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McREL Standards Activity


Multiplication and Addition


Purpose:As a result of this activity, students will be able to determine the effect of addition and multiplication on the size of a number.
Related Standard & Benchmarks:
Mathematics
 Standard 3.Uses basic and advanced procedures while performing the processes of computation
   Level II [Grade 3-5]
   Benchmark 6. Determines the effects of addition, subtraction, multiplication, and division on size and order of numbers
Student Product:Number line and the answers to several questions.
Material & Resources:Colored pencils or crayons, straight edge, paper (adding machine paper works well)
Teacher's Note:Don’t let the students choose 0 or 1 for the addend/multiplier unless you specifically want them to learn about the unique properties of these numbers.
Activity
Each student will create a number line that shows the increase along the numbers if you add the same number consecutively and if you multiply the same number consecutively. The student will need to make a number line. To begin, have the students choose a number between 2 & 9, and choose different colors to represent addition and multiplication. Next, have the student plot the numbers across the number line when his/her number is successively added starting at the number they chose. For example, using the number 3: 3+3=6, 6+3=9, 9+3=12, 12+3=15, 15+3=18, 18+3=21. Therefore, the numbers 3, 6, 9, 12, 15, 18, 21 will be plotted on the number line in the addition color, as follows: X X X X X X X ______________________________________________________________ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Now have the students use their number as the multiplier starting at the number they chose. For example, using the number 3: 3x3=9, 9x3=27, 27x3=81, 81x3=243 therefore the numbers 3, 9, 27, 81, 243 will be plotted on the number line in the multiplication color. X X X _______________________________________________________________________________ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Finally, have the students answer the following questions. Possible answers are in parentheses. 1. In what ways are the addition plot and multiplication plot different? {The multiplication plot is spaced further apart with each plot} 2. In what ways are the addition plot and multiplication plot the same? {Both plots start at the same number and all of the points on the multiplication plot would also be found on the addition plot if it was extended far enough} 3. How would you describe the distance between the dots on the number line for the addition plot? {The points on the addition plot are evenly spaced} 4. How would you describe the distance between the dots on the number line for the multiplication plot? {The points on the multiplication plot get further apart with each point} 5. If you wanted to get to a large number fast would you use multiplication or addition? {Multiplication} 6. How is a number changed by addition? {It increases by the amount being added} 7. How is a number changed by multiplication? {The factor you start with is repeatedly added the number of times you are multiplying by. (e.g., 3X4; 3+3+3+3)} 8. If you wanted the largest number, would you multiply two numbers or add the same two numbers, as long as 1 or 0 are not factors? {Multiply}