To begin the lesson, assess prior knowledge by drawing a long line on
the floor or sidewalk with a piece of chalk. Demonstrate how the line
can be marked off in equal intervals, and then assign a volunteer to
fill in the numbers 0-30 on the line.
Ask a volunteer to name a number between 2 and 4. Then, starting
at 0, have the volunteer hop a counter down the number line as the rest
of the class skip counts by that number (for example: 3, 6, 9, 12,
15, ...). Repeat with other volunteers using other numbers.
Inform students that they will find products using a number
line model. Write the following equation on the board: 4 × 5 = ____.
Then, demonstrate with a counter how hops of five can be taken on the
number line. You may wish to encourage students to count aloud as the
hops are made. When 20 is reached, complete the equation (4 × 5 = 20)
and encourage the students to translate it as, "When you take four hops
of five, you land on 20." After several examples with five as a factor,
ask a student to determine what size hop to use next. Work out and
record several multiplication equations. When students are ready,
encourage them to predict the products and then to verify their
predictions by moving a counter along the large number line that was
drawn on the floor or sidewalk.
After allowing time for exploration, give each student a copy of the Number Lines Activity Sheet and ask them to draw five examples of "hops" and then
trade them with a friend. (Note that the activity sheet contains
eight number lines. Students should use the first six of them for this
part of the lesson; an extra one is provided in case they make a
mistake. The last two number lines on the sheet will be used later in
the lesson, and students should not write on them yet.) The friend
should record the multiplication fact modeled on the number line using
an equation of the form n × s = ___, where n is the number of hops and s
is the size of each hop. When all pairs have finished, call the class
together to model what they did and to display their equations.
Number Lines Activity Sheet
Then say, "Show on your blue number line five hops of 3. Where
did you land?"  "What equation is that?" [5 × 3 = 15] Then ask them
to show three hops of 5 on the orange number line, record the equation,
and compare it to the equation from the blue number line. Encourage
them to explore other examples of the Order Property and state their
findings. [The Order Property states that the order in which two
numbers are multiplied does not affect the result. For instance,
3 × 5 = 15, and 5 × 3 = 15.]
Now give each student a copy of the Fact Mastery Record. Ask them to use a dark crayon to cover each product that they are sure of.
Fact Mastery Record
You may wish to talk about the properties of multiplying by 1
and by 0. This will assure that they cover at least the two rows and
two columns shaded pink on the chart. You might also want to point out
that, because of the order property, learning the products in the
unshaded portion will mean that they have also "learned" the products
in the cells that are shaded light blue. By noting these observations,
students will be able to color in many of the cells in the chart,
making the task of learning the multiplication facts seem less
overwhelming. Because this unit is highly dependent on proficiency in
naming products, you may wish to establish individual plans with
students who have many facts left to memorize.
As a concluding activity for the day, pose puzzles such as, "I
am a number between 14 and 19. You say my name when you hop by 5’s. Who
am I?" [15.] Encourage students to create and share similar problems.
You may also want to have them locate the products on the Fact Mastery Record.
Record your observations about student progress by using the Class Notes sheet. At this point in the unit, students should be able to:
- Model multiplication on a number line;
- Use the number line model to find products; and,
- Identify known multiplication facts on a chart.
Make notes about student progress toward each of these goals.
Recording the information in this manner may be useful when discussing
student progress with parents, administrators, and colleagues.
Move on to the next lesson, Setting the Pace.
Questions for Students
1. How would you model four hops of 6? What equation does this represent? Where would you find the product on the Fact Mastery Record?
[Four hops of 6 represents the equation 4 × 6 = 24. This result occurs on the Fact Mastery Record in the fourth row and sixth column; because of the Order Property, it also occurs in the sixth row and fourth column.]
2. What numbers did you land on when you hopped by 5 to 30?
[5, 10, 15, 20, 25, 30.]
3. What numbers did you land on when you hopped by 3 to 30?
[3, 6, 9, 12, 15, 18, 21, 24, 27, 30.]
4. Did any of your hops end on the same number? What equations did those hops represent?
[When hopping by 3 or by 5, you land on both 15 and 30. The equations for 15 are 3 × 5 = 15 and 5 × 3 = 15, and the equations for 30 are 10 × 3 = 30 and 3 × 10 = 30.]
- Which pairs worked most effectively together? Which pairs were less effective?
- Which students could easily model multiplication on the number line? What instructional experiences are appropriate now?
- Which students could easily identify the multiplication facts
that they knew by heart? Which students could not? What instructional
experiences do they need next?
- How can you ensure that all students will be able to quickly give the product for any pair of factors 0-9?
- What adjustments should be made the next time you teach this lesson?
- Model multiplication on the number line.
- Use the number line model to find products.
- Identify known multiplication facts on a chart.
NCTM Standards and Expectations
- Describe, extend, and make generalizations about geometric and numeric patterns.
- Represent and analyze patterns and functions, using words, tables, and graphs.
- Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
Common Core State Standards – Mathematics
Grade 3, Algebraic Thinking
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Grade 4, Num & Ops Base Ten
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Common Core State Standards – Practice
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.