Rounding to Nearest 10 or 100: Concrete Level

More Teaching Plans on this topic: Representational, Abstract

PHASE 2: Practice Strategies

Receptive/Recognition Level

*The student practice strategies described below can be used for both skills taught during initial acquisition through Teacher Directed Instruction. A detailed description for providing practice for one of the skills is provided below.

*The following description is for the skill rounding to the nearest ten using concrete objects and a number line.

A. Self-Correcting Materials

Purpose: to provide students with multiple opportunities to determine which “ten” a set of concrete objects displayed on a number line should be rounded.

Materials:

Teacher –

• Choose various places in the classroom for “rounding centers.”
• Set up several “rounding centers” – each center contains one or more number lines with discrete concrete objects displayed. Each example should be numbered to correspond with the learning sheet for that center.
• “Learning sheets” for each center. Each learning sheet has the following prompts/questions: How many total? How many to the higher “ten?” How many to the lower ten? Closest “ten?” For each question, two or three choices are provided. Students circle the appropriate choice. Each learning sheet has a colored circle to indicate which center it is for. The colored circle matches the colored circle on the master key for that center.
• A timer to determine when students should move to the next center and when to “check” their answers.
• A “Master Key” for each center that has the appropriate choice circled for each question and for each example. Color coding the answer keys by placing a different colored circle on each one that corresponds to the learning sheet for that center will be helpful.

Students -

• Pencils for circling the appropriate response on the learning sheets

Description:

Activity:

Teacher creates “rounding centers” around the room. Each center has one or more number lines (*depicting “tens”) with discrete concrete objects lined to represent a given value. Learning sheets for each “rounding center” are made available at each center. Each learning sheet has a set of questions for each example that “ask” the student to make the best choice based on their understanding of rounding (See “Materials” for suggestions of learning sheet questions/prompts). A “master key” for each center is placed in a folder or envelope that students can use to “check” their answers when the signal is given by the teacher. Students are assigned to particular “rounding centers.” The teacher signals students to begin, when to “check” their answers, as well as when to stop and move to the next center.

This activity could be used as an independent student practice activity where students work individually or it could be used as a structured peer tutoring or structured cooperative group activity (*See the descriptions for “Structure Peer Tutoring” and “Structured Cooperative Learning Groups” at the Instructional Strategies site. These descriptions can be found by clicking on “Instructional Strategies” on the Main MathVIDS Navigational Bar and then clicking on “Instructional Strategies Lists. Descriptions of these strategies can be found under the heading “Student Practice Strategies.) A game format could also be used, so that student teams earn points as they respond to the learning sheets and number line examples at the centers (*See the description for “Instructional Games” at the Instructional Strategies site. *For motivation, the teacher can also periodically sound a “bonus” signal that means “double points” for the example students are working on at the time the signal sounds; or, a “secret bonus tag” contained in an envelope can be placed at one or more of the centers. After the activity is over, the teacher reveals which “center” or example gets “double points.” Students place a mark on the learning sheet to indicate which example gets “bonus points.”

Self-Correcting Materials Steps:

1) Introduce self-correcting material (i.e. learning sheets and “Answer Keys.”).

2) Provide directions for using self-correcting materials at the centers, what you will do, what students will do, and reinforce any behavioral expectations for the activity.

3) Provide time for students to ask questions.

4) Model responding/performing skill within context of the self-correcting material.

5) Model how students can keep track of their responses by using the answer key at each center.

6) Have students practice one time so they can apply what you have modeled. Provide specific feedback/answer any additional questions as needed.

7) Monitor students as they work

8) Provide ample amounts of positive reinforcement as students practice.

9) Provide specific corrective feedback/ re-model skill as needed.

10) Review individual student response/learning sheets.

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Expressive Level

A. Structured Peer Tutoring

*The following description is for the skill rounding to the nearest ten using concrete objects and a number line. This student practice activity is very similar to the one described for “Receptive/Recognition Level” student practice. The main differences are that this practice activity is at the “Expressive Level” and it necessitates students working in pairs.

Purpose: to provide students with multiple opportunities to determine which “ten” a set of concrete objects displayed on a number line should be rounded.

Materials:

Teacher –

• Choose various places in the classroom for “rounding centers” or assign student pairs to a particular space.
• Set up several “rounding centers” – each center contains one or more number lines with appropriate concrete materials displayed; or each student pair is provided a number line and appropriate concrete materials.
• Sets of cards that have various numbers written on them (e.g. two-digit numbers for rounding to “tens” and three digit numbers for rounding to “hundreds.” *When you model how to round to “tens” with three-digit numbers or round to the nearest “hundred” with two-digit numbers, such examples can also be included.) Each card also has the answers to each question/prompt on the learning sheet written on the back.
• “Learning sheets” for each center/student pair. Each learning sheet has numbered sets of the following prompts/questions: What is the number? Represent the number on the number line. How many to the higher ten/hundred? How many to the lower ten/hundred? Which is the closest ten/hundred? The player responds to each prompt/question. The coach checks the player’s response by turning the number card over.
• A timer to determine when students should begin and when they should switch roles.
• A number line, appropriate concrete materials, a number card, and a learning sheet to model what to do.

Students -

• One number line and set of appropriate concrete materials per student pair.
• Learning sheets for each student.
• One set of number cards with answers written on back.
• Pencils for writing.
• One blank sheet of paper for each student so coaches can record points.

Description:

Activity:

Teacher creates “rounding centers” around the room or students can work in pairs at their desks. Each center or student pair has one or more number lines (*depicting “tens”) and discrete concrete objects. Learning sheets for each “rounding center”/student pair are made available. Each learning sheet has a set of questions for each example that students respond to based on their understanding of rounding (See “Materials” for suggestions of learning sheet questions/prompts). A “master key” for each center/student pair is provided so that the student playing the role of “coach” can “check” the player’s answers when the signal is given by the teacher. The practice period is divided into two equal time segments. For the first time segment, one student is the “player” and one student is the “coach,” and then students switch roles for the second time period. The teacher signals students to begin and when to switch roles. Coaches provide feedback and positive reinforcement for each example the player responds to. *Coaches can record “points” based on student responding if appropriate (e.g. two points for correct responses; one point for correct responses on the second try after feedback was provided.) Each coach can make tallies on a sheet of paper to keep track of their player’s score. The teacher circulates the room as students practice answering questions, providing specific corrective feedback, and providing positive reinforcement as appropriate.

*For motivation, the teacher can also periodically sound a “bonus” signal that means “double points” for the example students are working on at the time the signal sounds; or a “secret bonus tag” contained in an envelope can be placed at one or more of the centers. After the activity is over, the teacher reveals which “center” or example gets “double points.” The coach doubles the points for the player for that example.

Structured Peer Tutoring Steps:

1) Select pair groups and assign each pair a place to practice (try to match students of varying achievement levels if possible).

2) Review directions for completing structured peer tutoring activity and relevant classroom rules. Practice specific peer tutoring procedures as needed (see step #4).

3) Model how to perform the skill(s) within the context of the activity before students begin the activity. Model both what the coach does (e.g. reads the questions/prompts on the learning sheet; check answers using number card; provide corrective feedback; record points) and how the player responds (e.g. using concrete materials).

4) Divide the practice period into two equal segments of time. One student in each pair will be the player and will pick the top card from the set of cards and then will respond to the questions/prompts given by the coach, using concrete materials. The other student will be the coach and will say each question or prompt on the learning sheet. The coach will then write the response in the appropriate space on the player’s learning sheet, check the answer key, and provide feedback regarding the player’s response (e.g. positive verbal reinforcement for accurate responses and corrective feedback for inaccurate responses.) For inaccurate responses, the coach provides feedback and the player attempts the question a second time. The first response is crossed out and the second response is recorded. The “listener/describer” will also tally corrects and in-corrects based on the player’s responses.

5) Provide time for student questions.

6) Signal students to begin.

7) Signal students when it is time to switch roles.

8) Monitor students as they work in pairs. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate tutoring behaviors. Also provide corrective feedback and modeling as needed.

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