STRAND: PROBLEM SOLVING A. NONROUTINE PROBLEMS. 1. Solve nonroutine problems using the following problem-solving strategies.

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1 STRAND: PROBLEM SOLVING A. NONROUTINE PROBLEMS 1. Solve nonroutine problems using the following problem-solving strategies. Understanding the Problem < Dramatize the problem situation. < Use manipulatives or real objects to represent ideas. < Interpret pictures. < Interpret diagrams. < Ask questions. < Draw a diagram. < Rephrase the problem in your own words. < Identify wanted and given information. < Identify key words. Designing a Plan < Dramatize < Model the problem with manipulatives. < Choose an operation. < Draw a picture or diagram. < Collect and organize data. < Symbolize the problem with a number sentence. < Look for a pattern. < Guess and check. Implementing the Plan < Use counting to find a solution. < Apply the appropriate operation.

2 < Solve a number sentence. < Continue a pattern. < Guess and check. Evaluating the Response < State the answer to the problem in a complete sentence. < Tell how the solution to the problem was obtained. < Relate the answer to the problem. < Review and discuss the problem-solving process. < Show that the answer is reasonable. < Create similar problems. < Look for the possibility of more than one solution. 2. Classify objects in sets according to specific attributes. 3. Recognize, copy, extend, and create patterns. 4. Model patterns from one medium to another (auditory, visual, kinesthetic). B. STORY PROBLEMS (Oral, Written, Visual) 1. Use problem-solving strategies to find a solution to a story problem. 2. Name the operations (+, -, x, )) necessary to solve a one-step or multi-step story problem. 3. Write and solve a number sentence(s) for both one-

3 and two-step story problems. 4. Identify unnecessary information in a given story problem. 5. Supply the missing information necessary to solve a story problem. 6. Create story problems. 7. Write questions for story problems. 8. Write story problems based on a given number sentence or given numbers. STRAND: NUMBER CONCEPTS AND SKILLS A. NUMERATION 1. Match two sets of objects in a one-to-many, many-toone, and many-to-many correspondence. 2. Name and print any four-digit number that has been modeled concretely and pictorially. 3. Model any four-digit number using concrete materials. 4. Print the symbols of numbers from 0 to 9999 when given orally. 5. State the names of the numerals from 0 to 9999 when printed symbolically.

4 6. Read the names and print the symbols for numbers from 0 to 1000 when written in words. 7. Rote count forward and backward using any starting and ending point less than 10, Count and name the number of objects in any set less than 10, Identify the ones, tens, and hundreds and thousands place value in any four-digit number. 10. Identify the number of thousands, the number of hundreds, the number of tens, and the number of ones in any four-digit number. 11. Rename any four-digit number, using various combinations of thousands, hundreds, tens and ones. 12. Rewrite any four-digit number using expanded notation. 13. Name and print the number one more and one less, or ten more and ten less, or one hundred more and one hundred less, or one thousand more and one thousands less before or after a given number less than 10, Compare any two numbers less than 10,000 as greater than, less than, or equal to. 15. Round off a number to the nearest 10 and the nearest 100.

5 16. Estimate the number of objects in a given set based on real-life experiences. 17. Skip count by 2s, 3s, 4s, 5s, 10s, 100s, 1000s, using any starting point and ending point less than 10,000. B. ORDINAL NUMBERS 1. Order sets of objects or events, using appropriate vocabulary. 2. Assign ordinal values to objects or events up to thirty-first. C. FRACTIONAL NUMBERS 1. Demonstrate the concept of fraction as part of a whole for the proper fractions of halves, thirds, fourths, fifths, and tenths concretely and pictorially. 2. Demonstrate the concept of fraction as part of a set for the proper fractions of halves, thirds, fourths, fifths, and tenths concretely and pictorially. 3. Match the symbols to concrete and pictorial representation of fractions. 4. Compare and order proper fractions of like denominators. 5 Relate the concept of a fractional number to a decimal number for tenths. D. OPERATIONS AND PROPERTIES (Addition and

6 Subtraction with Whole Numbers) 1. Illustrate the meaning of additive subtraction concretely and pictorially. 2. Symbolize addition and subtraction using both horizontal and vertical notation and to use correct mathematical language. 3. Add and subtract two three-digit numbers without regrouping. 4. Add and subtract two three-digit numbers with regrouping. 5. Estimate sums and differences. 6. Recognize that addition and subtraction are inverse operations. 7. Recall from memory with proficiency the basic addition and subtraction facts when the sum or minuend can be up Demonstrate the mathematical properties of order (commutativity), grouping (associativity), and zero (additive identity) as they apply addition. E. OPERATIONS AND PROPERTIES (Multiplication and Division with Whole Numbers) 1. Illustrate the meaning of multiplication as repeated addition and rectangular arrays concretely and pictorially.

7 2. Symbolize multiplication using the sign and use correct mathematical language. 3. Multiply one-digit numbers whose product is less than or equal Illustrate the meaning of division as repeated subtraction and sharing concretely and pictorially. 5. Symbolize division using the sign and use correct mathematical language. 6. Divide a two-digit number (dividend) less than or equal 81 by a one-digit divisor without remainders. 7. Recall from memory the basic multiplication and division facts when the product or dividend is less than or equal Multiply one-digit numbers by 10 and multiples of Multiply any two-digit number by a one-digit number with and without regrouping. 10. Estimate products up three-digits. 11. Recognize that multiplication and division are inverse operations by combining and separating equivalent sets of objects. 12. Demonstrate the mathematical properties of order (commutativity), grouping (associativity), and one (multiplicative identity) as they apply multiplication.

8 13. Demonstrate the distributive property of multiplication over addition. STRAND: GEOMETRIC CONCEPTS AND SKILLS A. SOLID GEOMETRY (3-D) 1. Recognize three-dimensional objects in the environment; e.g., spheres, cylinders, cones, cubes, prisms (square and triangular), and pyramids (square and triangular). 2. Compare three-dimensional objects, noting similarities and differences. 3. Classify three-dimensional objects according to various attributes. B. PLANE GEOMETRY (2-D) 1. Recognize two-dimensional (plane) figures in the environment: e.g., circle, square, rectangle, triangle, trapezoid, rhombus, pentagon, hexagon, and octagon. 2. Match the faces of 3-D solids to 2-D geometric figures. 3. Compare 2-D figures, noting similarities and differences. 4. Classify 2-D figures according attributes such as number of sides, size, and shape.

9 5. Construct 2-D figures concretely. 6. Draw simple geometric figures such as a triangle, a rectangle, a square, a circle, a trapezoid, and a rhombus. 7. Trace the image of geometric figures which have been slid, flipped, or turned. 8. Identify symmetrical objects in the environment (line or turn symmetry, or both). 9. Identify objects in the environment that are the same size and shape (congruence). STRAND: MEASUREMENT CONCEPTS AND SKILLS A. LINEAR 1. Compare the lengths objects using the metre and the centimetre as the standard units. 2. Estimate the lengths of objects using the metre and the centimetre as the standard units. 3. Measure the length of objects using the metre and centimetre and the standard units. 4. Use appropriate symbols for the metre (m) and centimetre (cm). 5. Relate the number of centimetres in a metre. 6. Find the distance around a shape (perimeter).

10 B. AREA 1. Find the area of a region by covering it with nonstandard units. 2. Measure the area of a region using the square centimetre as the standard unit. 3. Estimate the area of a region using the square centimetre as the standard unit. C. VOLUME 1. Compare the volume of two rectangular prisms using nonstandard units. D. MASS 1. Compare the mass of objects using nonstandard units. 2. Measure the mass of objects using the kilogram as the standard unit. 3. Estimate the mass of objects using the kilogram as the standard unit. E. CAPACITY 1. Compare the capacity of two containers using nonstandard units. 2. Measure the capacity of containers using the litre as

11 the standard unit. 3. Estimate the capacity of containers using the litre as the standard unit. F. TIME 1. Read and write the time the nearest minute on both standard and digital clocks. G. MONEY 1. Identify and name coins. 2. Identify and relate paper currency (dollar bills) up to ten dollars. 3. Find the value of a collection of coins and bills worth less than ten dollars. 4. Make change up one dollar using coin collections. 5. Recognize and use the symbols for cent and dollar. STRAND: GRAPHING CONCEPTS AND SKILLS 1. Record data from the environment. 2. Construct graphs using data from the environment. 3. Interpret graphs.