School Improvement in Maryland

Gr. 4 Unit: Generate & Analyze Patterns

Unit Overview

In this unit, students focus on reasoning about number or shape patterns, connecting a rule for a given pattern with its sequence of numbers or shapes. Patterns that consist of repeated sequences of shapes or growing sequences of designs can be appropriate for instruction. For example, students could examine a sequence of dot designs in which each design has 4 more dots than the previous one and they could reason about how the dots are organized in the design to determine the total number of dots in the 100th design. In examining numerical sequences, fourth graders can explore rules of repeatedly adding the same whole number or repeatedly multiplying by the same whole number. Properties of repeating patterns of shapes can be explored with division. For example, to determine the 100th shape in a pattern that consists of repetitions of the sequence “square, circle, triangle,” the fact that when we divide 100 by 3 the whole number quotient is 33 with a remainder 1 tells us that after 33 full repeats, the 99th shape will be a triangle (the last shape in the repeating pattern), so the 100th shape is the first shape in the pattern, which is a square. Notice that the Standards do not require students to infer or guess the underlying rule for a pattern, but rather ask them to generate a pattern from a given rule and identify features of the given rule.

Essential Questions:

  • How can patterns help in problem solving?
  • How can multiple representations be used to express relationships?
  • How can expressions and equations be used to represent practical problems symbolically?
  • How can change be described mathematically?
  • Why are equations and inequalities useful?
  • What can we learn from studying patterns?
  • How can we use patterns to develop an understanding of our place value system?
  • What patterns are useful in computation?
  • Where are patterns in nature, architecture, music, words, and numbers?
  • What is the repeating and/or increasing unit in the pattern?
  • What strategies can be used to continue a sequence?
  • How does finding patterns help in counting and/or computation?
  • How is an equation like a balance scale?
  • How can relationships be expressed symbolically?
  • Why are variables used?
  • What strategies can be used to solve for unknowns?

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

Unit Lesson

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.

Available Model Lesson Plans

The lesson plan(s) have been written with specific standards in mind. Each model lesson plan is only a MODEL - one way the lesson could be developed. We have NOT included any references to the timing associated with delivering this model. Each teacher will need to make decisions related ot the timing of the lesson plan based on the learning needs of students in the class. The model lesson plans are designed to generate evidence of student understanding.

This chart indicates one or more lesson plans which have been developed for this unit. Lesson plans are being written and posted on the Curriculum Management System as they are completed. Please check back periodically for additional postings.

CCSC Alignment: 4.OA.C.5

Students explore both numeric and shape patterns in the lesson. They use the multiplication chart, a function table, manipulatives, and drawings to make sense of the patterns, extend them, and solve problems.

Available Model Lesson Seeds

The lesson seed(s) have been written with specific standards in mind. These suggested activity/activities are not intended to be prescriptive, exhaustive, or sequential; they simply demonstrate how specific content can be used to help students learn the skills described in the standards. Seeds are designed to give teachers ideas for developing their own activities in order to generate evidence of student understanding.

This chart indicates one or more lesson seeds which have been developed for this unit. Lesson seeds are being written and posted on the Curriculum Management System as they are completed. Please check back periodically for additional postings.

CCSC Alignnment: 4.OA.C.5

Students play a game in which they match a numeric or shape pattern with its rule.