Rounding to Nearest 10 or 100: Abstract Level

More Teaching Plans on this topic: Concrete, Representational

PHASE 2: Practice Strategies

Receptive/Recognition Level

Purpose: to provide students multiple opportunities to round to the nearest ten or hundred by writing numbers (instead of drawing pictures) to “count on” and “count back” to round to the nearest ten or hundred..

Learning Objective 3: Round to the nearest ten/hundred by drawing using a number line.

Instructional Game – Board Game

Materials:

Teacher -

• Generic game boards (*Game boards can be made by using manila folders or square pieces of tag-board and configuring multiple spaces (i.e. 15-30 spaces will provide multiple practice opportunities) on which students can move their game pieces. A rectangle can be drawn on the game-board to represent where the response cards are placed. (At the beginning of the year, students can be taught how to make game boards and then these game-boards can be used throughout the year!) Game-boards can be as colorful/creative or as simple in nature as appropriate given your time and your student’s ability level. Old or discarded commercially made game boards also can be used (e.g. “Monopoly,” “Life,” “Stratego,” etc.)
• Dice or spinners
• Multiple sets of cards that have: Front - 1.) the number to be rounded and the numbers representing counting on/counting back to the nearest ten/hundred written on either side (e.g. 30 21 32 33 34 35 36 37 38 39 40); 2.) below the example is written one or more questions with three choices; Back – 1.) the correct choice(s) is written. *To facilitate making these cards, you can make one set for each level of difficulty using plain paper so that the examples, questions, and choices are a size that can fit on one side of a 4x5 note-card. Number each example #1 - #20 in the top right corner so that each card has the number appear at the top right corner. Then you can make multiple copies of the one set, cut them out, paste them on note-cards, and laminate the note-cards. Students can assist in pasting the drawings/choices & answers on note-cards!
• A copy of the original set of problems so the teacher can check individual student response sheets.

Students -

• Each small group has a game-board, die or spinner, a set of cards.
• A sheet of paper to record which number example they respond to and whether they answered it correctly or not.

Description:

Activity:

Students play in small groups using a generic game board (See description under “Materials.”) Students respond to cards that depict the number to be rounded in a dark color (black or blue) and then numbers that count on and count back to the nearest ten or hundred in a contrasting color (red). A simple question is written below the example with three choices (e.g. What is the nearest ten? How many ones to the greater ten?” How many tens to the lesser hundred?). On the back is the correct answer. To move, students roll a die or spin a spinner. If they respond correctly, then they move the appropriate number of spaces. To evaluate student performance, students can record the question number they respond to on a sheet of paper and make a mark indicating whether they answered it correctly or incorrectly. To add more challenge, cards can be divided into two or three piles that represent more and more challenging questions. Students choose which level they want to answer. Students can be rewarded for answering more challenging questions correctly by moving one or more additional spaces.

Instructional Game Steps:

1) Introduce game.

2) Distribute materials.

3) Provide directions for game, what you will do, what students will do, and reinforce any behavioral expectations for the game.

4) Provide time for students to ask questions.

5) Model how to respond to the card prompts.

6) Provide time for students to ask questions about how to respond.

7) Model how students can keep track of their responses.

8) Play one practice round so students can apply what you have modeled. Provide specific feedback/answer any additional questions as needed.

9) Monitor students as they practice by circulating the room, providing ample amounts of positive reinforcement as students play, providing specific corrective feedback/ re-modeling skill as needed.

10) Play game.

11) Encourage students to review their individual response sheets, write the total number of “correct” responses under the “C” (Correct) column and do the same for the “H” (Help) column.

12) Review individual student response sheets to determine level of understanding/proficiency and to determine whether additional modeling from you is needed.

[ back to top ]

Expressive Level

Purpose: to provide students multiple opportunities to “solidify” connections between what they know about rounding to the nearest ten and hundred by drawing to rounding to the nearest ten and hundred at the abstract level. The use of a structured “planned discovery activity sheet” provides students who have learning problems appropriate cueing that allows them to independently make the connections between their “representational/drawing level” of understanding and their abstract level of understanding.

Learning Objective 1: Round to the nearest ten or hundred by identifying the “talking digit” in two and three digit numbers.

1. Planned Discovery Activity

Materials:

Teacher -

• Appropriate number of structured “planned discovery" activity sheets. The sheet contains multiple examples of the following: 1.) a drawing of rounding to the nearest ten or hundred (e.g. a number line with the appropriate drawings above that represent the number to be rounded, the “count on” drawings, and the “count back” drawings.); 2.) the following prompts/questions with a space provided to write the player’s answer: What number is being rounded? Rounding to nearest ten or hundred? What is the talking digit? What ten or hundred should number be rounded?

Example for rounding “162 to nearest hundred:”

What number is being rounded? _____________ Rounding to the nearest ten or hundred? ______________

What is the talking digit? _________________ What ten or hundred should number be rounded? _________

• Answer key for planned discovery activity sheet.
• Cue cards that show one example of rounding to tens and one example of rounding to hundreds with appropriate answers to the questions/prompts. Students who need additional prompting can use these cards as needed to respond to the planned discovery activity sheet.

Students -

• Each pair has two planned discovery activity sheets.
• “Example” cue cards if appropriate.
• Pencils for writing.

Description:

Activity:

Students work in pairs to respond to a planned-discovery learning sheet (See description under “Materials.”). Each sheet has drawings on a number line that represent rounding to the nearest ten or hundred (the numerical form of the value to be rounded is not written). Students respond by writing the number that is being rounded, identifying whether the drawing represents rounding to the nearest ten or hundred, identifying the “talking digit,” and identifying what ten or hundred the number should be rounded to. Students take turns responding to each example. The “coach” describes the drawings and then asks the “player” to respond to each question/prompt for that drawing. The coach writes the player’s answer in the appropriate space on that student’s planned-discovery learning sheet. The coach and player then refer to the answer key to check the player’s responses. If the player’s responses are correct, the students switch “roles” and move to the next example. If the player’s responses are incorrect, the coach and player discuss why the player’s response differed from the correct answer. After they have reached agreement, the students raise their hand to signal the teacher. When the teacher approaches them, the player (or coach and player) explain what they learned (why the response was not correct). For students who may need additional prompting/cueing, two example cards could be provided. One “example” could show a drawing representing rounding to tens with appropriate responses to the questions and one “example” could show a drawing representing rounding to hundreds with appropriate responses to the questions. Students could refer to these “example” cards as needed as they respond. The teacher circulates the room monitoring students as they work, providing positive reinforcement, specific corrective feedback, and listening to student explanations.

Planned Discovery Activity Steps:

1) Develop Planned Discovery Activity Learning Sheet as described under Materials.

2) Distribute the Planned Discovery Activity Learning Sheet and provide clear directions for completing the activity, including appropriate behavioral rules.

3) Model how to respond to one example on the Planned Discovery Learning Sheet (and model appropriate behaviors as needed).

4) Provide students with appropriate materials (e.g. Cue cards).

5) Monitor students as they practice, providing appropriate corrective feedback, prompting student thinking, providing positive reinforcement, and modeling or cueing as needed.

6) At the conclusion of the activity, provide students with solutions to the Planned Discovery Activity Learning Sheet. Emphasize why the answers are correct.

7) Review student response sheets and note special difficulties individual students may be having and/or progress they are making.

[ back to top ]