Unit: Powerful Patterns
3rd to 5th
Grace M. Burton
Start this lesson by reading a counting book of your choice. (Ten Black Dots
by Donald Crews is especially appropriate, but any book which uses a
"count on by 1" strategy will work.) Then ask students to tell what
happened in the book. Next, tell the students that in this lesson they
will explore patterns that grow according to a rule. Display the
following growing pattern (without the numbers):
Ask, "What will come next in this pattern?" [Students may find
this question easier to answer if they copy the pattern onto paper.]
Have the students explain how they got the answer. When someone has
given the correct answer, write the number of dots in each row. Solicit
student responses to add additional rows to this pattern and label
them. Ask the students if they know a name for this pattern and the
rule they would use to add more rows to the pattern.
Next display the pattern below and tell the students this is
called an L pattern. Ask students how each L is changing. After
students state the answer, or as a hint, write the number of dots used
below each L. Ask several students to state the rule they would use to
add more figures to the pattern. Call on students to draw the next
three L shapes in the pattern.
Distribute the Growing Pattern Activity Sheet to students.
Growing Patterns Activity Sheet
Have them add three more steps in the pattern and write a number
pattern to match the figures. Ask students to share their shape and
number patterns, explaining how they identified the pattern.
Collect students’ Growing Patterns Activity Sheets.
Move on to the last lesson, Looking Back and Moving Forward.
Questions for Students
1. What will come next in this pattern (first growing pattern)? How do you know?
[There will be 5 dots. I used the counting numbers.]
2. What is a name for this pattern?
[Counting on or counting numbers.]
3. What is the rule?
[You have to add one more to each row.]
4. How many dots are in the first figure of the L pattern? How many are in the second figure? The third?
[The first L figure has 1 dot. The second figure has 3 dots. The third figure has 5 dots.]
5. How is each L changing?
[Each L has two more dots.]
6. What is the rule for the L pattern?
[Add one dot at the top and add one dot at the bottom of the next L.]
7. How many dots in the next three L shapes in the pattern?
[The next L figures will contain 9, 11, and 13 dots.]
8. Have you ever seen this pattern before?
[It is the set of odd numbers.]
9. How long could we continue this pattern?
[We could keep going forever.]
10. What will be the next three figures in the triangle growing pattern (from student activity sheet)?
[They will be 5 triangles, 6 triangles, and 7 triangles.]
11. What number pattern did you use to describe the pattern?
[Possible answers include 1, 2, 3, 4, 5, 6, 7 (number of triangles); 3, 5, 7, 9, 11, 13, 15 (number of sides); 3, 4, 5, 6, 7, 8, 9 (number of vertices/corners). Accept all reasonable answers.]
Grade: PreK to 2nd
Make Venn diagrams and use sorted objects to create and extend linear patterns.
Grade: PreK to 2nd, 3rd to 5th
Playing With Patterns
Use patterns to explore doubling.
Exploring Other Number Patterns
Looking Back and Moving Forward