C1. Patterns and Relationships:
identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts
identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing patterns on the basis of their constant rates and initial values
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Provide students with a variety of linear growing patterns that have the same initial value. Ask the students to compare the patterns, identifying how they are similar and how they are different:
Provide students with a variety of linear growing patterns that have different initial values but grow at the same rate. Ask the students to compare the patterns, identifying how they are similar and how they are different:
create and translate repeating, growing, and shrinking patterns involving whole numbers and decimal numbers using various representations, including algebraic expressions and equations for linear growing patterns
Provide students with an algebraic equation for the nth term of a linear growing pattern that involves decimal numbers. Have them create a table of values for the first five terms of the pattern, then graph the line. Support them in making connections between the different representations by identifying the constant rate and the initial value in each representation.
Have students create and translate a variety of growing, shrinking, and non-linear patterns. It is important for students to stay flexible in their thinking about all kinds of patterns and how these can be represented in various ways.
determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns involving whole numbers and decimal numbers, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns
Number of Visible Faces
F = 2n + 3
= 2(9) + 3
= 18 + 3
Ask students to extend the following table of values to include terms 0, 5, and 6:
Have students make and test predictions about patterns so that they understand the role of pattern rules in making generalizations about a pattern, even when it is represented in various ways. For example, have students predict the distance travelled in 8 hours, using a strategy of their choice, given the following graph:
Provide students with different types of representations of patterns with missing elements so that they can think critically about possible pattern rules based on the information they are given. The more information that is missing, the more thinking and the more possibilities for patterns will emerge. For example, have students identify the missing numbers in the sequence below:
3.412, ______, 5.414, ______, ______, 8.417, _____, 10.419
Provide students with different patterns represented in tables of values with missing elements, such as the one shown below. Ask students to determine:
create and describe patterns to illustrate relationships among integers
Provide students with a partial number string pattern based on a key mathematical concept, such as the relationship between powers for different bases or the rules for addition and subtraction of integers. Ask students to complete the pattern. For example:
Have students use number patterns to show the multiplication and division facts for 11 and 12. For example:
Ask them to describe the patterns of the digits and explain how these patterns can help them recall these facts.