Pennsylvania Content Standards Grade Level Benchmarks 2.1 Numbers, Number Systems and Number Relationships

Transcription

1 2.1 Numbers, Number Systems and Number Relationships A. Count using whole numbers A. Count using whole numbers A. Count using whole numbers (to (to 100) by ones and tens (Rote (to 100) by 1 s, 2 s, 5 s and 1,000) by 1 s, 2 s, 3 s, 5 s, 10 s, counting). 10 s. 25 s and 100 s. A. Count using whole numbers (to 20) by ones. (Rote counting) A. Count using whole numbers (to 10,000) and by 2s, 3s, 5s, 10s, 25s, and 100s. Count backwards from 5 to 0. Count back-wards from 10 to 0. Count backwards from 20 to 0. B. Use concrete objects to represent quantities up to and including 10. (I ll show you 5 you match it.) B. Use concrete objects to represent quantities up to and including 20. B. Use concrete objects (a set) into equal parts using terms whole, half, third and quarter. B. Using concrete objects to identify a mixed number as a whole and parts. B. Use whole numbers and fractions to represent quantities. Divide concrete objects (a set) into two equal parts (fair share). Use terms part and whole. Divide concrete objects (a set) into equal parts (fair share) using terms whole, part and one-half. C. Represent equivalent forms of the same number through the use of concrete objects and drawings up to and including 5. C. Represent equivalent forms of the same number through the use of concrete objects and drawings up to and including 20. C. Represent equivalent forms of a whole number using concrete objects, drawings and word names C. Represent equivalent forms of a whole number using concrete objects, drawings and word names. C. Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols. D. Divide concrete objects (a set) into two equal parts (fair share). Use terms part and whole. D. Use drawings, diagrams or models to show the concept of fraction as part of a whole (1/2). D. Use drawings, diagrams or models to show the concept of fraction as part of a whole (1/3, ¼). D. Use drawings, diagrams or models to show the concept of fraction as part of a whole (1/6, 1/8). D. Use drawings, diagrams or models to show the concept of fraction as part of a whole. E. Sort all coins. E. Identify and name penny, nickel and dime. E. Name and state the value (cent sign) of a penny, nickel, dime and quarter. E. Count, compare and make change using a collection of coins up to one dollar. E. Count, compare and make change using a collection of coins and one-dollar bills. Count a given amount of Count a given amount of money. Record total money up to one-dollar using decimal, dollar and

2 money up to one-dollar cent sign. using pennies, nickels and dimes. Record using cent sign. F. Compare sets of objects up to and including 10 using terms more than, less than, same. F. Compare numbers up to 20 and label more than or less than. F. Identify and explain pattern on a number board. F. Identify odd and even numbers on the hundred s board. F. Apply number patterns (even and odd) and compare values of numbers on the hundred board. G. Use concrete objects to count, order and group up to and including 5. H. Use concrete objects to demonstrate under-standing of one-to-one correspondence up to and including 5. I. Identify the numbers 0 to 5. G. Use concrete objects to count, order and group up to and including 10. H. Using concrete objects to demonstrate understanding of one-to one correspondence up to and including 10. I. Identify the numbers 0 to 20 and write numbers 0 to 10. G. Use concrete objects to count, order and group up to 100. H. Demonstrate understanding of one-to-one correspondence. I. Identify the numbers 0 to 20 and write numbers 0 to 10. G. Use concrete objects to count, order and group up to H. Demonstrate understanding of one-to-one correspondence. I. Demonstrate an understanding of place-value using base 10 blocks to 1,000. Write numbers in standard and expanded form with place values depicting 1 s, 10 s and 100 s. G. Use concrete objects to count, order and group. H. Demonstrate understanding of one-to-one correspondence. I. Apply place-value concepts and numeration to counting, ordering and grouping. J. Estimate quantities to 10. J. Estimate quantities to 10. J. Estimate quantities to 20. J. Estimate quantities to the nearest 10 s and 100 s places. Round numbers to the nearest 10. J. Estimate, approximate, round or use exact numbers as appropriate. K. Write a number family which includes two addition and two subtraction number sentences. K. Describe the inverse relationship between addition and subtraction. L. Add and subtract two-digit numbers mentally without K. Describe the inverse relationship between addition and subtraction.

3 regrouping. L. Demonstrate knowledge of basic facts in four basic operations. 2.2 Computation and Estimation A. Use concrete objects to show A. Determine the sum of 2 or 3 A. Apply addition and joining (addition) of groups addends to 20 by using subtraction in everyday (sets) in quantities up to and manipulatives, drawing situations using concrete including 5. pictures, and writing number objects. sentences. A. Use concrete objects to show joining (addition) of groups (sets) in quantities up to and including 5. A. Apply addition and subtraction situations using concrete objects. Use concrete objects to show separating (subtraction) a group (set) in quantities up to and including 5. B. Use concrete objects to show separating (subtraction) a group (set) in quantities up to and including 5. Calculate the difference of any two numbers to 20 without regrouping by using manipulatives, drawing pictures, and writing number sentences. B. Use concrete objects to show joining (addition) of groups (sets) in quantities up to and including 5. Use concrete objects to show separating (subtraction) a group (set) in quantities up to and including 5. (Corresponds to Standard A.) B. Use concrete objects to show joining (addition) of groups (sets) in quantities up to and including 20. Use concrete objects to show separating (subtraction) a group (set) in quantities up to and including 5 (corresponds to Standard A). B. Determine the sum of 2 or 3 addends to 20 by using manipulatives, drawing pictures, and writing number sentences. Calculate the difference of any two numbers to 18 without regrouping by using manipula-tives, drawing pictures, and writing number sentences (corresponds to Standard A). B. Add 3 two-digit numbers with and without regrouping. Subtract two-digit numbers with and without renaming. B. Solve single and double- digit addition and subtraction problems with regrouping in vertical form. C. Rote count using whole numbers (to 100) by ones and tens. (Corresponds to C. Count using whole numbers (to 100) by 1 s, 2 s, 5 s and 10 s. (Corresponds with Standard A.) C. Use concrete object to demonstrate concept of repeated addition. C. Demonstrate concept of multiplication as repeated addition and arrays. Berks County Intermediate Unit Standard A.) Mathematics Benchmarks Grades Pre-K - 3

4 Standard A.) D. Make estimates of objects in a set up to and including 10 and verify. D. Using concrete objects use the concept of repeated subtraction. D. Demonstrate concept of division as repeated subtraction and as sharing. E. Orally state a reason for guesses. E. Make estimates of objects in a set up to and including 20 and verify. E. Make estimates of objects in a set up to and including 50 and verify. E. Use rounding to the nearest 10 to estimate answers. E. Use estimation skills to arrive at conclusions. F. Rote count using whole numbers to 20 by ones. (Corresponds to Standard A and B.) F. Orally state a reason for guesses. F. Orally or in writing state a reason for an estimation. F. Use estimation to determine reasonableness of answers to addition and subtraction problems up to 1,000. F. Determine the reasonableness of calculated answers. G. Rote count using whole numbers to 20 by ones. (Corresponds to Standard A.) G. Using manipulatives demonstrate and orally explain single-digit addition of sums to 10. G. Orally or in writing explain and describe the computation process in addition and subtraction. G. Orally or in writing explain and describe the computation process in regrouping. G. Explain addition and subtraction algorithms with regrouping. 2.3 Measurement and Estimation A. Compare measurable A. Compare measurable A. Compare measurable characteristics of different characteristics of different characteristics of different objects (temperature, length, objects on the same objects on the same dimensions weight) using the words dimensions (time, (time, temperature, area, length, longer, shorter, hotter, colder, temperature, length, weight). weight, perimeter). heavier, lighter and the same. A. Use non-standard items to measure objects (e.g., hands, shoe lengths). A. Compare measurable characteristics of different objects on the same dimensions (time, temperature, area, length, weight, capacity, perimeter). B. Determine the measurement of

5 B. Determine the length and B. Measure and record the length height of objects with nonstandard of familiar objects to the units. (e.g., hands, nearest inch or centimeter shoe lengths, jelly beans). B. Identify measurable characteristics of different objects (temperature, length, weight). C. Name and order the 4 seasons and days of the week. C. Name and order the months of the year, locate and report the date (including month, day and year) on a calendar, and identify yesterday s, today s and tomorrow s date. B. Measure and record the length, temperature and weight of familiar object to the nearest 1/2, cm, 5 s, pound or kilogram C. Project the date(s) for the following week. objects with non-standard and standard (e.g., US customary and metric) units. C. Determine and compare elapsed times. E. Measure perimeter using nonstandard units (walk hallway, room). F. Using concrete objects to represent non-standard units, estimate the measurements up to 5 units. G. Order time events using terms morning, afternoon and night. H. Identify different attributes of objects (e.g., smaller, larger, size, shape). D. Tell time (analog) to the hour. E. Compare objects using terms same, longer, shorter, heavier and lighter. F. Measure perimeter using nonstandard units (walk hall-way, room, play-ground, gymnasium, classroom). G. Using concrete objects to represent non-standard units, estimate the measurements up to 20 units. H. Identify different attributes of objects (e.g., color, shape, size). D. Tell time to the nearest hour and half-hour using analog and digital clocks. E. Compare objects using terms same, longer, shorter, heavier, lighter, warmer, colder, wider, narrower and degrees of volume. F. Use concrete objects to determine perimeter. G. Estimate and measure familiar objects to nearest foot. H. Describe the various attributes of an object and identify how it can be measured (e.g., temperature, length, weight). D. Read and represent time to the nearest half-hour and in 5- minute intervals. E. Choose an appropriate unit of measurement. F. Use concrete objects to determine area and perimeter. G. Estimate and measure objects to the nearest inch or centimeter. H. Describe the different attributes of an object and how it can be measured (e.g., time, temperature, area, length, weight, perimeter). D. Tell time (analog and digital) to the minute. E. Determine appropriate unit of measure. F. Use concrete objects to determine area and perimeter. G. Estimate and verify measurements. H. Demonstrate that a single object has different attributes that can be measured in different ways (e.g. length, mass/ weight, time, area, temperature, capacity and perimeter).

6 2.4 Mathematical Reasoning and Connections A. Verify predictions about A. Verify predictions about A. Verify and explain predictions quantity, size, and shape of quantity, size, and shape of about quantity, size, and shape objects by using concrete objects by drawing pictures. of objects. objects. A. Use terms relating to quantity (more/less) and size (smaller/larger/ shorter/longer) to describe basic shapes (square/circle/rectangle/ triangle). A. Make, check and verify predictions about the quantity, size and shape of objects and groups of objects. B. Use nonstandard units to measure in everyday situations. B. Use measurement in everyday situations to measure to the nearest inch, centimeter. B. Use measurement in everyday situations to measure to the nearest pd/kg, 5, 1/2. B. Use measurements to determine the geography of the school building.

7 2.5 Mathematical Problem Solving and Communication A. Use appropriate problemsolving A. Use appropriate problem A. Select appropriate problem strategies (e.g., role- solving strategies (e.g., pictures, solving strategy (e.g., guess and play, making or using pictures) guess and check) to solve check, working backwards) to to solve a problem in the problem. solve problem. environment. A. Solve problems using concrete objects. (Corresponds to Standard A). A. Use appropriate problem solving strategies such as guess and check and working backwards. B. Solve a problem in their environment using role- play and/or concrete objects. B. Identify what information is needed to solve a problem. B. Describe what information is needed to solve a problem through the use of pictures and manipulatives. B. Describe what information is needed to solve a problem. B. Determine when sufficient information is present to solve a problem and explain how to solve a problem. C. Tell others how to solve a problem that occurred. C. Select concrete material to solve a problem. C. Select and use an appropriate method, materials, and strategy to solve problems using concrete objects or mental math. C. Select and use an appropriate method, materials, and strategy to solve equations using mental math, paper and pencil, or concrete objects. C. Select and use an appropriate method, materials and strategy to solve problems, including mental mathematics, paper and pencil, and concrete objects. 2.6 Statistics and Data Analysis A. Gather, organize, sort, count A. Gather, organize and display and display data using pictures, data using pictures, tallies, given the framework for a bar charts, bar graphs, and graph. pictographs. A. Gather, organize, sort, count and display data to form a pictograph. A. Gather, organize, and display real life data on a bar graph and/or pictograph using the terms most, least, same, highest, lowest, more than, and fewer than. A. Gather, organize and display data using pictures, tallies, charts, bar graphs, and pictographs.

8 B. Tell about the data presented in the pictograph. B. Using manipulatives, describe the data presented in a bar graph or pictograph. B. Describe data on a given graph. B. Answer questions based on data from graphs. B. Formulate and answer questions based on data shown on graphs. C. Use a chart that displays an event and guess what will happen next (e.g., birthdays, weather, holidays, weekends). C. Use a chart that displays data and predict what will occur (e.g., milk count, temperature). C. Use a chart or table that displays data over time and predict what will occur. C. Use a chart or table that displays data over time and predict what conditions will change the data. C. Predict the likely number of times a condition will occur based on the analyzed data. D. Tell about the data presented in the pictograph. (Corresponds to Standard A). D. State an opinion on whether a given statement is reasonable. D. State an opinion on whether a given statement is reasonable based on a comparison of data using the terms most, least, same, highest, lowest, more than, and fewer than. D. State an opinion on whether a given statement is reasonable based on a comparison to data. D. Form and justify an opinion on whether a given statement is reasonable based on a comparison to data. 2.7 Probability and Predictions A. Predict the likelihood of events. A. State and explain the likelihood A. Predict the likelihood of an A. Predict and measure the of a chance event using the event and verify the prediction. likelihood of events and terms likely, unlikely, or recognize that the results of an certain. experiment may not match predicted outcomes. B. Predict the likelihood of common, everyday events (e.g., what is the likelihood that it will rain in our classroom today?). B. Identify a spinner which if fair or unfair B. Identify a spinner which is fair or unfair and explain why. B. Design a fair and an unfair spinner. C. Tell some possible results from an experiment. C. List or draw possible results of an experiment. C. List and explain the possible results of an experiment. C. Describe the possible results of an experiment. C. List or graph the possible results of an experiment.

9 D. Collect and describe data using D. Analyze data using the D. Collect and describe data using concepts of largest, smallest, most often, least often. concepts of largest, smallest, most often, least often, and middle. concepts of largest, smallest, most often, least often and middle. 2.8 Algebra and Functions A. Identify, describe, extend A. Identify, describe, and extend A. Identify, describe, extend, and patterns based upon shape, size, patterns based on shape, size, replicate patterns based on color or sound using concrete color or sound using concrete shape, size, color or sound. objects. objects. A. Identify a pattern based upon shape, size, color or sound using concrete objects. A. Recognize, describe, extend, create and replicate a variety of patterns including attribute, activity, number and geometric patterns. B. Use concrete objects to model the events in a number story. B. Use concrete objects and trial and error to represent a number story. B. Use concrete objects and symbols (+, -, =) to create number sentences. B. Solve number sentences using concrete objects and symbols (+, -, =). B. Use concrete objects and trial and error to solve number sentences and check if solutions are sensible and accurate.) C. Use concrete objects to show a missing addend. D. Describe or draw a simple story problem. C. Use manipulatives to determine a missing addend in a number sentence in which the sum is 10 or less. D. Create a simple story problem using concrete objects or pictures. C. Use manipulatives to determine a missing addend in a number sentence in which the sum is 20 or less. D. Create and solve story problems using number sentences and pictures. C. Use manipulatives to determine a missing addend in a number sentence. D. Demonstrate, solve, and describe story problems using addition or subtraction equations. C. Substitute a missing addend in a number sentence. D. Create a story to match a given combination of symbols and numbers.) E. Use concrete objects to show equal and not equal. E. Use concrete objects to show equal and not equal. E. Use concrete objects to show the concepts of variable and inequalities. E. Use concrete objects to show the concepts of variables, equations, and inequalities. F. Describe the meaning of solutions and symbols. E. Use concrete objects and symbols to model the concepts of variables, expressions, equations, and inequalities. F. Explain the meaning of solutions and symbols.

10 G. Gather, sort and display data to form pictorgraph. G. Gather, sort count, and display data using a pictograph. G. Read, organize and compare data on a bar graph and/or pictograph using the following vocabulary: most, least, same, highest, lowest, more than, fewer than. G. Organize and compare data using bar graphs, tallies, and/or pictographs. G. Gather information and display it in the form of a table or a chart. H. Identify data shown in tables and charts. H. Identify data shown in tables and charts. H. Identify data shown in tables and charts. H. Identify and interpret data shown in tables and charts. H. Describe and interpret the data shown in tables and charts. I. Use concrete objects to demonstrate function rule (e.g., input output). I. Demonstrate simple function rules. J. Locate points on a simple grid. J. Analyze simple functions and relationships and locate points on a simple grid. 2.9 Geometry A. Identify two- dimensional A. Identify and label twodimensional A. Identify and label two- geometric shapes using concrete shapes dimensional shapes. objects (e.g., pattern blocks). A. Find circle, square, triangle and rectangle in real life A. Name and label geometric shapes in two and three dimensions (circle/sphere, square/cube, triangle/ pyramid, rectangle/prism.

11 B. Make shapes using concrete objects using pipe cleaners, straws, blocks, clay, wikki sticks. B. Construct two-dimensional geometric shapes using concrete objects (e.g., geoboard). B. Construct and reproduce a twodimensional shape (e.g., geoboard, dot paper). B. Construct and reproduce a twodimensional shape (e.g., geoboard, dot paper). B. Build geometric shapes using concrete objects (e.g., manipulatives). C. Draw a circle, triangle and square. C. Draw two-dimensional geometric shapes (e.g., hexagon, rhombus). C. Draw two-dimensional geometric shapes (e.g., hexagon, rhombus). C. Draw two and three dimensional geometric shapes and construct rectangles, squares and triangles on the geoboard and on graph paper satisfying specific criteria. D. Identify common twodimensional geometric shapes (e.g., circle, square, triangle and rectangle) using concrete objects. E. Use geometric shapes (e.g., cubes, blocks and other 3-D materials) to build objects. D. Find and name twodimensional geometric figures in real life. D. Name and describe twodimensional geometric figures in real life. D. Name and describe twodimensional geometric figures in real life. D. Find and describe geometric figures in real life. E. Identify and draw lines of symmetry in geometric figures. F. Identify symmetry in nature. G. Fold paper to demonstrate the reflection about a line. H. Show relationships between and among figures using reflections. I. Predict how shapes can be changed by combining or dividing them. I. Use concrete objects to create new shapes. I. Use concrete objects to create new shapes. I. Combine shapes to create new shapes by using concrete objects or drawings. I. Combine shapes to create new shapes by using concrete objects or drawings.

12 2.10 Trigonometry A. Construct angles from straight A. Identify the number of sides and A. Identify and give examples of lines using wikki sticks and pipe angles in a square, triangle, and right angles in real life objects. cleaners. rectangle. A. Identify angles (corners) and lines in the environment. A. Identify right angles in the environment. B. Construct angles and triangles from straight line using wikki sticks, pipe cleaners, straws. B. Construct right angles and right triangles from straight lines using wikki sticks, pipe cleaners, straws. B. Model right angles and right triangles using concrete objects. B. Model right angles and right triangles using concrete objects.

13 2.11 Concepts of Calculus A. Order whole numbers from A. Order whole numbers from least to greatest value 0 to 20. least to greatest to 1,000. A. Identify least and greatest quantities using concrete objects. A. Order whole numbers from least to greatest between 1 and 100. A. Identify whole number quantities and measurements from least to most and greatest value. B. Identify least and greatest in a pictograph. B. Identify least and greatest values represented in a bar graph or a pictograph up to and including 20. B. Identify least and greatest values represented in bar graphs and pictographs. B. Identify least and greatest values represented in bar graphs and pictographs. B. Identify least and greatest values represented in bar graphs and pictographs. C. Given situations, identify which is faster or slower. C. Identify faster and slower situations that occur in real life. C. Describe rates of change as faster and slower using real life situations. C. Categorize rates of change as faster and slower. C. Categorize rates of change as faster and slower. D. Identify a pattern of objects or shapes. (Corresponds with Standard A.) D. Identify a pattern of numbers, shapes or objects (corresponds to Standard A). D. Identify a pattern of numbers or objects and continue the pattern (corresponds to Standard A). D. Identify and extend a pattern of numbers or objects (corresponds to Standard A). D. Continue a pattern of numbers or objects that could be extended infinitely.