 = =10-3 The sum of a number x and 4 equals 12. Number or Fact families that work on part part whole After two rounds, 24 students are eliminated from a spelling bee. There are 96 students remaining. Write an equation you can use to fi nd the number of students that started the spelling bee Variable Let s be the number of students that started. Equation s 24 = 96

4 MCA-III Online Items

5 Number and Operation MCA-III MCA-M th Grade Quick Sheet Read and write decimals using place value to describe decimals in terms of groups from millionths to millions Cont MCA-III 6-8 Items MCA-M 3-4 items Vocabulary place value What is ? What number is in the Hundredths Place Write forty-two hundredths as a number Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find more than a number and less than a number. Test makers like using the number line for these questions. What numbers would be between? Vocabulary place value What Number is greater than.001 What number is.01 greater than 23.22? What number is.001 less than ?

6 MCA-III Online Items

7 Number and Operation MCA-III MCA-M th Grade Quick Sheet Cont. MCA-III 6-8 Items MCA-M 3-4 items Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Limits Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 15, 16 and 20 Mixed numbers are less than 10 Vocabulary place value /5.2 Fraction Bar to number-line Using Reference Points Such as 0, 1/2, 1 Is 3/8 Closer to 0 or 1, Is 3/8 closer to 0 or 1/

8 Order and Equivalence Key concepts: There are many different fractions equal to any given fraction. Between any two fractions there are many others. Big Push Nation Wide Example: Compare 3/5 and 5/7 Stages in Order and Equivalence 1. Construct and examine (Students may use a partition strategy to solve). 2. Numerical Components 7/11 or 7/13-7/11 is greater because 13ths is smaller than 11ths 3. Reference Points 0, 1/2, 1 8/11 and 7/15 8/11 is greater than 1/2 and 7/15 is less than one half. Half of any denominator can be divided by two. 4. Numerical Conversions Convert to common denominator, Convert to decimal. These strategies are learned in school, the one big issue with theses strategies is students cling to them for ease but have no real understanding of what they mean.

9 Modeling Fractions Activity Working with 2/3, 3/4, 5/6 and 7/8, Geogebra Tool Notice that each of these fractions is one part away from the whole. What fraction is this? Area Model Improper 2 Fractions What fraction is this? Fractions 1/2 to 1/16 on a number line Which fraction is the greatest? Do you notice any thing about the number relationship. Fraction 0, 1/2, 1 Fractions0-1.ggb Order Fractions Numberline

10 Reference Points 0 1 1/5 Fraction Bar to number-line Using Reference Points Such as 0, 1/2, 1 Is 3/8 Closer to 0 or 1, Is 3/8 closer to 0 or 1/2 Fraction Reference Points : Using fraction bars for partitioning a number line Materials-empty fraction bar, (various fraction bars), Number line with 0,1/2 and 1 reference points. Frame different fractions as shown above. Place out a fraction bar. Color 2/5 of the fraction bar red. Is 2/5 closer to 0 or 1? Is 2/5 closer to 0 or 1/2? Cont. w/ other combinations involving 4ths, 5ths 6ths, 7ths Denominators 2, 3, 4, 5, 6, 8, 10 and 12, 15, 16, 20 Fractions Reference Point s Move to using only an empty number line and reference points. Number line with 0,1/2 and 1 reference points. Frame different fractions as shown above. Place out a fraction bar. Color 2/5 of the fraction bar red. Is 2/5 closer to 0 or 1? Is 2/5 closer to 0 or 1/2? Cont. w/ other combinations involving 4ths, 5ths 6ths, 7ths to 12ths Fraction Bars jad.best.vwh.net/java/fractions/fractions.html

11 Numerical Components Relationship Numerator/Denominator Fraction Numeric Components : Using fraction bars to demonstrate numeric components. Materials-empty fraction bar, (various fraction bars), Number line with 0,1/2 and 1 reference points. Frame different fractions as shown to the right. 3/8- I know 3/8 is close to 1/2 because 4/8 reduces to 1/2. Place out a fraction bar. Color 3/8 of the fraction bar green. Is 3/8 closer to 0 or 1? Is 2/5 closer to 0 or 1/2? Cont. w/ other combinations involving 4ths, 5ths 6ths, 7ths Eventually we want kids to think in relationship to equivalent fraction and size of partitioned number of parts. Fraction Numeric Componets Move to screening fraction bars. Same as above 0 1 1/11 Fraction Numeric Components : Using fraction bars to demonstrate numeric components. Materials-empty fraction bar, (various fraction bars), Number line with 0,1/2 and 1 reference points. Frame different fractions as shown to the right. Place out a fraction bar. Color 8/11 and 9/14 on both fraction bars. green. Ask student which is greater? Point out sizes of the partitioned parts. Show the relationship of the numerator and denominator. Show in example. Fraction Numeric Components Move to screening fraction bars. Same as above 1/14 8/11 is greater than 9/14. The distance between the Numerators and denominators. I know 14ths are less. 8/11 is 3 away 9/14 is 5 away 14ths has a lesser parition.

12 Compare and to see which is greater? Line them up. Representation of Decimals on a Number Line To represent a decimal on a number line, partition each segment of the number line into ten equal parts. To represent on a number line partition the segment between 0 and 1 into ten equal parts Fractions to Decimals

13 Draw and Identify Pictures Fraction slider that helps demonstrate partitioning. Adjustable to any value Using a number line to combine partitioning and fractinal parts. Materials-Geogebra numberline model, with 0, and 1 reference points. Select different fractions by clicking on the boxes and sliding the slider to adjust equal parts. Partitioning with a numberline, Ask students: 1. How many equal parts? 2.How many parts are shaded? 3. Is this closer to 1 or 0? Name the numerator and Denominator. Distances from 0 to 1 Parts/Whole Using a number line to combine partitioning and fractinal parts. Materials-Geogebra numberline model, with 0, and 1 reference points. Select different fractions by clicking on the boxes and sliding the slider to adjust equal parts. Ask students: 1. How many equal parts? 2.How many parts are shaded? 3. Is this closer to 1 or 0?

14 Number and Operation MCA-III MCA-M th Grade Quick Sheet Cont. MCA-III 6-8 Items MCA-M 3-4 items Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. Vocabulary place value Limits Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 25, 50 and 100 Mixed numbers are less than 10 1/2 is equivalent to a. 4/8 b. 1/4 c. 2/5 d. 3/8 Write 4/10 in lowest terms. Write.63 as a fraction Round numbers to the nearest 0.1, 0.01 and Vocabulary place value Limits Numbers can be given up to millionths What is 6.37 rounded to the nearest tenth?

15 Acitivities Equivalent Fraction Algorithm Many students simply count the pieces What product tells how many parts are shaded? We want to move to thinking to use multiplication instead What product tells how many parts in the whole? 3/4= 3x3 4x3 = = 3 4 x x = /30 Screened /5 = 24/ = 3 4 x x = = 3 4 x x = With the covered square you can see 4 columns and six rows to the shaded part. So there must be 6x4=24

16 Drag and Drop MCA-III Question Sampler Cont. MCA-III 6-8 Items MCA-M 3-4 items Place the following fractions on the number line. Place the following decimals on the number-line 5/4 1 1/ /2 1 7/ Which term is greater.75 or 8/9? Explain your thinking. Convert the fraction 2/3 to a decimal.

17 MCA-III Question Sampler Cont. MCA-III 6-8 Items MCA-M 3-4 items

18 MCA-III Online Items Cont. MCA-III 6-8 Items MCA-M 3-4 items

19 Fraction Number line Fraction Websites Multiple fraction activities and lessons that fit with the grade 5 fraction standards Compare, Name, Equivalent and parts of a whole Open site, Run your mouse over the word shape left bottom. All sites interactive

20 Number and Operation MCA-III MCA-M th Grade Quick Sheet Cont. MCA-III 6-8 Items MCA-M 4-6 items Add and subtract decimals and fractions using efficient and generalizable procedures, including standard algorithms. Limits Addends, minuend and subtrahend denominators are limited to 2, 3, 4, 5, 6, 8, 10 and 12 Mixed numbers are less than 10 Items do not require conversion between fractions and decimals Items must not have context Model addition and subtraction of fractions and decimals using a variety of representations. Limits Addends, minuend and subtrahend denominators are limited to 2, 3, 4, 5, 6, 8, 10 and 12 Mixed numbers are less than 10 Items do not require conversion between fractions and decimals

21 2/6 + 3/6= Early Addition Skills 0 1/6 2/6 3/6 4/6 5/6 1 1/3 1/2 2/3 5/6 + 3/6= 1 2/6 or 1 1/3 0 1 More than 1 because 6/6 is one

22 1 Work Space Cloned Pieces _

23 1. Copy the problem. 2.Draw and divide equal-sized rectangles for each fraction. One rectangle is cut horizontally into an equal number of pieces based on the first denominator (bottom). The other is cut vertically, using the second denominator. The number of shaded pieces in each rectangle is based on the numerator (top). Label each rectangle, with the fraction it represents. 3.Superimpose the lines from each rectangle onto the other rectangle, as if one rectangle is placed on top of the other one. 4. Rename the fractions as twelfths, because the new rectangles are divided into twelve equal parts. Change the numerators to match the number of twelfths in each figure. 5. Draw an empty rectangle with twelfths, then combine all twelfths by shading the same number of twelfths in the new rectangle as the total that were shaded in both rectangles from the previous step. 6. Simplify if necessary. Fraction Area Model : Using the fraction area method to demonstrate addition of fractions. Materials-empty fraction square,, Partition 1/4 in the first fraction square. Color in the numerator. Partition 1/3 in the second square. Color in the numerator. Superimpose the lines from each rectangle onto the other rectangle, as if one rectangle is placed on top of the other one Rename the fractions as twelfths, because the new rectangles are divided into twelve equal parts. Change the numerators to match the number of twelfths in each figure. Draw an empty rectangle with twelfths, then combine all twelfths by shading the same number of twelfths in the new rectangle as the total that were shaded in both rectangles from the previous step. See Attachments for Fraction addition overlays

24 Number and Operation MCA-III MCA-M th Grade Quick Sheet Cont. MCA-III 6-8 Items MCA-M 4-6 items Estimate sums and differences of decimals and fractions to assess the reasonableness of results. Limits Assessed within Solve real-world and mathematical problems requiring addition and subtraction ofdecimals, fractions and mixed numbers, including those involving measurement, geometry and data. Limits Addends, minuend and subtrahend denominators are limited to 2, 3, 4, 5, 6, 8, 10 and 12 Mixed numbers are less than 10 Fractions and decimals may be used within the same item A carpenter bought a piece of wood that was 7.87 centimeters long. Then she sawed 7.32 centimeters off the end. How long is the piece of wood now? centimeters Pilot test last year had a lot of problems dealing with baking and cooking.

25 MCA-III Online Items Cont. MCA-III 6-8 Items MCA-M 4-6 items

26 Number and Operation MCA- Item Samplers

27 Algebra MCA-III MCA-M 7-9 5th Grade Quick Sheet Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Limits In a growing pattern, 3 applications of the rule must be shown, though not necessarily consecutively In a table or graph, 3 input-output pairs must be given; pairs are not required to be consecutive Multiply by 5 in x out MCA-III 4-6 Items MCA-M 3-4 Items Vocabulary ordered pair, graph How would you describe your pattern? What shapes are in your pattern? Is your pattern a growing or shrinking pattern? How many shapes are added or removed from each term? What's the rule? Lily earns 4 dollars an hour. Use a rule, and a table to show the relationship between how many hours Lily works In Out Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. Limits Scale increments on grids are limited to 1, 2 and 5 Rules may be expressed using variables Graph the following 1,4 2,8 3,12 Students must be able to record the information in a table from information given. Time Hour h hx

28 Growing Shrinking Patterns How would you describe your pattern? What shapes are in your pattern? Is your pattern a growing or shrinking pattern? How many shapes are added or removed from each term? What is the rule? What are the next three terms?

29 MCA-III Online Items MCA-III 4-6 Items MCA-M 3-4 Items

30 Algebra MCA-III MCA-M 7-9 5th Grade Quick Sheet MCA-III 2-3 Items MCA-M 1-2 Items Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Vocabulary expression, Limits Expressions may not contain nested parentheses Items must not have context Name the property. Are the values equal? 10 + (6 x 2) - 5 x 4 = 6 x (3 x 4) (6 x 3) x 4 Find the missing numbers. 4(7 + 8) = 4( ) + 4( ) (3+7) (5x3) + (5x7) Solve mentally using the distributive property. 6 x 53 4 x MCA-III Online Items

31 Algebra MCA-III MCA-M 7-9 5th Grade Quick Sheet Determine whether an equation or inequality involving a variable is true or false for a given value of the variable MCA-III 4-6 Items MCA-M 3-4 Items Limits Allowable symbols: < and > Items must not have context Vocabulary inequality Relation Thinking Vocabulary: Inequality When x =2 Tell if this statement is true or false 5x +6 = Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities. Vocabulary: Inequality Limits < and > symbols are allowed Vocabulary inequality 38+74= =10+9+C Evaluate expressions and solve equations involving variables when values for the variables are given. Vocabulary: expression Limits Items must not have context Vocabulary expression, 5+k when k =3

32 MCA-III Online Items MCA-III 4-6 Items MCA-M 3-4 Items

33 Algebra MCA Sampler

34 Geometry and Measurement MCA-III 8-10 Items MCA-M 2-3 Items 5th Grade Quick Sheet MCA-III 3-4 MCA-M Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. Limits Prisms and pyramids are limited to triangular, rectangular, pentagonal, hexagonal and octagonal Edge Vocabulary cube, prism, pyramid, cone, cylinder, edge, face, base, three-dimensional, triangular, rectangular Face Face Vertex Recognize and draw a net for a three-dimensional figure. Vocabulary net, cylinder, cube, prism, pyramid, edge, face, base, three-dimensional, triangular, rectangular

35 MCA-III Online Items MCA-III 3-4 MCA-M

36 Geometry and Measurement MCA-III 8-10 Items MCA-M 2-3 Items 5th Grade Quick Sheet Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. Triangle Parallelogram b x h MCA-III 5-6 MCA-M 4-5 Vocabulary formula Break a shape into triangles to determine area Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. Limits When finding surface area, a graphic of the prism or net must be given When finding surface area, dimensions of figures are whole numbers Surface areas and volumes are no more than 360 Vocabulary surface area, volume, net. The surface area of a polyhedron is equal to the sum of the area of all of its faces. Said another way, the surface area is the total area covered by the net of a polyhedron. Let's take a look at a cube. Go to section 2

37 Geometry and Measurement MCA-III 8-10 Items MCA-M 2-3 Items Understand that the volume of a three-dimensional figure can be found by counting the total number of same-sized cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Assessed within th Grade Quick Sheet b MCA-III 5-6 MCA-M 4-5 Unstack to see the layers Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes. Length x Width x Height Limits The definition of B as the area of the base must be given Base Height Vocabulary volume, base, height

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40 Mass. Data Analysis MCA-III 6-8 MCA-M 6-8 5th Grade Quick Sheet MCA-III 6-8 MCA-M Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a "leveling out" of data. Limits When finding mean, data sets contain, at most 9 numbers When finding median, data sets contain, at most 15 numbers Numbers are less than 100 Median Vocabulary mean, median, range, minimum, maximum Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data. Vocabulary double-bar graph, line graph Double-bar graphs have no more than 9 categories Line graphs have no more than 10 data points Scales are in increments of 1/2, 1, 2, 4, 5, 10, tenths if in decimal form or must be consistent with real world applications What are some things that the double bar graph tells us? Students may respond with numbers of boys and girls who chose each sport. They may compare numbers for example, more girls than boys chose soccer, and the same number of boys and girls chose softball. Categories How do the two graphs compare?

41 MCA-III Online Items MCA-III 6-8 MCA-M

42 Use the graph to answer the following questions:what is the Mean Mode Range

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44 Number and Operation Compare decimal denominator dividend divisor equivalent factor improper fraction mixed numbers numerator operation quotient represent solve strategy 4th Grade Vocabulary Algebra variable Geometry and Measurement area cloclwise congruent counter clockwise horizontal image reflection rotation symmetry transformation translation vertex vertical Data Analysis Survey timeline venn diagram Number and Operation digits, value, plot, locate, point equal fewer, more, less, greater estimate, round, nearest, closest least, greatest, compare, order, value add, subtract, sum, difference, result multiply, divide, product fraction, plot, locate, point equal, least, greatest 3rd Grade Vocabulary Data Analysis Algebra pictograph, tally chart, bar graph, line plot, table, data, title, label, key, represent rule, input, output, value number sentence, equation, value, represent Geometry and Measurment parallel, perpendicular, right, figure sides, angles, vertices, figure perimeter, length, width, side, figure tool, ruler, yardstick, meter stick, tape measure a.m., p.m. unit greatest, least, fewest, most, value thermometer, temperature, degrees, increase, decrease These and additional Math Vocabulary from Bridges can also be found: Student Journal Glossary Family Support Pages

45 Calculator Online General Websites

46 This multimedia resource includes interactive math activities, print activities, learning strategies, and videos that illustrate how math is used in everyday life. The resource addresses the following mathematics topics: Fractions; Integers; Percentages; Rate/Ratio/Proportion; Square Roots; Exponents; Patterns; Algebra; Linear Equations; Polynomials; Angles; Circles; Surface Area and Volume; Area and Perimeter; Triangles; Pythagoras; Trigonometry; Similarity and Congruence; Transformations; Shape Classification; Data Display and Graphs; Central Tendency and Distribution; and Probability. Glossary Math Vocabulary on the intranet

47 MCA Mathematics

48 Sample Questions Multiple Choice Multiple Choice Answer by clicking on the letter A,B,C,D. Click Circle (Radio Button) Type on Keyboard

49 Test Navigation Move about the test

50 Multiple Choice To Select answer choices click on the bubbles or any part of the answer choice. Pull down bar to see the rest of the question.

51 Drag and Drop Navigation Click on the objects to move. Click again to change if needed.

52 Palette Navigation 1. Click on each of the shapes you would like to move to the answer box. 2. To remove an answer choice. Click on the delete button. Move your cursor to the answer choice you would like to delete. Click on item. Select and move To remove click on delete and object

53 Hot Spot Navigation 1. Click on the shapes or objects you want to select. 2. Student may have to select more than one answer 3. To remove an answer selection simply double click the object.

54 Line Graph Navigation 1. Use the add arrow tool to graph a line. Select two points to for a line. 2. To remove or change an answer. Selcet Delete. Simply click on answer choice to remove. 3. Some item may require a third point. Click on add point to do so

55 Fill In Navigation Fill in: 1. Type in from on screen 9 key. 2. Use key board. To Delete: 1. Delete key on 9 Key Panel 2. Backspace on keyboard

56 Bar Graph Navigation Click on where they would like the graph to reach. To change the answer simply click on the graph where you want it to be.

57 Type In Type In Sample Questions Hot Spot Hot Spot Graphing Drag and Drop Link to See samples in action Drag on words, pictures to answer the question

58 MTAS Item Sampler Grade 5

59 Vocabulary Sum Difference Product Quotient Addition Subtraction Limits 1 3 digit number Two operations between subtraction and addition Number Corner Grade 1: Wednesday s Workout, Thursday s Thinking, Friday s Figuring Grade 3: Building Computa>onal Fluency - all months Multiplication Division Limits 1 operation 2 digit by 1 digit is allowed No remainders Equal sized Groups Repeated addition Repeated Subtraction 15-5= =5 Equal Shares 3x8=

60 Teacher Directions Student Support Present: M5_Sample Say: You have 8 markers. The teacher gives you 2 more markers. Then you give 4 markers to a friend. How many markers do you have now? Present the answer options in order. Point to each option as you say it. A. 6 B. 10 C. 14 Present: M5_Sample 1.2 Say: Here are 8 markers. Point to the row of 8 markers. You get 2 more markers, so add 2. Point to the row of 2 markers. You give 4 markers away, so take away 4. Briefly cover up 4 of the markers in the row of 8 markers to show that they should be subtracted. How many markers do you have now? Re-present the answer options in order. Point to each option as you say it. A. 6 B. 10 C. 14 Answer Options A. 6 B. 10 C. 14

61 Vocabulary Fraction Decimal place value mixed number order numerator denominator Decimals Number Corner Grade 3: Magne,c Board - February Grade 3: Calendar Grid - April Order and locate Fractions Limits Denominators are limited to 2, 3, 4, 5, 6, 8, 10 and 12 Fraction Bar to number-line 0 1 1/5 Using Reference Points Such as 0, 1/2, 1 Is 3/8 Closer to 0 or 1, IS 3/8 closer to 0 or 1/2

62 Reference Points 0 1 1/5 Fraction Bar to number-line Using Reference Points Such as 0, 1/2, 1 Is 3/8 Closer to 0 or 1, Is 3/8 closer to 0 or 1/2 Fraction Reference Points : Using fraction bars for partitioning a number line Materials-empty fraction bar, (various fraction bars), Number line with 0,1/2 and 1 reference points. Frame different fractions as shown above. Place out a fraction bar. Color 2/5 of the fraction bar red. Is 2/5 closer to 0 or 1? Is 2/5 closer to 0 or 1/2? Cont. w/ other combinations involving 4ths, 5ths 6ths, 7ths Denominators 2, 3, 4, 5, 6, 8, 10 and 12 Fractions Reference Point s Move to using only an empty number line and reference points. Number line with 0,1/2 and 1 reference points. Frame different fractions as shown above. Place out a fraction bar. Color 2/5 of the fraction bar red. Is 2/5 closer to 0 or 1? Is 2/5 closer to 0 or 1/2? Cont. w/ other combinations involving 4ths, 5ths 6ths, 7ths to 12ths Fraction Bars jad.best.vwh.net/java/fractions/fractions.html

63 Numerical Components Relationship Numerator/Denominator Fraction Numeric Components : Using fraction bars to demonstrate numeric components. Materials-empty fraction bar, (various fraction bars), Number line with 0,1/2 and 1 reference points. Frame different fractions as shown to the right. 3/8- I know 3/8 is close to 1/2 because 4/8 reduces to 1/2. Place out a fraction bar. Color 3/8 of the fraction bar green. Is 3/8 closer to 0 or 1? Is 2/5 closer to 0 or 1/2? Cont. w/ other combinations involving 4ths, 5ths 6ths, 7ths Eventually we want kids to think in relationship to equivalent fraction and size of partitioned number of parts. Fraction Numeric Componets Move to screening fraction bars. Same as above 0 1 Fraction Numeric Components : Using fraction bars to demonstrate numeric components. Materials-empty fraction bar, (various fraction bars), Number line with 0,1/2 and 1 reference points. Frame different fractions as shown to the right. Place out a fraction bar. Color 8/11 and 9/14 on both fraction bars. green. Ask student which is greater? Point out sizes of the partitioned parts. 8/11 is greater than 9/14. The distance between the Numerators and denominators. I know 14ths are less. 8/11 is 3 away 9/14 is 5 away 14ths has a lesser parition. Show the relationship of the numerator and denominator. Show in example. Fraction Numeric Components Move to screening fraction bars. Same as above

64 Modeling Fractions Activity Working with 2/3, 3/4, 5/6 and 7/8, Geogebra Tool Notice that each of these fractions is one part away from the whole. What fraction is this? Area Model Improper 2 Fractions What fraction is this? Fractions 1/2 to 1/16 on a number line Which fraction is the greatest? Do you notice any thing about the number relationship. Fraction 0, 1/2, 1 Fractions0-1.ggb Order Fractions Numberline

65 Vocabulary growing, repeating, pattern rule input output ordered pair graph Limits When creating a rule from pairs, 3 input-output pairs must be given; pairs are not required to be consecutive Output should not exceed 100 X Y ? What is the rule?

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67 Vocabulary equation, expression, true variable Limits: No inequalities 1 variable Whole numbers unless dealing with money values. 1 or two digit n Concepts of relation thinking x = 2.00 A..25 B..50 C..75

68 Teacher Directions Present: M5_Sample Say: Here is an equation: three times m equals eighteen Point to the equation. What does m equal? (3 m=18). Present the answer options in order. Point to each option as you say it. A. 3 B. 6 C. 15 Supports Present: M5_Sample 2.2 Say: You can use blocks to find what m equals. There are 18 blocks altogether. Point to the line of 18 blocks. Put the blocks into 3 equal groups. Point to each of the circles. The number of blocks in each group is m. What does m equal? Re-present the answer options in order. Point to each option as you say it. A. 3 B. 6 C. 15 Answer Options A. 3 B. 6 C. 15

69 Vocabulary Face edge cube prism pyramid triangular rectangular Edge Face Face Vertex Number Corner Grade K: Calendar Grid - February Grade 1: Calendar Grid - January Grade 1: Calendar Grid - March Grade 3: Calendar Grid - March

70 See Regular education slide Number Corner Grade 3 Number Corner - December, February Data Collector

71 Teacher Directions Present: M5_Sample 3.1 Say: Here is a table about the weather. It shows how many days it was sunny, snowy, or rainy. Point to each type of weather as you refer to it. How many days altogether was the weather snowy or rainy? Present the answer options in order. Point to each option as you say it. A. 6 B. 10 C. 12 A. 6 B. 10 Re-present: M5_Sample 3.1 Say: Here is the number of snowy days. Point to the number of snowy days. Here is the number of rainy days. Point to the number of rainy days. How many days altogether...with your finger, draw a circle around the numbers of snowy and rainy days...was the weather snowy or rainy? Re-present the answer options in order. Point to each option as you say it. A. 6 B. 10 C. 12 C. 12

72 The MTAS Object Lists for mathematics and science include examples of objects and other variations in the presentation of the MTAS tasks. Some common ways to vary task presentation include (1) enlarging, embossing, or texturizing print and (2) supplementing numbers in tasks with some type of counter. These variations may be used with nearly all math and science tasks unless explicitly prohibited in the task script. Keep in mind that these lists provide recommendations only; test administrators may use different objects and/or text formats to make tasks more accessible for individual students as long as students are not provided with additional content information. For example, several math tasks incorporate a number line with an unlabeled point. Number lines used in classrooms may not be appropriate for all of the MTAS tasks if all points are labeled. Please contact MDE (mde.testing@state.mn.us) if you have questions about objects that may be used to represent MTAS tasks. Task Objects Grade 5 Sample 01 Present task using objects: 14 markers Present answer options using objects and/or raised numerals: 6 markers and/or the numeral 6 10 markers and/or the numeral markers and/or the numeral 14 Note: Total markers needed: 44 markers Grade 5 Sample 02 Present task using textured or plastic pieces: 2 numerals: 3, 18 1 letter: m 1 multiplication sign 1 equal sign Present additional information for score 2 using counters and circles: 18 counters 3 felt cut-out circles Present answer options using counters and/or raised numerals: 3 counters and/or the numeral 3 6 counters and/or the numeral 6 15 counters and/or the numeral 15 Note: Total counters needed: 42 counters Grade 5 Sample 03 Present task using sticky string (or other) for lines on the table. Use pictures and raised/textured numerals or counters: Sun Snowflake Raindrops 3 numerals: 2,4 and 8 14 counters Present answer options using counters and/or raised numerals: 6 counters and/or the numeral 6 10 counters and/or the numeral counters and/or the numeral 12 Note: Total counters needed: 42 counters