Grade 4 - Number (Number Operations)

The sub-organizer contains the following sections:
Prescribed Learning Outcomes-Part 1
Suggested Instructional Strategies-Part 1
Suggested Assessment Strategies-Part 1
Recommended Learning Resources-Part 1

Prescribed Learning Outcomes-Part 2
Suggested Instructional Strategies-Part 2
Suggested Assessment Strategies-Part 2
Recommended Learning Resources-Part 2

PRESCRIBED LEARNING OUTCOMES

It is expected that students will apply arithmetic operations on whole numbers and illustrate their use in solving problems.

It is expected that students will:

demonstrate and describe the process of addition and subtraction of numbers up to 10 000, using manipulatives, diagrams, and symbols
demonstrate the process of multiplication (three-digit by one-digit numbers), using manipulatives, diagrams, and symbols
demonstrate the process of division (two-digit by one-digit numbers), using manipulatives, diagrams, and symbols
recall multiplication and division facts up to 81

To view the prescribed learning outcomes for Number (Number Operations) in other grades click on an icon below.

SUGGESTED INSTRUCTIONAL STRATEGIES

Understanding how number operations relate to real-world experiences is critical to being able to solve problems, and this understanding also forms the basis for the future learning of algebra. Knowing "how and why" deepens students' understanding of mathematics. Thus, it is important to select activities that focus on interesting questions and problem situations that encourage students to apply their mathematical understanding in appropriate and efficient ways.

In small groups, have students share a tub of base-ten blocks. Have them place numerals on place-value mats. Then have them add or subtract further numbers to or from these on the mats.
Have students talk about how they use addition and subtraction in their daily lives and how they see adults using these skills. This could be done in groups, with each group reporting to the class.
Have students create transformations based on an example such as:

3 x 246 = (3 x 200) + (3 x 40) + (3 x 6) = 738
246 + 246 + 246 = 738
3 x 246 = 738

Have them use calculators to check the products and to see that the products are the same in each example.
Have students take a variety of objects (up to 50) and divide them into various numbers of equal-size groups. Then have them record the results.
In groups, have students discover, study, and discuss patterns and connections in the times tables to help them learn both multiplication and division facts.

SUGGESTED ASSESSMENT STRATEGIES

Watching students as they work individually and in groups provides opportunities for noting the extent to which they have refined their ideas and understanding. The questions they ask and the suggestions they offer can reveal a great deal about their understanding and confidence with number operations.

Observe

Watch students as they work with base-ten materials and note which students are regrouping numbers as needed and which are regrouping with both addition and subtraction.
Have students devise and solve story situations in which they need to divide to get the answer. How do they approach the activity (eagerly, immediately, cautiously)? Do they demonstrate the process of division by using manipulatives, diagrams, or symbols?

Record

Have students work in groups to make booklets or use audio-visual equipment to make presentations about how and why people use mathematical operations in their daily lives (at home, at work, or in the community). To what extent do students share materials, ask one another questions, and assist one another? To what extent do students understand the range of applications of mathematics to everyday activities?

RECOMMENDED LEARNING RESOURCES

Print Materials

101 Winning Ways with Base Ten Grades 4-6
Big Magic Number Puzzles
Box Cars & One-Eyed Jacks
Collectors' Clubhouse
Cooperative Problem Solving
Creative Maths Age 7-9
Division
Electrical Connections
Interactions 4-6
The Maharajas' Tasks
Mathematics From Many Cultures
Mental Math in the Middle Grades
The Problem Solver 4: Activities for Learning Problem-Solving Strategies
Problem Solving with Number Tiles
Quest 2000: Exploring Mathematics Grade 4
Trading Post Module Notes

Video

Mathematics: Assessing Understanding

CD-ROM

Math Made Fun

PRESCRIBED LEARNING OUTCOMES

It is expected that students will:

justify their choice of method for multiplication and division (using estimation, calculators, mental mathematics, manipulatives, algorithms)
verify solutions to multiplication and division problems by using estimation and calculators
verify solutions to multiplication and division problems by using the inverse operation

It is expected that students will demonstrate an understanding of the addition and subtraction of decimal fractions.

It is expected that students will:

demonstrate an understanding of the addition and subtraction of decimal fractions (tenths and hundredths) by using concrete and pictorial representations

SUGGESTED INSTRUCTIONAL STRATEGIES

Real-life problems often require complex solutions. The ability to understand a problem and to identify and justify a plan for solving it is essential if students are to become flexible thinkers. As students are faced with increasingly complex problems, they better understand the purposes for their calculations, as well as the reasons for choosing specific calculation methods.

Have students write problems requiring the use of one of the four arithmetic operations. They could work in groups and exchange problems when finished. Have them explain how they approached each problem (estimation, calculators, mental mathematics, manipulatives, algorithms) and justify their answers and the methods they used. For example:
- To solve this problem I _______.
- This was a good method to use because _______ . Next time I will _______ , because _______.
Challenge students with problems that require the use of calculators and large numbers. For example: Suppose you have $10 000 to spend to improve your community. Create a spending plan. List the articles you would buy, how much they cost, and the money you would have left. Have students develop little dramas to demonstrate their spending plans, perhaps using pictures from catalogues or other pictorial representations to illustrate how the money was spent.
Have students estimate the answers for calculations such as 342 x 24. Then have them use calculators to check their estimates. After doing such activities, have students work in groups to discuss how they estimated and the methods they used to check their answers.
Have students make question cards showing the addition or subtraction of decimal fractions. On the backs of the cards, have them represent the answer pictorially.

SUGGESTED ASSESSMENT STRATEGIES

As students engage in various problem-solving activities, ask them questions such as: Why? How would you convince someone? How did you figure that out? These will help students explain and justify their answers or conjectures. Their inability to reason and communicate their reasoning to others will further develop their number sense.

Observe

Listen to individual students justify the decisions they made while problem solving. Use a checklist to note student's understanding.
Have students estimate the answers to multiplication questions involving two- and three-digit numbers. Then have them use calculators to find the answers. (e.g., Write down your estimate of the answer for 426 x 23 + 400 x 20. Now use the calculator to check your estimate.) Which students talk about how they came up with their estimates? Which students seem unable to use the calculator to check their estimates? Which seem uninterested in using the calculator?

Record

Develop and assign projects that require large-scale estimations, such as painting, flooring, or going on a trip. You could have students brainstorm a list of possibilities. Remind students to check their work and include evidence of how they verified their solutions. Assess their work in terms of their choice of operations, the reasonableness of their estimations, and the appropriateness and accuracy of their verifications.
Videotape the various problems students act out to solve. Have them watch the video and categorize the problems by the operations used (addition, subtraction, multiplication, or division).

Reflect

Which students were able to justify the calculation strategies or technologies they used when they solved problems?
How might you have those who are confident and accurate assist those who are not?

RECOMMENDED LEARNING RESOURCES

Print Materials

101 Winning Ways with Base Ten Grades 4-6
Big Magic Number Puzzles
Box Cars & One-Eyed Jacks
Collectors' Clubhouse
Cooperative Problem Solving
Creative Maths Age 7-9
Division
Electrical Connections
Interactions 4-6
Kids 'n' Calculators: How to Use the Calculator as a Teaching Tool
The Maharajas' Tasks
Mathematics From Many Cultures
Mental Math in the Middle Grades
The Problem Solver 4: Activities for Learning Problem-Solving Strategies
Problem Solving with Number Tiles
Quest 2000: Exploring Mathematics Grade 4
Trading Post Module Notes

Video

Mathematics: Assessing Understanding
Mathematics: What Are You Teaching My Child?

CD-ROM

Math Made Fun

Previous Organizer | Prev

Next Organizer

Maintained by:Mathematics Coordinator

Revised: October 20, 1997

BC Ministry of Education