PAN-ASIA MATHEMATICS:  GRADE 3

Number Sense and Operations:

Standard One: Students will engage in problem solving, communicating, reasoning, connecting and representing.

Benchmarks:

1. Exhibit an understanding of the base ten number system.
2. Mentally add or subtract 10 or 20 from a number.
3. Know factors of 100.
4. Use knowledge of the factors of 100 to understand the structure of multiples.
5. Use knowledge of factors of 100 to understand the structure of 1000.
6. Estimate quantities up to 1000.
7. Use landmark numbers to calculate “distances” within 1000.
8. Read and write numbers in the hundreds and thousands.
9. Represent, order, and compare numbers.
10. Use landmark numbers to combine and compare quantities.
11. Combine and compare 3-digit numbers and totals to 1000.
12. Demonstrate an understanding of fractions as parts of wholes.
13. Describe in simple terms the relationships among commonly used factors and their multiples.
14. Know that fractional parts must be equal.
15. Understand the relationship between fractions and division.
16. Select, use, and explain models to relate common fractions and mixed numbers, find equivalent fractions, and order fractions.
17. Use conventional fraction words and notation.
18. Group unit fractions that have a numerator of 1.
19. Know common equivalents, especially relationships among halves, thirds, and sixths.
20. Relate notation for common fractions (1/2,1/4,3/4,1/5,1/10) to notation for decimals on the calculator (0.5,0.25,0.75,0.2,0.1).
21. Recognize classes to which a number may belong, and identify the numbers in those classes; use these in the solution of problems.
22. Explore numbers that can be divided evenly.
23. Select, use, and explain the various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations.
24. Understand that the operation of multiplication is adding equal groups.
25. Recognize the connection between skip counting, grouping, and multiplication.
26. Find factors of numbers using factor pairs.
27. Demonstrate understanding of the relationship between multiplication and division.
28. Identify whether word problems can be solved by using multiplication or division.
29. Use knowledge of factors and multiples to solve multiplications and division problems.
30. Select, use, and explain the commutative, associative, and identity properties of operations in whole number problem situations.
31. Examine how parts and wholes are related in addition and subtraction.
32. Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.
33. Solve addition problems that have multiple addends.
34. Have more than one way to solve a computation problem and use one method to check another.
35. Know multiplication facts through 11 times 11.
36. Add, subtract and multiply accurately and efficiently.
37. Solve combining and comparing problems with numerical strategies and record solutions using standard addition and subtraction notation.
38. Use different notations for the same problem.

Geometry

Measurement

Data Analysis, Statistics and Probability

Discussion, Presentation, Composition

Data Analysis, Statistics, and Probability

Standard One: Students will engage in problem solving, communicating, reasoning, connecting and representing as they:

Benchmarks:

• 1.1 Formulate questions, collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.
• 1.2 Interpret and pose questions about data collected.
• 1.3 Construct, draw conclusions and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line plots, and tallies.
• 1.4 Describe the shape of the data and analyze it for patterns.
• 1.5 Examine a set of data to determine what is typical.
• 1.6 Represent data on a line plot.
• 1.7 Classify outcomes as likely or unlikely.
• 1.8 Predict the likelihood of outcomes.

Geometry

Standard Two: Students will engage in problem solving, communicating, reasoning, connecting and representing as they:

Benchmarks:

• 2.1 Compare and analyze attributes and other features of 2-D and 3-D shapes.
• 2.2 Analyze how shapes are the same and how they are different.
• 2.3 Visualize how components of shapes are put together to form whole shapes.
• 2.4 Describe, compare, and represent 2-D shapes. 
• 2.5 Compare the areas of two shapes.
• 2.6 Explore relationships among shapes.
• 2.7 Estimate and measure the perimeters of various figures.
• 2.8 Describe, model, compare and classify 2-D and 3-D shapes.
• 2.9 Understand that shapes can be oriented in space without losing their properties.
• 2.10 Estimate and measure turn.
• 2.11 Understand turn as a change in orientations.
• 2.12 Identify common measurement for turns—degrees—and understand that there are 360 degrees in one full turn, 180 degrees in a half-turn and 90 degrees in a quarter turn.
• 2.13 Name turns, or angles, as acute, right, or obtuse.
• 2.14 Describe paths.
• 2.15 Describe a path using mathematical ideas and language e.g., intersecting, parallel and perpendicular lines.
• 2.16 Describe and apply techniques such as reflections, rotations, and translations for determining if two shapes are congruent.
• 2.17 Describe physical motions precisely as a series of slides, flips, and turns.
• 2.18 Compare shapes to determine congruence through motions such as rotations (turns) and reflections (flips).
• 2.19 Relate geometric ideas to number.
• 2.20 Measure area by covering a flat surface with square units.
• 2.21 Compare areas of rectangles that have different dimensions.
• 2.22 Understand the structure of a rectangular prism as arrays of cubes.
• 2.23 Design patterns for boxes that will hold a given number of cubes.
• 2.24 Identify symmetry in 2-D shapes.

Measurement

Standard Three: Students will engage in problem solving, communicating, reasoning, connecting and representing as they:

Benchmarks:

• 3.1 Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute.
• 3.2 Use a nonstandard unit to measure distance.
• 3.3 Compare the effects of measurement using different sizes.
• 3.4 Measure weight using a pan balance.
• 3.5 Determine volume of rectangular prisms.
• 3.6 Carry out simple unit conversions within a system of measurement.
• 3.7 Understand and use important equivalencies of time, money, and linear measurement.
• 3.8 Identify time…compute elapsed time and use a calendar.
• 3.9 Use the calendar as a tool for problem solving.
• 3.10 Estimate and find area and perimeter of a rectangle, triangle, or irregular shape, models, grids or by measuring.
• 3.11 Measure area by covering a flat surface with square units.
• 3.12 Compare area of rectangles that have different dimensions.
• 3.13 Compare the area of two shapes and explore the relationship between them.
• 3.14 Find the area of complex shapes by identifying smaller units of area (e.g. square and half units)
• 3.15 Estimate and measure the perimeters of various figures.
• 3.16 Identify and use appropriate metric and English units and tools to estimate, measure, and solve problems involving length and area.
• 3.17 Use standard measures in complex situations.

Number Sense and Operations

Standard Four: Students will engage in problem solving, communicating, reasoning, connecting and representing as they:

Benchmarks:

• 4.1Exhibit an understanding of the base ten number system.
• 4.2Mentally add or subtract 10 or 20 from a number.
• 4.3Know factors of 100.
• 4.4Use knowledge of the factors of 100 to understand the structure of multiples.
• 4.5Use knowledge of factors of 100 to understand the structure of 1000.
• 4.6Estimate quantities up to 1000.
• 4.7Use landmark numbers to calculate “distances” within 1000.
• 4.8Read and write numbers in the hundreds and thousands.
• 4.9Represent, order, and compare numbers.
• 4.10Use landmark numbers to combine and compare quantities.
• 4.11Combine and compare 3-digit numbers and totals to 1000.
• 4.12Demonstrate an understanding of fractions as parts of wholes.
• 4.13Describe in simple terms the relationships among commonly used factors and their multiples.
• 4.14Know that fractional parts must be equal.
• 4.15Understand the relationship between fractions and division.
• 4.16Select, use, and explain models to relate common fractions and mixed numbers, find equivalent fractions, and order fractions.
• 4.17Use conventional fraction words and notation.
• 4.18Group unit fractions that have a numerator of 1.
• 4.19Know common equivalents, especially relationships among halves, thirds, and sixths.
• 4.20Relate notation for common fractions (1/2,1/4,3/4,1/5,1/10) to notation for decimals on the calculator (0.5,0.25,0.75,0.2,0.1).
• 4.21Recognize classes to which a number may belong, and identify the numbers in those classes; use these in the solution of problems.
• 4.22Explore numbers that can be divided evenly.
• 4.23Select, use, and explain the various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations.
• 4.24Understand that the operation of multiplication is adding equal groups.
• 4.25Recognize the connection between skip counting, grouping, and multiplication.
• 4.26Find factors of numbers using factor pairs.
• 4.27Demonstrate understanding of the relationship between multiplication and division.
• 4.28Identify whether word problems can be solved by using multiplication or division.
• 4.29Use knowledge of factors and multiples to solve multiplications and division problems.
• 4.30Select, use, and explain the commutative, associative, and identity properties of operations in whole number problem situations.
• 4.31Examine how parts and wholes are related in addition and subtraction.
• 4.32Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.
• 4.33Solve addition problems that have multiple addends.
• 4.34Have more than one way to solve a computation problem and use one method to check another.
• 4.35Know multiplication facts through 11 times 11.
• 4.36Add, subtract and multiply accurately and efficiently.
• 4.37Solve combining and comparing problems with numerical strategies and record solutions using standard addition and subtraction notation.
• 4.38Use different notations for the same problem.

Discussion, Presentation and Composition

Benchmarks:

• 5.1 Use agreed upon rules to participate in large and small group discussions.
• 5.2 Express ideas in an organized way.
• 5.3 Explain their mathematical thinking in writing.
• 5.4 Maintain a system for collecting, referring to, and sharing their work.