table of contents grade 4 maps... · table of contents grade 4 page 1 mission statement ... unit 1:...

Table of Contents Grade 4

Mission Statement Page 2 Year overview by term Page 3 Math Facts Page 4-6 Term 1 Page 7-9 Term 2 Page 10-12 Term 3 Page 13-15 Term 4 Page 16-55 Sample MCAS questions by standard

Students should be active learners and lessons should be taught using a variety of

resources and manipulatives to ensure that all learning styles are met. Each term can be

thought of as a thematic unit composed of various lessons and activities. Lessons from

Trailblazers, our primary math curriculum, are listed next to each standard in the maps.

Supplementary resources are available through teacher developed lessons, Groundworks,

and other educational materials.

1

Haverhill Public Schools Elementary Math Curriculum Maps

Mission Statement Strand - the mathematical content

1. Number sense and operations 2. Data, statistics, and probability 3. Patterns, relations, and algebra 4. Measurement 5. Geometry

Standard – a specific objective that students should know and be able to do as learners of mathematics by the end of each grade level. The following mathematics maps were developed for the purpose of teaching for

mastery all Massachusetts mathematics standards. The standards listed in each term are

not necessarily intended to be followed in sequential order by number. The order in

which they are taught will depend upon the use of curriculum resources. This flexibility

allows for teachers to use their professional creativity to best meet their students needs.

Term 1 (August/September/October) Data Analysis, Statistics, and Probability

Term 2 (November/December/January)

Patterns, Relations, and Algebra

Term 3 (January/February/March)

Term 4 (April/May/June)

Number Sense and Operations 4.N.1 4.N.7

Measurement

Geometry

4.N.2 4.N.8 4.N.3 4.N.9 4.N.4 4.N.14 4.N.16 4.N.10 4.N.15 4.N.11 4.N.17 4.N.3 4.N.12 4.N.4 4.N.5 4.N.6 4.N.13 4.N.13 review 4.N.18

2 June 2007

3 June 2007

Math Facts Math Facts, computations, and mental math should be taught continuously from September through June for mastery. Computations: Concepts should be taught using All-Partials/Forgiving methods followed by Compact/standard algorithms. Grade 1 - Addition facts to 10 plus doubles Subtraction facts to 10 Grade 2 - Addition facts to 20 Subtraction facts to 20 Grade 3 - Addition and subtraction facts to 20 Multiplication facts to 10 Division facts to 10 Grade 4 - Addition and subtraction facts to 20 Multiplication facts to 12 Division facts to 12 Grade 5 - Addition and subtraction facts to 20 Multiplication facts to 12 Division facts to 12 Conversion table (5.N.5)

1/2

2/2

1/4

2/4

3/4

4/4

1/5

2/5

3/5

4/5

5/5

0.5

1.0

0.25

0.5

0.75

1.0

0.2

0.4

0.6

0.8

1.0

50%

100%

25%

50%

75%

100%

20%

40%

60%

80%

100%

1/10

2/10

3/10

4/10

5/10

6/10

7/10

8/10

9/10

10/10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Term 1 Haverhill Public Schools Grade 4 Mathematics Map

Data Analysis, Statistics, and Probability Focus/Standard TB/Supplemental Lessons DPP’s Vocabulary

� 4.D.1 Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.

Unit 1: lessons 1, 4 (Adv. book) Unit 1: lesson 2 (Note: the terms numerical and categorical data are not covered in this standard).

Unit 1: T collect organize survey data display

� 4.D.2

Match a representation of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data.

• Supplemental lessons needed on matching graphs to data. Suggested supplements, see Houghton Mifflin chapter 14, lesson 4 (intro to circle graphs)

listsdata table circle graph

� 4.D.3 Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies.

Unit 1: lesson 5 Unit 5: lessons 1, 7 Unit 13: lesson 1 • Supplemental lesson needed

on pictographs and line plots.

• Supplement for line graphs: Houghton Mifflin, chapter 14, lesson 3.

Unit 1: Q Unit 6: F Unit 9: T Unit 13: O Unit 14: I, J

bar graph pictograph line graph line pot tally chart predict construct axis (pl:axes) exploratory vocabulary: mean median mode

� 4.D.4 Represent the possible outcomes for a simple probability situation, e.g., the probability of drawing a red marble from a bag containing three red marbles and four green marbles.

Unit 14: lessons 3, 4, 5, 6, 8

Unit 14: P, R

probability

� 4.D.5 List and count the number of possible combinations of objects from three sets, e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?

• Suggested supplemental lessons: see Problem Solver 4/Organized lists strategy

Unit 6: R Unit 15: A

organized list combinations

4 June 2007

� 4.D.6 Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners, or coins.

Unit 14: lessons 1, 2 (game)

certainlikely unlikely impossible possible spinner

� 4.N.1 Exhibit an understanding of the base ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers.

Unit 3: lesson 4 Unit 6: lessons 1, 3 • Supplemental lessons needed

on place value. Suggested supplements: Houghton Mifflin Chapter 1: lessons 2, 3, 10, 11, 12

digitcompare order whole number

� 4.N.2 Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3.

• Suggested supplements: Houghton Mifflin Chapter 1: lessons 4, 5

expanded form

� 4.N.3 Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line.

• Suggested supplement: Houghton Mifflin Chapter 9: lessons 1, 2

fractionnumerator denominator

� 4.N.4 Select, use, and explain models to relate common fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 11/2), find equivalent fractions, mixed numbers, and decimals, and order fractions.

Unit 12: lessons 1, 3, 4 (game), 6, 7, 8 • Suggested supplements:

Houghton Mifflin Chapter 9: lessons 3, 4, 5, 6, 7 , 8

mixed number

� 4.N.16 Round whole numbers through 100,000 to the nearest10, 100, 1000, 10,000, and 100,000

• Suggested supplements: Houghton Mifflin Chapter 1: lessons 6, 7

round

� 4.N.10 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.

Unit 3: lesson 7 Unit 4: lesson 6 Unit 13: lesson 4

equationnumber sentence

� 4.N.11 Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g. 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500.

Unit 3: lesson 1, 3 (game) Unit 4: lesson 5 (game) Unit 6: lesson 11 (game)

June 2007 5

� 4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently.

Unit 3: lesson 5 Unit 7: lesson 12

calculatecompute

Exploratory Concepts and Skills

Explore the concepts of median, mode, maximum and minimum, and range. Discuss what data-collection methods are appropriate for various types of investigations. Explore situations that involve probabilities of equally likely events. Investigate the construction of simple circle graphs.

June 2007 6


Patterns, Relations, and Algebra Focus/Standard TB/Supplemental Lessons DPP’s Vocabulary

� 4.P.1 Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, …

Unit 7: lesson 4 Unit 15: lesson 3 • Supplemental lessons needed

Unit 4: B Unit 15: I

pattern sequence increase decrease extend rule

� 4.P.2 Use symbol and letter variables (e.g., ∆, x) to represent unknowns or quantities that vary in expressions and in equations or inequalities (mathematical sentences that use =, <, >).

Unit 5: T

variable equation number sentence inequality equal greater than> less than <

� 4.P.3 Determine values of variables in simple equations, e.g., 4106 – ∇ = 37, 5 = µ + 3, and – µ = 3.

� 4.P.4 Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships.

� 4.P.5 Solve problems involving proportional relationships, including unit pricing (e.g., four apples cost 80¢, so one apple costs 20¢) and map interpretation (e.g., one inch represents five miles, so two inches represent ten miles).

proportionrelationship

� 4.P.6 Determine how change in one variable relates to a change in a second variable, e.g., input-output tables.

Unit 15: lessons 4, 6

Unit 15: P, R

input output

� 4.N.7 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solutions of problems.

Unit 4: lessons 1, 2, 4 • Suggested supplements:

Houghton Mifflin Chapter 7: lesson 10, Chapter 8: lesson 13

• Supplemental lessons needed on odd/even/ square numbers

factormultiple square number odd/even numbers

June 2007 7

� 4.N.8 Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations.

multiplyproduct divide dividend divisor quotient

� 4.N.9 Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations, e.g., 37 x 46 = 46 x 37, (5 x 7) x 2 = 5 x (7 x 2).

Unit 7: lessons 1, 2 • Suggested supplements:

Houghton Mifflin,Chapter 2: lesson 1 Chapter 4: lessons 1, 7

commutativeassociative operations order of operation



equation number sentence





calculatecompute

� 4.N.14 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits).

Unit 7: lesson 7 Unit 11: lessons 1, 2, 3, 4, 5 • Suggested supplements:

Houghton Mifflin Chapter 2

compactalgorithm

� 4.N.15 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders).

Unit 13: lessons 2, 3 • Suggested supplements:

Houghton Mifflin Chapter 8: lessons 1-11

� 4.N.17 Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer.

Unit 6: lessons 4, 5, 6 Unit 7: lessons 6, 8 • Supplemental lessons needed

on estimation strategies.

estimate regroup

June 2007 8


Use concrete materials to build an understanding of equality and inequality. Explore properties of equality in number sentences: when equals are added to equals, then the sums are equal; when equals are

multiplied by equals, then the products are equal, e.g., if = 5, then 3 x = 3 x 5.

June 2007 9


Measurement Focus/Standard TB/Supplemental Lessons DPP’s Vocabulary

� 4.M.1 Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute.

• Supplemental lessons needed on units of measure. Suggested supplements: Houghton Mifflin chapter 6: lesson 4

Unit 2: D Unit 19, M

length area weight volume attribute

� 4.M.2 Carry out simple unit conversions within a system of measurement, e.g., hours to minutes, cents to dollars, yards to feet or inches, etc. :

• Suggested supplements: Houghton Mifflin chapter 6

• Houghton Mifflin chapter 3: lessons

6, 7 (money)

Unit 4: H Unit 10: N, Z

Standard units of measure: inch millimeter foot centimeter yard meter mile kilometer ounce milligram pound gram ton kilogram second milliliter minute liter hour cent pint dollar quart gallon

� 4.M.3 Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since…) and using a calendar (e.g., days since…)

• Suggested supplements: Houghton Mifflin chapter 3: lessons 1, 2, 3, 4

Unit 1: G, I, O Unit 2: A, E Unit 3: E Unit 4: Q Unit 5: F Unit 8: P Unit 9: T Unit: 16, M

analog clock digital clock AM/PM clockwise counterclockwise

June 2007 10

� 4.M.4 Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring

Unit 2: lessons 1, 2, 3, 4 • Supplemental lessons needed on

perimeter. Suggested supplements: Houghton Mifflin chapter 11: lessons 11,12,13.

• Suggested supplements: Houghton Mifflin chapter 6 lesson 7

Unit 2: J. Z Unit 3: N Unit 5: L Unit 7: BB Unit 8: H Unit 12: P Unit 16: E, F

area perimeter length width

� 4.M.5 Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature

Unit 9: lesson 2 taught with 4.G.2 addresses angle measurement. Unit 9: lesson 6

• Supplemental lessons needed

Unit 1: R Unit 8: J, K, L Unit 11: M

protractor (angle ruler)

� 4.P.3 Determine values of variables in simple equations,

e.g., 4106 – ∇ = 37, 5 = µ + 3,

and – µ = 3.

� 4.P.4 Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships.

� 4.P.5 Solve problems involving proportional relationships, including unit pricing (e.g., four apples cost 80¢, so one apple costs 20¢) and map interpretation (e.g., one inch represents five miles, so two inches represent ten miles).

proportionrelationship

� 4.P.6 Determine how change in one variable relates to a change in a second variable, e.g., input-output tables.

Unit 15: lessons 4, 6

Unit 15: P, R input output

June 2007 11








calculatecompute

� 4.N.13 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders.

remainder


Develop the concepts of area and perimeter by investigating areas and perimeters of regular and irregular shapes created on dot

paper, coordinate grids, or geoboards. Use concrete objects to explore volumes and surface areas of rectangular prisms. Investigate the use of protractors to measure angles. Identify common measurements of turns, e.g., 360° in one full turn, 180° in a half turn, and 90° in a quarter turn. Investigate areas of right triangles. Understand that measurements are approximations and investigate how differences in units affect precision.

June 2007 12


Geometry Focus/Standard TB/Supplemental Lessons DPP’s Vocabulary

� 4.G.1 Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes.

Unit 9: lessons 2, 3 Unit 9: lesson 5 taught with 4.G.2 addresses faces, corners, and edges.

faces corners sides right angle diagonal symmetry 2-dimensional 3-dimensional

� 4.G.2 Describe, model, draw, compare, and classify two- and three-dimensional shapes, e.g., circles, polygons—especially triangles and quadrilaterals—cubes, spheres, and pyramids.

Unit 9: lesson 4 (adv. book), 5 Unit 9: lesson 2 taught with 4.G.1 addresses polygons and non-polygons. • Supplemental lessons needed

on polygons. Suggested supplements: Houghton Mifflin chapter 11: lesson 4

Unit 1: F, G, H

compare classify polygon circle square rhombus trapezoid rectangle quadrilateral triangle parallelogram cube sphere pyramid prism

� 4.G.3 Recognize similar figures. • Supplemental lessons on similarity. Suggested supplements: Houghton Mifflin chapter 11: lesson 10

similar

� 4.G.4 Identify angles as acute, right, or obtuse.

Unit 2: lessons 6, 7 • Supplemental lessons on

angles. Suggested supplements: Houghton Mifflin chapter 11: lesson 2

Unit 2: W, BB Unit 3: P Unit 4: K Unit 9: A, I, J Unit 10: L Unit 14: J

acute angle obtuse angle right angle

June 2007 13

� 4.G.5 Describe and draw intersecting, parallel, and perpendicular lines.

Unit 9: lesson 1 • Supplemental lesson needed

on parallel, perpendicular, and intersecting lines. Suggested supplements: Houghton Mifflin chapter 11: lesson 1

Unit 9: N Unit 14: G

lines parallel perpendicular intersecting

� 4.G.6 Using ordered pairs of numbers and/or letters, graph, locate, identify points, and describe paths (first quadrant).

• Supplemental lessons needed on ordered pairs. Suggested supplements: Houghton Mifflin chapter 11: lessons 5, 6, 15

ordered pairpoint

� 4.G.7 Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent.

• Supplemental lesson needed on congruence. Suggested supplements: Houghton Mifflin chapter 11: lesson 9

• Supplemental lesson needed on flips, slides, and turns

reflections (flips)rotation (turns) translation (slides) congruent

� 4.G.8 Identify and describe line symmetry in two-dimensional shapes.

• Supplemental lesson needed on symmetry. Suggested supplements: Houghton Mifflin chapter 11: lesson 7

Unit 9: P Unit 10: J

line symmetry

� 4.G.9 Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes.

Unit 9: lesson 5 taught with 4.G.2 also addresses this standard • Supplemental lessons needed

Suggested : Houghton Mifflin chapter 11: lesson 3








calculatecompute

June 2007 14

June 2007 15

� 4.N.13 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders.

remainder

� Review Facts and Computations


Predict and describe results of transformations (e.g., translations, rotations, and reflections) on two-dimensional shapes. Investigate two-dimensional representations of three-dimensional objects.

Grade 4 Sample MCAS Questions for Number Sense: 4.N.1 2005 #24

The chart below shows the height, in feet, of four different mountains in Colorado.

The height of Mt. Evans is between the two greatest heights shown on the chart above. Which of the following could be the height of Mt. Evans? A. 14,208 feet B. 14,241 feet C. 14,275 feet D. 14,264 feet

4.N.2 2004 #21

Shannon read that fourteen thousand, nine hundred eighty-seven people live in Dukes County. Which of the following is another way to write this number? A. 10,000 + 4,000 + 900 + 80 + 7 * B. 14,000,987 C. 14 x 100 + 9 x 10 + 87 D. 1 + 4 + 9 + 8 + 7

2003 # 23 The points on the timeline below represent four important dates in history.

Which point on the timeline best represents the location of 1609?

A. W B. X * C. Y D.

June 2007

16

4.N.3 2005 #28

Tyler has the group of plates shown below. He used exactly ¾ of the plates to set the table for a family dinner. How many plates did he use?

2005 #36 Which of the following is shaded to represent 1/8 of the circle?

June 2007

17

4.N.4 2006 #16

The picture below shows four fractions and a number line. Wilson’s homework is to place a point on the number line for the location of each of the fractions.

If Wilson places the fractions correctly, which fraction will be closest to 0 on the number line? A. 1/6 B. 1/3 C. 1/12 D. 1/4

2003 # 7

Duncan put blue marbles and green marbles in a bag. Exactly ¾ of the marbles in the bag are blue. Which of the following could be the total number of marbles in the bag? A. 3 B. 6 C. 7 D. 8 *

4.N.5 2006 # 25

June 2007

18

Which of the following is a list of three fractions that are each equivalent to 0.50?

2005 #7

Which of the following is a true statement?

4.N.6 2005 #15 Which of the following is read “fifty-three hundredths”?

A. 5300 B. 53.00 C. 0.53 D. 0.053

2004 #36 One nickel is worth 5 hundredths of a dollar. Which of the following represents 5 hundredths of a dollar? A. $5.00 B. $0.50 C. $0.05 * D. $0.005

4.N.7 2006 #15

June 2007

19

Mr. Simon gave exactly 3 pencils to each student in the Math Club.

Which of the following could be the total number of pencils he gave to the students in the Math Club? A. 13 B. 22 C. 27 D. 31

2006 #29 Short Answer

Write an even number that is greater than 3 and is a factor of 20.

4.N.8 2006 # 7Which of the following models represents 3 x 2?

2004 # 32

Carlos is solving the number sentence shown below. 15 x 12 = ? Which of the following methods could he use to find the correct solution? A. (15 + 10) + (15 + 2) B. (15 + 10) x (15 + 2) C. (15 x 10) x (15 x 2) D. (15 x 10) + (15 x 2) *

4.N.9 2006 #36

June 2007

20

Which of the following goes in the blank to make the statement below true? 98 X 19 = ? A. 20 X 80 B. 99 X 18 C. 20 X 90 D. 19 X 98 2003 #14 What number goes in the to make the number sentence below true? (42 + 35) + 26 = 42 + ( + 26) A. 35 * B. 42 C. 77 D. 103

4.N.10 2006 #13 Open Response

June 2007

21

Hudson’s Bakery sells cakes in three different sizes – small, medium, and large. The picture below shows the cost of each size of cake at the bakery.

a. Wilma bought 1 small cake and 2 medium cakes. What was the total cost of the cakes Wilma bought?

Show your work or explain how you got your answer. b. Justin has $85.00 to spend on cakes. What is the greatest number of cakes he can buy with exactly

$85.00? Show your work or explain how you got your answer.

c. Sheila bought a group of cakes that cost a total of $70.00. At least 2 of the cakes she bought were different sizes. List a group of cakes that Sheila could have bought.

Show your work or explain how you got your answer.

2006 # 23

Mr. Thomas walks every day. The distance that he walks each day is between 4 miles and 8 miles. Which of the following could be the total number of miles Mr. Thomas will walk in 30 days? A. 100 B. 200 C. 500 D. 900

4.N.11 2006 #1 Since 6 x 3 =18, what is 600 x 3?

June 2007

22

A. 180 B. 1,800 C. 18,000 D. 180,000

2004 # 34 Each expression shown below has the same value.

2 x 6 3 x 4 24 ÷ 2

Which of the following has the same value as each of the three expressions above? A. 72 ÷ 12

B. 72 ÷ 9 C. 72 ÷ 8 D. 72 ÷ 6 *

4.N.12 2006 # 22 Haley swam 22 laps each day for 18 days. Then she swam 25 laps each day for

10 days. What was the total number of laps she swam over the 28 days? A. 75 B. 546 C. 646 D. 4066

2005 #6

The chart below shows the number of college athletes who participated in four different sports in the academic year 1998–1999.

According to the chart, how many men and women participated in soccer in 1998–1999? A. 25,758 B. 33,230 C. 35,758 D. 37,921

4.N.13 2005 #20

What is the remainder for the division problem shown below?

June 2007

23

496 ÷ 6 = ? A. 0 B. 1 C. 3 D. 4

2006 #5

Classes that visit the Life Science Museum are divided into groups of

4 students for each tour guide. Which of the following classes would not be able to form groups of 4 students with none left over? A. a class of 36 students B. a class of 40 students C. a class of 46 students D. a class of 52 students

4.N.14 2000 #11

Compute:

4.N.15 1999 #28

4.N.16 2006 #6 What is 869 rounded to the nearest 10?

June 2007

24

A. 800 B. 860 C. 870 D. 900

2005 #19

A factory made 13,424 ice cream sandwiches in an 8-hour period. What is 13,424 rounded to the nearest hundred? A. 10,000 B. 13,000 C. 13,400 D. 13,500

4.N.17 2006 # 33

Jake needs to order 238 chairs for a party. He can order the chairs in sets of 100 and in sets of 10. Which of the following is closest to the number of chairs that Jake needs to order? A. 24 sets of 100 B. 1 set of 100 and 13 sets of 10 C. 2 sets of 100 and 3 sets of 10 D. 2 sets of 100 and 4 sets of 10

2004 #38

Rufus bought 6 items at the mall. No item cost more than $5 or less than $2. Which of the following could be the total cost of the 6 items Rufus bought? A. $7 B. $10 C. $22 * D. $31

4.N.18 2006 #32 What is the solution to the problem shown below?

June 2007

25

2005 #14

All the sections of the models below are the same size. The model below is shaded to represent 1 whole.

A fractional part of each model below has been shaded. Which fraction should you get if you add the fractions represented by the shaded parts of the models?

June 2007

26

Grade 4 Sample MCAS Questions for Data Analysis, Statistics, and Probability 4.D.1 2001 #15

The pictograph shows the number of T-shirts sold each day of School Spirit Week. About how many MORE T-shirts were sold on Tuesday than on Friday? A. 4 B. 5 C. 40 D. 45 2004 #8 Each time Rosa takes her dog for a checkup, Dr. Azim records the dog’s weight. Which of the following is the best way for the doctor to record the dog’s weight at each checkup in order to see any changes in the weight? A. pictograph B. tally chart C. line graph * D. circle graph

4.D.2 2003 #36

June 2007

27

Ms. Truman’s students recorded the temperature at 2:15 P.M. each day for 6 school days. The data are shown below. Monday 46�F Tuesday 58�F Wednesday 66�F Thursday 49�F Friday 38�F Monday 50�F

Which graph below best represents the temperatures recorded from Monday to Monday?

2005 #32

June 2007

28

The chart below shows the votes for class president.

Which graph below most accurately reflects this information?

4.D.3 2002 #32

June 2007

29

The line plot below shows how students scored on last weeks vocabulary test.

How many students scored 95 or higher on the test?

A. 5 students B. 7 students C. 12 students D. 16 students

2003 #23

June 2007

30

On the first day of school, Ms. Forsythe always asks her students, “How many of you read at least 2 books over the summer?” The graph below shows the data she has collected over the last four years.

Based on the data in the graph, which of the following is a reasonable conclusion?

A. The number of girls reading at least 2 books increased each year.

B. The number of boys reading at least 2 books increased each year.

C. The number of boys reading at least 2 books in Year 1 is half the number of girls reading at least 2 books in Year 1.

D. The number of students in the class increased each year. 4.D.4 2002 #6 Sasha has a bag with 5 grey balls

3 white balls

June 2007

31

4 striped balls. If she takes a ball out of the bag without looking, what are her chances of getting a white ball? 6 A. 1 chance out of 3 B. 3 chances out of 9 C. 3 chances out of 12 D. 9 chances out of 12

2004 #35

A box of instant oatmeal contains 5 packs of Peaches & Cream oatmeal and 3 packs of Brown Sugar & Cinnamon oatmeal, as shown below. The packs are mixed up in the box.

Shilpa opened the box and took out 1 pack of oatmeal without looking. What is the probability that the pack she took out contained Peaches & Cream oatmeal?

4.D.5 2004 #5

Darnae is planning to decorate her room. She will choose 1 color of paint, 1 color of carpet, and 1 pattern for the wallpaper. The colors and patterns she will choose from are shown below.

June 2007

32

How many different combinations of 1 paint color, 1 carpet color, and 1 wallpaper pattern are possible? A. 7 B. 8 C. 10 D. 12 *

4.D.6 2001 #9

Jake is tossing a chip onto different targets. The chip has the best chance of landing on a SHADED space in which target?

June 2007

33

2006 #6

Celestine put the tiles shown below into an empty bag and mixed them up. The back of each tile is blank.

If Celestine picks 1 tile from the bag without looking, which of the following best describes the chances that she will pick a tile with the letter H on it? A. certain B. likely C. unlikely D. impossible

June 2007

34

Grade 4 Sample MCAS Questions for Patterns: 4.P.1 2006 #8

Mike is using an addition rule to shade a number pattern on a hundreds chart. The first three numbers in Mike’s number pattern are 4, 10, and 16. The picture below shows the numbers he has shaded so far.

If Mike continues using the same rule, what should be the next number after 88 that he shades on the chart? A. 100 B. 94 C. 92 D. 89

2006 # 35

June 2007

35

The first ten shapes in a pattern are shown below. The pattern repeats after every 5 shapes.

If the pattern continues to repeat in the same way, what will be the 13th shape in the pattern?

4.P.2 2005 # 18

June 2007

36

Max and Sam wrote a number sentence to show that Max is older than Sam. In their number sentence,

• M represents Max’s age in years, and • S represents Sam’s age in years.

Which number sentence shows that Max is older than Sam?

2004 #15

On a test, Hannah scored 8 points higher than Todd. On the same test, Hannah scored 7 points lower than Juanita. • H represents Hannah’s score on the test. • T represents Todd’s score on the test. • J represents Juanita’s score on the test. Based on the information above, which of the following must be true?

A. J<T B. T<J C. H>J D. J<H

4.P.3 2006 #9

June 2007

37

Two number sentences are shown below.

What values for and make both number sentences true?

2006 #12 What is the value of that makes the number sentence below true? 3098 - = 923

4.P.4 2006 #18

June 2007

38

Corey is 10 years younger than James. James is 15 years old. Which of the following represents Corey’s age in years? A. 15 + 10 B. 15 – 10 C. 15 ÷ 10 D. 15 x 10

2002 # 18

Micah left for school with 4 boxes of pencils. Each box had 6 pencils. At school, he gave away 4 pencils from one box. Which number sentence below can be used to find the total number of pencils that were left?

A. 4 x 6 – 4 = ? B. 4 x 6 + 2 = ?

C. 3 x 6 + 4 = ? D. 3 x 6 – 2 = ?

4.P.5 2006 # 31

June 2007

39

The pictures below show how two different groups of shapes balance a scale.

a. If 1 block weighs 10 pounds, what is the weight, in pounds, of 1 ball? Show or explain how you got your answer.

b. What is the total number of blocks needed to balance 6 balls? Show or explain how you got your

answer.

c. What is the total number of balls needed to balance 10 cans? Show or explain how you got your answer.

2005 # 26 One large box of cookies contains the same number of cookies as 6 small boxes. Each small box contains an equal number of cookies. The boxes of cookies are shown below.

A large box of cookies contains 84 cookies. What is the total number of cookies that a small box contains? A. 9 B. 11 C. 14 D. 20

4.P.6 2006 # 21

June 2007

40

A number machine uses a rule to change each number that is put into it to a different number. The same rule is used every time. The picture below shows what happened when the numbers 6, 9, and 11 were put into the number machine.

Which of the following could be the rule used by the number machine? A. multiply by 2 B. multiply by 6 C. add 3 D. add 6

2006 # 39 An input-output table is shown below.

Which of the following could be the rule for the input-output table?

June 2007

41

Grade 4 Sample MCAS Questions for Measurement: 4.M.1 2005 #3

Ms. Roland measured the length of a board she was using to make a shelf. Which of the following could be the length of the board? A. 6 square feet B. 6 pounds C. 6 gallons D. 6 feet

4.M.2 2006 #30 Jerry’s dog is 2 feet 6 inches tall. How many inches tall is Jerry’s dog? 2004 #16 Ms. Fuller bought a roll of gold ribbon to make bows for gift packages.

There were 6 feet of ribbon on the roll. How many inches of ribbon were on the roll? A. 18 B. 36 C. 60 D. 72 *

June 2007

42

4.M.3 2006 #37

Paula wants to mark her birthday on the calendar below. For 2007, she knows that her birthday is six days after Thanksgiving. Thanksgiving is always the fourth Thursday in November.

Using the calendar above, what date is Paula’s birthday in 2007?

A. Thursday, November 22 B. Tuesday, November 27 C. Wednesday, November 28 D. Thursday, November 29

2005 #38

Hong wanted to take the 5:10 P.M. bus. She arrived at the bus stop 25 minutes before 5:10 P.M. What time did Hong arrive at the bus stop?

A. 5:35 P.M. B. 4:45 P.M. C. 4:40 P.M. D. 4:25 P.M.

4.M.4 2006 #10

June 2007

43

The picture below shows the shaded figure that Diego drew on a piece of grid paper.

a. What is the area, in square units, of the shaded figure? Show or explain how you got your answer. b. What are the dimensions (length and width), in units, of a rectangle with the same area as the shaded

figure? Show or explain how you got your answer.

c. What is the perimeter, in units, of the rectangle you described in part (b)? Show or explain how you got your answer.

2005 # 10

June 2007

44

Thyra has a rectangular piece of colored paper. The shaded shape on the grid below represents Thyra’s piece of paper.

a. What is the area, in square inches, of the piece of paper? Show your work or explain how you got your answer.

b. What is the perimeter, in inches, of the piece of paper? Show your work or explain how you got your

answer. c. Thyra cut the paper into 2 smaller rectangles that were each the same size. What is the perimeter, in

inches, of each of the smaller rectangles? Show your work or explain how you got your answer. 4.M.5 2006 #4

June 2007

45

Lisa measured the length and width of the rectangular floor of her room. She used the measurements to find the area of the floor. Which of the following could be the area of the floor of Lisa’s room? A. 120 square feet B. 120 cubic feet C. 120 inches D. 120 yards

2005 # 5 Lysella made the bookmark shown below.

Which of the following is 1 inch longer than the bookmark Lysella made?

June 2007

46

Grade 4 Sample MCAS Questions for Geometry: 4.G.1 2004 #20

How many faces does the figure shown below have?

A. 6 *

B. 5 C. 4 D. 3

2003 #38 Ms. Crow glued 4 white cubes together as shown below. Then she painted the entire figure red.

How many faces of the 4 cubes were painted red? A. 4 B. 9 C. 18 * D. 24 4.G.2 2006 #19

June 2007

47

Which of the following is not a quadrilateral?

2005 #4

Which of the following is a three-dimensional shape?

A. quadrilateral B. pyramid C. triangle D. rectangle

4.G.3 2003 #22

June 2007

48

Which of the following appears to be a pair of congruent shapes?

4.G.4 2000 #22 Which angles in the figure are ACUTE angles?

.G.5 2006 #28

4

June 2007

49

Points A, B, X, Y, Z, and W, and line AB are shown on the grid below.

What are two points shown on the grid that can be connected to form a line segment perpendicular to

2005 #31

line AB?

Ursula is drawing a map of the area near her school. The first part of her map is shown below. Copy

Ursula’s map into your Student Answer Booklet. Use your copy of the map to complete the followingtasks.

reet is perpendicular to Oak Lane. On your map, draw Rose Street so that it is perpendicular to

. Shady Glen is parallel to Rose Street. On your map, draw Shady Glen so that it is parallel to Rose Street.

. Broadway intersects Shady Glen to form an acute angle. Draw Broadway on your map. Mark the acute

4.G

a. Rose StOak Lane.

b

cangle on your map. .6 2006 #17

June 2007

50

The points on the grid below represent the locations of Gina’s home, a pond, and a baseball field. The

grid lines represent the streets in Gina’s neighborhood.

a. Write the ordered pair that best represents the location of Gina’s home on the grid.

. Moving along the grid lines, the shortest distance from Gina’s home to the baseball field is 3 units. how

. Moving along the grid lines, the shortest distance from Gina’s home to her school is 7 units. Write an

003 #31 open response

b

Moving along the grid lines, what is the shortest distance, in units, from Gina’s home to the pond? Sor explain how you got your answer.

cordered pair that could be the location of her school. Show or explain how you got your answer.

2

he map below shows the location of some places in Keith’s hometown. T

June 2007

51

a. hat ordered pair names the location of the Bank?

. What is located at (2, 6)?

c. Moving along the grid lines, the shortest distance from the Store to the Bank is 3 blocks. Moving along

. Moving along the grid lines, the shortest distance from the Library to the Soccer field is 7 blocks. What

.G.7 2001 #35

W b

the grid lines, what is the shortest distance from the Store to the Zoo?

dordered pair could name the location of the Library?

4

Which shows the letter after it has been FLIPPED ONCE?

June 2007

52

4.G.8 2005 #25

f the shaded shapes shown below appears to have exactly 1 line of symmetry?

Which o

June 2007

53

003 #332

The picture below shows one of the squares Yvette sewed for a quilt.

June 2007

54

How many lines of symmetry does the quilt square have?

A. 0 B. 2 C. 4 * D. 8

4.G.9 2004 #33

The cube shown below was cut into three pieces.

Which of the following groups could be the three pieces of the cube?

June 2007

55

table of contents grade 4 maps... · table of contents grade 4 page 1 mission statement ... unit 1:...

Documents