Exploring One Half with Pattern Blocks
Creator: Lisa Martin
Grade Level: Second Grade
Big Idea: Standard 1: Numbers and Operations
Essential Question: How can we show and talk about parts of something?
CSO: M.02.1.7 Students will identify and explain fractions as part of a whole and as part of a set/group using models.
LS: 21C.O.PK-2.1.LS.2 Student can accurately interpret and create simple visuals (e.g. charts, maps, graphs and models) and use this information to solve problems and communicate information.
21C.O.PK-2.2.LS.4 Student engages in discovery, exploration and experimentation to reach unexpected answers. Student makes unusual associations and provides a variety of solutions to problems.
21C.O.PK-2.3.LS.1 Student manages negative emotions, aligns his/her goals to the goals of others, and works cooperatively and productively with others in small groups.
TT: 21C.O.PK-2.1.TT.2 Student demonstrates correct keyboarding posture and correct hand and finger placement for the home row, knows how to use keyboard to create lower and upper case letters, knows how to locate and use the letters, numbers and special keys (e.g. enter, space bar, arrow keys, delete, shift, punctuation keys, number keys, left and right hand position), knows how to use a mouse to point and click, place cursor at a specified location, click and drag, and right click.
Launch:Begin the lesson with the students in a whole group setting.
Activating Prior Knowledge-Briefly discuss their previous experience with fractions. (This is intended to be the first fraction lesson in second grade.) Read Eating Fractions by Bruce McMillan. Use (teacher-made) foam manipulatives which correlate to the story. Remind students this book will be available during Math Workstations.
Specialized Vocabulary- whole, fraction, equal, part, ½, one-half
Display pocket chart with words listed. Students suggest definitions which may include pictures for the teacher to create and display with the corresponding term. These will be revisited during the debriefing to check for accuracy.
Investigation: Display a hexagon on the overhead projector. Ask students how to show ½ . Model their response. Model a few more examples.Elicit student input to determine if they understand their task. Demonstrate how to record their results using triangle grid paper and markers. Students should reproduce the figures they created on the triangle grid paper and cut around the representation. Show the chart paper (see materials) which is labeled ½ and not ½, where groups will post their results. Explain procedure for groups to post results. Assign small groups to work with different kinds of pattern blocks. Groups should consist of 3-4 students. Assure students they will all have a chance to use the different materialslater in the unit.
Group 1 – overhead pattern blocks on overhead projector
Group 2 – virtual pattern blocks on computer (See Materials List for link. This group will require a brief explanation if they haven’t used this program before.)
Group 3 – traditional pattern blocks on floor or at tables.(Form additional groups
using these materials to control the size of the groups.)
Monitor groups as they work. Have them post results on the chart paper, which is labeled ½ and not ½, as they create them. If students do not attempt to use multiple pattern blocks to show the fractions, you can suggest they do so. Students who seem to catch on quickly to the concept can be challenged to show different fractions and post them on the not ½ chart. After groups have posted several results, gather them in front of the chart.
Summarize/Debrief:Ask the students to observe the chart for a few minutes. Then discuss the figures in general and specifically the ones they believe show ½. Use the overhead to recreate some of the figures that students are unsure about. Allow students to use the overhead to clarify their comments. Create a figure that shows 1/3 (or demonstrate with one the students posted). Ask students how they would describe the fractional part. Continue examining and discussing any additional fraction representations that students made. Explain that there are other fractions to describe parts of a whole, and we’ll be learning those later. Briefly revisit the vocabulary chart making any revisions that seem appropriate. Determine through discussion that they understand fractions must be equal parts. End the discussion by talking with students about what they could write in their math notebooks/journals concerning this activity. An exit slip could also be used. After writing, students work independently at Math Work-stations. (Some suggested Math Workstations are listed later in this plan.)
Possible Questions-
What do you notice about the figures?
Do you agree that all of the figures show ½? Why? Why not?
How can we prove it?
Do the two parts need to look alike to show ½?
Are all of the figures divided into equal parts? How can we know for sure?
Why do we have fractions? (Discussion of this question should help students
re-focus on the essential question on how we show and talk about parts of
something)
Anticipating Confusion-
Some students may have a conceptual knowledge of ½ but grasping the preciseness of the fraction could be difficult.
Some students may think the symbol ½ means one and one-half.
This exploration will lead some students to wonder about other
fractions. This is appropriate but should be pursued in a future lesson. Otherwise some students may not grasp the initial concept.
Some students may make non-congruent figures which still represent ½. Using triangles to overlay will help some students accept this representation. This discussion will also help students begin to see the relationship between part of a set and part of a group.
Math Workstations-Students can work independently on Math Workstations after the whole group lesson. These can be adapted to fit the existing structure each teacher has established for independent practice.
Possible Math Workstation Activities for this Topic
*computer station using virtual pattern blocks with task cards listing various fractions to be demonstrated
*magnetic pattern blocks with task cardslisting various fractions to be demonstrated
*wooden or plastic pattern blocks with blank cards to label fractional parts or task cards
*colored tiles with blank cards to label fractional parts or task cards
*labeled fraction bars
*math literature selection with manipulatives such as Eating Fractions by
Bruce McMillan
Materials:
- Eating Fractions by Bruce McMillan with teacher-madefoammanipulatives (Magnets on the back will make them easy to display and manipulate.)
- pocket chart with vocabulary cards
- overhead pattern blocks and overhead projector
- several sheetsper group of pattern block triangle paper from About Teaching Mathematics: A K-8 Resource, 3rd ed. by Marilyn Burns, copyright 2007 Math Solutions Publications
- overhead transparency of triangle paper
- markers, a pair of scissors, and a gluestick for each group
- chart paper labeled ½ and not ½
- wooden or plastic pattern blocks
- computer station with pattern block program i.e. Investigations in Number, Data, and Space: Shapes, Halves, and Symmetry software or
- math journals or notebooks
- preprogrammed task cards with directions for workstations
- blank cards to label fractional parts
- labeled fraction bars
- colored tiles
Duration: 60 to 90 minutes
Teacher Notes:
This activity is an exploration. It provides students with the opportunity to apply mathematical precision to the common term “half”.It is meant to be the introductory activity for a unit on fractions.
It is important that the students have had time to free explore with pattern blocks prior to this lesson.
Refer to the pattern blocks using their proper names i.e. rhombus, triangle, trapezoid and hexagon.
Examples of ½ using pattern blocks: 3 triangles on a hexagon, 1 triangle on a rhombus, 2 of the same pattern blocks touching one another, 1 trapezoid on a hexagon, etc.
The exploration stage of this lesson can be done with all of the groups using only wooden or plastic pattern blocks. It is necessary that the teacher have some way to project the images during the launch and debriefing.
This same exploration could be revisited to teach other fractions later in the unit.