• repeating patterns in real life:
  • 24-hour clock
  • appropriate warm-up and cool-down activities for daily physical activity
  • morning routine
• growing patterns in real life:
  • distance travelled as time passes
  • growth of a plant over time
  • number of pages they have read in their book over the week
• shrinking patterns in real life:
  • height of a ball over successive bounces
  • amount of sap as it boils down to make maple syrup
  • height of a snowperson on a warm spring day

• Repeating patterns have a pattern core that is repeated over and over.
• In growing patterns, there is an increase in the number of elements or the size of the elements from one term to the next.
• In shrinking patterns, there is a decrease in the number of elements or the size of the elements from one term to the next.
• Many real-life objects and events can be viewed as having more than one type of pattern.

Note

• Growing and shrinking patterns are not limited to linear patterns.

Have students collect pictures or make diagrams of patterns that they find in real life and create a pattern wall. Have them describe the regularities that they see in any of the patterns. Some real-life examples may be viewed in more than one way. For example, a staircase can be viewed as a repeating pattern because the rise for each step is the same. The staircase can also be viewed as a growing pattern because each step goes up the same height so that the distance from the ground increases consistently. For each step down, the distance to the ground also decreases consistently.

• representations for a growing pattern:

• representations for a shrinking pattern:

• Growing patterns are created by increasing the number of elements or the size of the elements in each iteration (term).
• A growing pattern can be created by repeating a pattern’s core. Each iteration shows how the total number of elements grows with each addition of the pattern core.

• Shrinking patterns are created by decreasing the number of elements or the size of the elements in each iteration.
• In translating a pattern from a concrete representation to a table of values and a graph, each iteration of the pattern can be referred to as the term number, and the number of elements in each iteration can be referred to as the term value. The term value is dependent on the term number. The term number (x) is represented on the horizontal axis of the Cartesian plane, and the term value (y) is represented on the vertical axis. Each point (x, y) on the Cartesian plane is plotted to represent the pattern. In a table of values, the term number is shown in the left-hand column and the term value is shown in the right-hand column.
• A pattern’s structure is the same when a pattern is translated from one representation to another.

Note

• The creation of growing and shrinking patterns in this grade is not limited to linear patterns.
• For (x, y), the x-value is the independent variable and the y-value is the dependent variable.

• extending patterns in multiple directions:
  • What does position 0 look like? What does position 5 look like?
• making near and far predictions:
  • How many toothpicks are needed to show position 0?
  • How many toothpicks are needed to show position 10?
  • How many toothpicks are needed to show position 100? 99? 101?
• identifying missing shapes, numbers in sequences and tables of values, and points on a graph:

• Patterns can be extended because they are repetitive by nature.
• Pattern rules are generalizations about a pattern, and they can be described in words.
• Patterns can be extended in multiple directions, showing what comes next and what came before.
• To make a near prediction about a pattern is to state or show what a pattern will look like just beyond the given representation of that pattern. The prediction can be verified by extending that pattern.
• To make a far prediction about a pattern is to state or show what a pattern will look like well beyond the given representation of that pattern. Often calculations are needed to make an informed prediction that can be justified.
• Identifying the missing elements in a pattern represented using a table of values may require determining the term number (x) or the term value (y).
• Identifying the missing elements in a pattern represented on a graph may require determining a point (x, y) within the given representation or beyond it, in which case the pattern will need to be extended.
• The algebraic expression that represents a linear growing pattern is also referred to as the general term or the nth term. It can be used to solve for the term value or the term number.

Note

• Determining a point within the graphical representation of a pattern is called interpolating.
• Determining a point beyond the graphical representation of a pattern is called extrapolating.

• number pattern to show the relationships between ones, tenths, and hundredths:

• number pattern to show the relationship between the addition and subtraction facts for 7 when applied to decimal hundredths:

• number pattern to show the relationship between multiplication and division facts for 7:

• Patterns can be used to understand relationships among numbers.
• There are many patterns within the decimal number system.

Note

• Many number strings are based on patterns and on the use of patterns to develop a mathematical concept.
• The use of the word “strings” in coding is different from its use in “number strings”.