Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA Number, Number Sense and Operations Standard Grades 3-4

Ohio Benchmarks Grades 3-4 Grade-Level Indicators Grade 3 Grade-Level Indicators Grade 4 A. Use place value structure of the base-ten 2. Use place value concepts to represent whole numbers and number system to read, write, represent and decimals using numerals, words, expanded notation and physical 2. Use place value structure of the base-ten number system to read, compare whole numbers and decimals. models. For example: write, represent and compare whole numbers through millions and a. Recognize 100 means “10 tens” as well as a single entity (1 decimals through thousandths. hundred) through physical models and trading games b. Describe the multiplicative nature of the number system; e.g., 3. Round whole numbers to a given place value. Grade 3 - 8 the structure of 3205 as 3 x 1000 plus 2 x 100 plus 5 x 1. Grade 4 - 6 c. Model the size of 1000 in multiple ways; e.g., packaging 1000 objects into 10 boxes of 100, modeling a meter with centimeter and decimeter strips, or gathering 1000 pop-can tabs. d. Explain the concept of tenths and hundredths using physical such models, as metric pieces, base ten blocks, decimal squares or money.

3. Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, <, >, =, ≤, ≥.

B. Recognize and generate equivalent representations 1. Identify and generate equivalent forms of whole numbers; e.g., 1. Identify and generate equivalent forms of fractions and decimals. for whole numbers, fractions and decimals. 36, 30+6, 9 x 4, 46-10, number of inches in a yard. For example: 7. Recognize and use decimal and fraction concepts and notations a. Connect physical, verbal and symbolic representations of Grade 3 – 7 1 5 Grade 4 - 4 as related ways of representing parts of a whole or a set; e.g., 3 fractions, decimals and whole numbers; e.g., , , “five 3 2 10 of 10 marbles are red can also be described as 10 and 3 tenths,” 0.5, shaded rectangles with half, and five tenths. tenths are red. b. Understand and explain that ten tenths is the same as one whole in both fraction and decimal form.

C. Represent commonly used fractions and mixed 5. Represent fractions and mixed numbers using words, numerals numbers using words and physical models. and physical models. Grade 3 – 4 Grade 4 - 3

Prepared by the Region 10 State Support Team – 8-9-10 1 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

D. Use models, points of reference and equivalent forms 3. Use mathematical language and symbols to compare and order; 5. Use models and points of reference to compare commonly used of commonly used fractions to judge the size of e.g., less than, greater than, at most, at least, <, >, =, ≤, ≥. fractions. fractions and to compare, describe and order them. 6. Compare and order commonly used fractions and mixed Grade 3 – 5 numbers using number lines, models (such as fraction circles or Grade 4 - 4 bars), points of reference (such as more or less than ½ ), and equivalent forms found using physical or visual models.

E. Recognize and classify numbers as prime or 4. Identify and represent factors and multiples of whole numbers composite and list factors. through 100, and classify numbers as prime or composite. Grade 3 – 0 Grade 4 - 6

F. Count money and make change using both coins and 4. Count money and make change using coins and paper bills to ten 8. Solve problems involving counting money and making change, paper bills. dollars. using both coins and paper bills. Grade 3- 6 Grade 4 - 5

G. Model and use commutative and associative properties 11. Model and use the commutative and associative properties for for addition and multiplication. addition and multiplication. Grade 3 – 4 Grade 4 - 0

H. Use relationships between operations, such as 10. Explain and use relationships between operations, such as: subtraction as the inverse of addition and division as a. relate addition and subtraction as inverse operations; the inverse of multiplication. b. relate multiplication and division as inverse operations; Grade 3 – 7 c. relate addition to multiplication (repeated addition); Grade 4 - 0 d. relate subtraction to division (repeated subtraction).

I. Demonstrate fluency in multiplication facts with factors 13. Demonstrate fluency in multiplication facts through 10 and 14. Demonstrate fluency in adding and subtracting whole numbers through 10 and corresponding divisions. corresponding division facts. and in multiplying and dividing whole numbers by 1- and 2-digit Grade 3 – 3 numbers and multiples of ten. Grade 4 - 4

Prepared by the Region 10 State Support Team – 8-9-10 2 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

J. Estimate the results of whole number computations 13. Estimate the results of whole number addition and subtraction 9. Estimate the results of computations involving whole numbers, using a variety of strategies, and judge the problems using front-end estimation, and judge the fractions and decimals, using a variety of strategies. reasonableness. reasonableness of the answers. (Grade 2) Grade 3 – 5 Grade 4 - 7 15. Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates.

K. Analyze and solve multi-step problems involving 12. Add and subtract whole numbers with and without regrouping. 8. Use geometric models to solve problems in other areas of addition, subtraction, multiplication and division using mathematics, such as number (multiplication/division) and whole numbers. 14. Multiply and divide 2- and 3-digit numbers by a single-digit measurement (area, perimeter, border). Grade 3 – 7 number, without remainders for division. Geometry and Spatial Sense Grade 4 - 8 6. Use associative and distributive properties to simplify and perform computations; e.g., use left to right multiplication and the distributive property to find an exact answer without paper and pencil, such as: 5 x 47 = 5 x 40 + 5 x 7 = 200+35 = 235.

7. Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money.

12. Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.

Prepared by the Region 10 State Support Team – 8-9-10 3 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

L. Use a variety of methods and appropriate tools 8. Model, represent and explain multiplication; e.g., repeated 11. Develop and explain strategies for performing computations (mental math, paper and pencil, calculators) for addition, skip counting, rectangular arrays and area model. For mentally. computing with whole numbers. example: a. Use conventional mathematical symbols to write equations for 13. Use a variety of methods and appropriate tools for computing with Grade 3 – 9 word problems involving multiplication. whole numbers; e.g., mental math, paper and pencil, and Grade 4 - 5 b. Understand that, unlike addition and subtraction, the factors calculator. in multiplication and division may have different units; e.g., 3 boxes of 5 cookies each. 14. Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit 9. Model, represent and explain division; e.g., sharing equally, numbers and multiples of ten. repeated subtraction, rectangular arrays and area model. For example: a. Translate contextual situations involving division into conventional mathematical symbols. b. Explain how a remainder may impact an answer in a real- world situation; e.g., 14 cookies being shared by 4 children.

M. Add and subtract commonly used fractions with like 9. Estimate the results of computations involving whole numbers, denominators and decimals, using models and paper fractions and decimals, using a variety of strategies. and pencil. Grade 3 – 0 10. Use physical models, visual representations, and paper and pencil Grade 4 - 5 to add and subtract decimals and commonly used fractions with like denominators.

Prepared by the Region 10 State Support Team – 8-9-10 4 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

Measurement Standard Grades 3-4

Ohio Benchmarks Grades 3-4 Grade-Level Indicators Grade 3 Grade-Level Indicators Grade 4 3. Identify and select appropriate units to measure: A. Select appropriate units for 1. Identify and select appropriate units for measuring: perimeter, area, weight, volume (capacity), time and a. length – miles, kilometers and other units of measure as temperature using: appropriate. a. perimeter – string or links (inches or centimeters).  objects of uniform size; b. volume (capacity) – gallons; b. area – tiles (square inches or square centimeters). c. Volume – cubes (cubic inches or cubic centimeters).  U.S. customary units; e.g., mile, square inch, cubic c. weight – ounces, pounds, grams, or kilograms; inch, second degree Fahrenheit, and other units as d. temperature – degrees (Fahrenheit or Celsius). appropriate;  metric units; e.g., millimeter, kilometer, square 4. Read thermometers in both Fahrenheit and Celsius scales. centimeter, kilogram, cubic centimeter, degree Celsius, and other units as appropriate. Grade 3 – 8 Grade 4 - 10

1. Relate the number of units to the size of the units used to B. Know that the number of units is inversely related to the measure an object; e.g., compare the number of cups to fill a size of the unit for any item being measured. pitcher to the number of quarts to fill the same pitcher. Grade 3 – 0 Grade 4 - 5

C. Develop common referents for units of measure for 2. Establish personal or common referents to include additional 2. Demonstrate and describe perimeter as surrounding and area length, weight, volume (capacity) and time to make units; e.g., a gallon container of milk; a postage stamp is about as covering a two-dimensional shape, and volume as filling a comparisons and estimates. a square inch. three-dimensional object. Grade 3 – 10 Grade 4 - 7 5. Estimate and measure length, weight and volume (capacity), using metric and U.S. customary units, accurate to the nearest 1 1 2 or 4 unit as appropriate.

Prepared by the Region 10 State Support Team – 8-9-10 5 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

D. Identify appropriate tools and apply counting 4. Develop and use strategies to find perimeter using string or techniques for measuring side lengths, perimeter, and 4. Read thermometers in both Fahrenheit and Celsius links, area using tiles or a grid, and volume using cubes; e.g., area of squares, rectangles, and simple irregular two- scales. count squares to find area of regular or irregular shapes on a dimensional shapes, volume of rectangular prisms, and grid, layer cubes in a box to find its volume. time and temperature. 6. Use appropriate measurement tools and techniques to Grade 3 – 19 construct a figure or approximate an amount of specified Grade 4 - 10 length, weight or volume (capacity); e.g., construct a rectangle 1 with length 2 2 inches and width 3 inches, fill a measuring 3 cup to the 4 cup mark.

7. Make estimates for perimeter, area and volume using links, tiles, cubes and other models.

E. Tell time to the nearest minute. Grade 3 – 6 3. Tell time to the nearest minute and find elapsed time Grade 4 - 0 using a calendar or a clock.

Prepared by the Region 10 State Support Team – 8-9-10 6 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

Geometry and Spatial Sense Grades 3-4

Ohio Benchmarks Grades 3-4 Grade-Level Indicators Grade 3 Grade-Level Indicators Grade 4

A. Provide rationale for groupings and comparisons of 1. Analyze and describe properties of two-dimensional shapes 3. Identify similarities and differences of quadrilaterals; e.g., two-dimensional figures and three-dimensional objects. and three-dimensional objects using terms such as vertex, squares, rectangles, parallelograms and trapezoids. edge, angle, side and face. 4. Identify and define triangles based on angle measures Grade 3 – 6 (equiangular, right, acute and obtuse triangles) and side lengths Grade 4 - 5 (isosceles, equilateral and scalene triangles).

B. Describe and identify points, lines and planes in the 5. Describe points, lines and planes, and identify models in the environment. environment. Grade 4 - 6

C. Describe and identify intersecting, parallel and 1. Identify, describe and model intersecting, parallel and perpendicular lines or segments in the environment. perpendicular lines and line segments; e.g., use straws or other Grade 4 - 3 material to model lines.

D. Identify and draw right, obtuse, acute and straight 2. Identify and describe the relative size of angles with respect angles. to right angles as follows: a. Use physical models, like straws, to make different sized angles by opening and closing the sides, not by Grade 3 – 9 changing the side lengths. Grade 4 - 2 b. Identify, classify and draw right, acute, obtuse and straight angles.

E. Use attributes to describe, classify and sketch plane 1. Analyze and describe properties of two-dimensional shapes 2. Describe, classify, compare and model two- and three- figures and build solid objects. and three-dimensional objects using terms such as vertex, dimensional objects using their attributes. Grade 3 – 17 edge, angle, side and face. Grade 4 - 5 5. Build a three-dimensional model of an object composed of cubes; e.g., construct a model based on an illustration or actual object.

Prepared by the Region 10 State Support Team – 8-9-10 7 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

F. Develop definitions of classes of shapes. 3. Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids. Grade 4 - 5 4. Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles).

G. Find and name locations in coordinate systems. 3. Find and name locations on a labeled grid or coordinate 6. Specify locations and plot ordered pairs on a coordinate plane, system; e.g., a map or graph. using first quadrant points. Grade 3 – 8 Grade 4 - 5

H. Identify and describe line and rotational symmetry in 4. Draw lines of symmetry to verify symmetrical two-dimensional two-dimensional shapes and designs. shapes.

Grade 3 – 6 Grade 4 - 0

I. Describe, identify and model reflections, rotations and 7. Identify, describe and use reflections (flips), rotations (turns), and translations, using physical materials. translations (slides) in solving geometric problems; e.g., use Grade 4 - 2 transformations to determine if 2 shapes are congruent.

J. Describe a motion or series of transformations that 7. Identify, describe and use reflections (flips), rotations (turns), and show two shapes are congruent. translations (slides) in solving geometric problems; e.g., use Grade 4 - 4 transformations to determine if 2 shapes are congruent.

Prepared by the Region 10 State Support Team – 8-9-10 8 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

Patterns, Functions and Algebra Grades 3-4 Ohio Benchmarks Grades 3-4 Grade-Level Indicators Grade 3 Grade-Level Indicators Grade 4

A. Analyze and extend patterns, and describe the rule in 1. Extend multiplicative and growing patterns, and describe the 2. Represent and analyze patterns and functions using words, words. pattern or rule in words. tables and graphs. Grade 3 - 13 2. Analyze and replicate arithmetic sequences with and without a Grade 4 - 10 calculator.

B. Use patterns to make predictions, identify 3. Use patterns to make predictions, identify relationships, and 1. Use models and words to describe, extend and make relationships, and solve problems. solve problems. generalizations of patterns and relationships occurring in Grade 3 – 6 computation, numerical patterns, geometry, graphs and other Grade 4 - 8 applications.

C. Write and solve open sentences and explain 5. Write, solve and explain simple mathematical statements, such 5. Represent mathematical relationships with equations or strategies. as 7 + △ > 8 or inequalities. Grade 3 – 7 ∆ + 8 = 10. Grade 4 - 3 6. Express mathematical relationships as equations and inequalities.

D. Represent an unknown quantity as a variable using a 2. Represent and analyze patterns and functions using words, tables symbol, including letters. and graphs. Grade 3 – 4 Grade 4 - 2

E. Use variables to create and solve equations 4. Model problem situations using objects, pictures, tables, 4. Use rules and variables to describe patterns and other representing problem situations. numbers, letters and other symbols. relationships. Grade 3 – 7 Grade 4 - 4

F. Construct and use a table of values to solve problems 7. Create tables to record, organize and analyze data to discover 3. Construct a table of values to solve problems associated with a associated with mathematical relationships. patterns and rules. mathematical relationship. Grade 3 – 7 Grade 4 - 4

G. Describe how a change in one variable affects the 8. Identify and describe quantitative changes, especially those 6. Describe how a change in one variable affects the value of a value of a related variable. involving addition and subtraction; e.g., the height of water in a related variable; e.g., as one increases the other increases or as Grade 3 – 5 glass becoming 1 centimeter lower each week due to one increases the other decreases. Grade 4 - 6 evaporation.

Prepared by the Region 10 State Support Team – 8-9-10 9 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

Prepared by the Region 10 State Support Team – 8-9-10 10 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

Data Analysis & Probability Grades 3-4 Ohio Benchmarks Grades 3-4 Grade-Level Indicators Grade 3 Grade-Level Indicators Grade 4

A. Gather and organize data from surveys and classroom 1. Collect and organize data from an experiment, such as 1. Create a plan for collecting data for a specific purpose. experiments, including data collected over a period of recording and classifying observations or measurements, in time. response to a question posed. Grade 3 – 1 Grade 4 - 5

B. Read and interpret tables, charts, graphs (bar, picture, 4. Support a conclusion or prediction orally and in writing, using 2. Represent and interpret data using tables, bar graphs, line plots line, line plot), and timelines as sources of information, information in a table or graph. and line graphs. identify main idea, draw conclusions, and make predictions. 5. Match a set of data with a graphical representation of the data. 5. Propose and explain interpretations and predictions based on Grade 3 – 9 data displayed in tables, charts and graphs. Grade 4 - 9 7. Analyze and interpret information represented on a timeline.

C. Construct charts, tables and graphs to represent data, 6. Translate information freely among charts, tables, line plots, 2. Represent and interpret data using tables, bar graphs, line plots including picture graphs, bar graphs, line graphs, line picture graphs and bar graphs; e.g., create a bar graph from and line graphs. plots and simple Venn diagrams. the information in a chart. Grade 3 – 5 3. Interpret and construct Venn diagrams to sort and describe Grade 4 - 4 data. 4. Compare different representations of the same data to evaluate how well each representation shows important aspects of the data, and identify appropriate ways to display the data.

D. Read, interpret and construct graphs in which icons 2. Draw and interpret picture graphs in which a symbol or picture represent more than a single unit or intervals greater represents more than one object. than one; e.g., each  = 10 bicycles or the intervals on an axis are multiples of 10. 3. Read, interpret and construct bar graphs with intervals greater Grade 3 – 8 Grade 4 - 6 than one.

E. Describe data using mode, median and range. 8. Identify the mode of a data set and describe the information it 6. Describe the characteristics of a set of data based on a Grade 3 – 5 gives about a data set. graphical representation, such as range of the data, clumps of Grade 4 - 5 data, and holes in the data. 7. Identify the median of a set of data and describe what it indicates about the data.

8. Use range, median and mode to make comparisons among related sets of data.

Prepared by the Region 10 State Support Team – 8-9-10 11 Mathematics Indicator Analysis - Benchmark Band – Grades 3-4 Green – most frequently addressed indicators on the OAA Yellow – somewhat frequently addressed indicators on the OAA

F. Conduct a simple probability experiment and draw 9. Conduct a simple experiment or simulation of a simple event, 9. Conduct simple probability experiments and draw conclusions conclusions about the likelihood of possible outcomes. record the results in a chart, table or graph, and use the results from the results; e.g., rolling number cubes or drawing marbles Grade 3 -6 to draw conclusions about the likelihood of possible outcomes. from a bag. Grade 4 - 7 10. Represent the likelihood of possible outcomes for chance situations; e.g., probability of selecting a red marble from a bag containing 3 red and 5 white marbles.

11. Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain).

12. Place events in order of likelihood and use a diagram or appropriate language to compare the chance of each event occurring; e.g. impossible, unlikely, equal, likely, certain.

G. Identify and represent possible outcomes, such as 10. Use physical models, pictures, diagrams and lists to solve 13. List and count all possible combinations using one member from arrangements of a set of up to four members and problems involving possible arrangements or combinations of each of several sets, each containing 2 or 3 members; e.g., the possible combinations from several sets, each two to four objects. number of possible outfits from 3 shirts, 2 shorts, and 2 pairs of containing 2 or 3 members. shoes. Grade 3 – 3 Grade 4 - 3

H. Use the set of possible outcomes to describe and 10. Represent the likelihood of possible outcomes for chance predict events. situations; e.g., probability of selecting a red marble from a bag Grade 3 – 3 containing 3 red and 5 white marbles. Grade 4 - 2 11. Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain).

Prepared by the Region 10 State Support Team – 8-9-10 12