Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Before this lesson, the class worked on number sense and number patterns. This lesson begins with students exploring the pattern blocks with a partner. Some students are asked to describe the shapes and patterns they are creating. The class reconvenes and students receive instructions for a game. To play, students reach into a paper bag filled with pattern blocks, select a block, and describe the characteristics of that block without looking at it. As one student describes a block, another student illustrates it on an individual chalkboard. Students describe such characteristics of the pattern-block shapes as the number of sides and the number of corners. After students identify their pattern-block pieces, they learn the mathematical term for that piece: hexagon, trapezoid, square, triangle, or rhombus. Fractional ideas emerge as students realize that a trapezoid is half of a hexagon or that a triangle is one-sixth of a hexagon. The lesson concludes as students problem solve to find all the ways to cover the hexagon with other blocks and draw the combinations on their chalkboards. Students work in pairs and then are challenged to explain how they know they have found all the different ways.
Topics for Discussion
The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.
Understanding the Role of Free Exploration
- Why did Ms. Christiansen give the students time to explore the pattern blocks at the beginning of the lesson? What might have happened if she had not given them time to explore?
- Knowledge often emerges from students' explorations. Describe the mathematics and mathematical relationships that emerged in the lesson through exploring pattern blocks.
- Why do students of all ages need time for a free exploration of materials?
- List ways to build in and manage time for free exploration.
- Ms. Christiansen asked a pair of students, "Can you build something together?" Under what circumstances do you think free exploration should be an individual activity? A pair activity?
- Ms. Christiansen asked students, "Can you explain what you are doing here?" and "Tell me about your discovery." Identify reasons for asking students to talk about their free exploration. What did Ms. Christiansen learn about her students from their free explorations?
Developing Geometry and Fraction Concepts
- In the lesson, many students referred to the various blocks by color rather than by name. At what point would you want students to use the formal geometric names?
- Look closely at the tan pattern block and the blue pattern block. How are these blocks alike? How are they different? What mathematical term or terms should be used to name these blocks? Why?
- What was the purpose of having students use their sense of touch to feel the pattern blocks hidden in the paper bag? What did you notice about the language students used to describe the hidden pattern blocks? How did Ms. Christiansen guide their descriptions?
- Why did the children draw shapes on their slates or minichalkboards while other children described the hidden pattern blocks?
- Students reported the various ways to cover a hexagon with the other blocks. Then Ms. Christiansen asked the children, "How do we know that you have gotten them all?" Describe the responses of students to this question. Did any of their reasoning surprise you? In what way? How would you have answered this question?
- At several times throughout the lesson, students mentioned or referred to fractions. Describe how the work with the pattern blocks promoted the development of fraction concepts.
- How would you follow up on this lesson to further develop students' understanding of fraction concepts?
Students from preschool through high school enjoy working with pattern blocks. Research or think of more activities that use pattern blocks to help students develop an understanding of mathematical ideas in the areas of geometry, fractions, and measurement. If you are working in a group, each person should choose and study one activity to teach to the others in the group.