MATHEMATICS Grade 2 Standard: Number, Number Sense and Operations. Organizing Topic Benchmark Indicator Number and Number Systems

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1 Standard: Number, Number Sense and A. Use place value concepts to represent whole numbers using numerals, words and physical models. 1. Use place value concepts to represent, compare and order whole numbers using physical models, numerals and words with ones, tens, and hundreds. For example: Recognize 10 can mean 10 ones or a single entity (1 ten) through physical models and trading games Read and write 3-digit numerals (e.g., 243 as two hundred forty three, 24 tens and 3 ones, or 2 hundreds and 43 ones, etc.) and construct models to represent each. B. Recognize, classify, compare and order whole numbers. 2. Recognize and classify numbers as even or odd. C. Represent commonly used fractions using words and physical models. 5. Represent fractions (halves, thirds, fourths, sixths and eighths) using words, numerals and physical models: Recognize that a fractional part can mean different amounts depending on the original quantity. Recognize that a fractional part of a rectangle does not have to be shaded with contiguous parts. Identify and illustrate parts of a whole and parts of sets of objects. Compare and order physical models of halves, thirds, and fourths in relation to 0 and Represent and write the value of money using the sign and in decimal form when using the \$ sign. D. Determine the value of a collection of coins and dollar bills. E. Make change using coins for values up to one dollar. 3. Count money and make change using coins and a dollar bill. F. Count using numerals and ordinal numbers. No 2 nd Grade Indicators G. Model, represent and explain addition as combining sets and counting on. No 2 nd Grade Indicators

3 Standard: Measurement A. Explain the need for standard units of measure. No 2 nd Grade Indicators Measurement Units Measurement Units B. Select appropriate units for length, weight, volume (capacity) and time using: Objects (e.g., non-standard units) U.S. customary units: inch, foot, yard, ounce, pound, cup, quart, gallon, minute, hour, day, week and year Metric units: centimeter, meter, gram and liter C. Develop common referents for units of measure for length, weight, volume (capacity) and time to make comparisons and estimates. 1. Identify and utilize appropriate units of measure for: Length centimeters, meters, inches, feet, or yards Volume (capacity) liters, cups, pints, or quarts Weight grams, ounces or pounds Time hour, half-hours, quarter-hours, or minutes and time designations, a.m. or p.m. 2. Establish personal or common referents for units of measure to make estimates and comparisons (e.g., the width of a finger is a centimeter, a large bottle of soda pop is 2 liters, a small paper clip weighs about one gram. 4. Tell time to the nearest minute interval on digital and to the nearest 5 minute interval on analog (dial) timepieces. Use Measurement Techniques and Tools D. Apply measurement techniques to measure length, weight and volume (capacity). 4a. Tell time to the half hour and quarter hour using analog and digital clocks. (1 st grade Indicator) 5. Estimate and measure the length and weight of common objects, using metric and U.S. customary units, accurate to the nearest unit. 6. Select and use appropriate measurement tools (e.g., a ruler to draw a segment 3 inches long, a measuring cup to place 2 cups of rice in a bowl, a scale to weigh 50 grams of candy).

4 Standard: Measurement Measurement Units E. Recognize that using different units of measurement will yield different numbers for the same measurement. 3. Describe and compare the relationships among units of measure, such as centimeters and meters; inches, feet and yards; cups, pints and quarts; ounces and pounds; and hours, half-hours, and quarter-hours; (e.g., how many inches in a foot). Use Measurement Techniques and Tools 7. Make and test predictions about measurements, using different units to measure the same length or volume.

5 Standard: Geometry and Spatial Sense Characteristics and Properties A. Describe and create plane figures, circle, rectangle, square, triangle, hexagon, trapezoid, parallelogram and rhombus, and identify them in the environment. B. Describe solid objects; cube, rectangular prism, sphere, cylinder, cone and pyramid and identify them in the environment. 1. Identify, describe, compare, and sort three-dimensional objects (i.e. cubes, spheres, prisms, cones, cylinders and pyramids) according to the shape of the face or the numbers of faces, edges, or vertices. 2. Predict what new shapes will be formed by combining or cutting apart existing shapes. Spatial Relationships Characteristics and Properties Transformations and Symmetry C. Sort and compare two-dimensional objects and three dimensional objects according to their characteristics and properties. D. Identify, explain and model (superposition, copying) the concept of shapes being congruent and similar. 4. Identify and determine whether two-dimensional shapes are congruent (same shape and size) or similar (same shape different size) by copying or using superposition (lay one thing on top of another). 3. Recognize two-dimensional shapes and three-dimensional objects from different positions. No 2 nd Grade Indicators E. Recognize two- and three-dimensional objects from different positions. F. Describe location, using comparative (before, after), directional (above, below), and positional (first, last) words. G. Identify and draw figures with line symmetry. 5. Create and identify two-dimensional figures with line symmetry (e.g., what letter shapes, logos, polygons are symmetrical?)

6 Standard: Patterns, Functions and Algebra Use Patterns, Relations and Functions A. Sort, classify and order objects by size, number and other properties and describe the attributes used. No 2 nd Grade Indicators Use Patterns, Relations and Functions Use Patterns, Relations and Functions Use Algebraic Representations Use Algebraic Representations Use Algebraic Representations B. Extend sequences of sounds and shapes or simple number patterns and create and record similar patterns. 1. Extend simple number patterns (both repeating and growing patterns), and create similar patterns using different objects, such as using physical materials or shapes to represent numerical patterns. C. Create and extend patterns and describe the rule in words. 2. Use patterns to make generalizations and predictions; e.g., determine a missing element in a pattern. 3. Create new patterns with consistent rules or plans, and describe the rule or general plan of existing patterns. D. Model problem situations using objects, pictures, numbers, 4. Use objects, pictures, numbers and other symbols to and other symbols. represent a problem situation. E. Solve open sentences and explain strategies. 5. Recognize equivalence and extend the concept to situations involving symbols; e.g., 4+5=9 and 9=4+5 and 4+5=3+6= F. Represent an unknown quantity as a variable using a symbol. 5a. Compare numbers as greater than, less than, or equal to. 6. Use symbols to represent unknown quantities and identify values for symbols in an expression or equation using addition and subtraction; e.g., _ + 1 = 10, _ -2 = 4. Analyze Change G. Describe and compare qualitative and quantitative change. 7. Describe qualitative and quantitative changes, especially those involving addition and subtraction; e.g., a student growing taller versus a student growing two inches in one year.

7 STANDARD: Data Analysis and Probability Data Collection A. Pose questions and gather data about everyday situations 1. Propose questions, use observations, interviews and and familiar objects. surveys to collect data, and organize data in charts, picture graphs and bar graphs. Statistical Methods Data Collection Statistical Methods Data Collection Statistical Methods Probability B. Sort and classify objects by attributes and organize data into categories in a simple table or chart. C. Represent data using objects, picture graphs and bar graphs. D. Describe the probability of chance events as more, less or equally likely to occur. 6. Recognize that data may vary from one population to another; e.g., favorite TV shows of students and of parents. 1. Propose questions, use observations, interviews and surveys to collect data, and organize data in charts, picture graphs and bar graphs. 4. Write a few sentences to describe and compare categories of data represented in a chart or graph, and make statements about the data as a whole. 2. Read, interpret and make comparisons and predictions from data represented in charts, line plots picture graphs and bar graphs. 3. Read and construct simple timelines to sequence events. 5. Identify untrue or inappropriate statements about a given set of data. 7. List some of the possible outcomes of a simple experiment, and predict whether given outcomes are more, less or equally likely to occur. 8. Use physical models and pictures to represent possible arrangements of 2 or 3 objects.

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