| Subject
Matter: |
Mathematics |
| Grade Level:
|
2 |
| Time Allotment:
|
Two 60-minute class sessions |
Overview
Young mathematicians often have difficulties
with the concepts of borrowing and carrying in dealing with two-digit
numbers in subtraction and addition operations. In the introductory
activity, they will practice decisions to regroup or just go for
it! Using online video clips and interactive Web sites, the concepts
of regrouping will be illustrated. Students will practice step-by-step
strategies for solving regrouping problems in addition and subtraction.
As a culminating activity, students will role play as bankers to
solve more problems in regrouping.
Learning Objectives
Students will be able to:
- Review the place value system and double-digit addition and
subtraction.
- Create and manipulate double-digit regrouping.
- Identify ways to use regrouping.
Oregon Standards Available at:
http://www.ode.state.or.us/cifs
Mathematics – Calculations and Estimations
Compute fluently and make reasonable estimates.
- Develop and evaluate strategies for adding and subtracting
whole numbers.
- Add and subtract pairs of any two-digit numbers.
Media Components
Video
Check the link at http://www.opb.org/edmedia/trs/
to find access to the video(s) from unitedstreaming™ referenced in this lesson plan.
- "Math Investigations, Part One" (26:00)
o Clip: "Segment 6: Trains (Addition and
Subtraction)" (03:53)
- "Mathica's Mathshop: Merry Band"
(15:00)
o Clip: "Addition Using 100s, 10s, and 1s"
(03:53)
Web
Materials
Per Student:
- Unifix math cubes (or any other base-10 math manipulatives
capable of representing 1s, 10s and 100s)
- Computer with Internet access: Java-enabled and Macromedia Shockwave
installed
- Individual chalkboard and chalk/eraser or dry-erase board with
marker/eraser
Per Class:
Prep for Teachers
When using media, provide students with a Focus for Media Interaction,
a specific task to complete and/or information to identify during
or after viewing of video, Web sites or other multimedia elements.
Session 1:
- Bookmark all Web sites into your Portaportal Web page and download
all video clips. Preview them for specific points you will use
to teach students to borrow and carry. Especially heed the cue
to stop the "Train" segment to more slowly demonstrate
the subtraction in the 10s column.
- Make large posters of this adage for the classroom wall: More
on top, no need to stop! More on the floor, you gotta go next
door and get 10 more! Number's the same? Zero's the
game.
- Prepare a PowerPoint presentation using the regrouping problems
found at the end of this lesson plan. The object is to build the
slide show so that only one problem appears at a time.
Session 2:
- Bookmark the Web pages found at http://www.dositey.com/addsub/as85/add3r.htm
and
http://www.dositey.com/addsub/subra4.htm.
- Schedule the computer lab or mobile lab and allow one computer
per student if possible. Check to see if the proper Windows Media
Player and/or QuickTime plug-ins are installed on the demonstration
computer you will use for instruction. Make sure that this computer
can be connected to a projector or a large-screen monitor for
large-group instruction.
- Have enough tables/desks so that there are two "bankers"
for every two "customers." Set them up so that the
bankers sit behind the desk and the two customers have room to
line up in front of the desk.
- Prepare deposit and withdrawal slips with two-digit numbers
for students to use in banking for the culminating activity.
- Make "visors" (like old-fashioned bankers wore)
that say "1s" and "10s." You will need
a pair for each "bank." Each bank will need to have
a set of place value blocks or math cubes (manipulatives) to use
for money.
Introductory Activity
Step 1: Play the video clip, "Segment 6:
Trains (Addition and Subtraction)" (03:53), from the video,
"Math Investigations, Part One" (26:00). As a Focus
for Media Interaction, ask students to copy the problem
on their boards and follow along with the steps as it is solved.
They will continue to use their individual boards to work with the
problem throughout the solution in the video clip.
Step 2: Pause the clip as the
subtraction problem appears written on the screen (70 cars minus
27 cars). Say, "Uh, oh! We have a problem here. Who knows
what it is?" (Answers will vary but look for "You can't
take 7 away from 0.") You reply, "We have to borrow
or regroup to solve this problem. Here's an easy way to remember
what to do."
Step 3: Direct the students to learn the adage
that you have placed on a large poster on the wall that says: "More
on top, no need to stop! More on the floor, you gotta go next door
and get 10 more! Number's the same? Zero's the game."
You could even introduce it as a rap lyric for interest.
Step 4: Ask the children, "How does our
rap help us decide what to do here?" "Do we need to
stop or do we need to go next door?" (Answer: Go next door
and borrow 10 more.)
Step 5: Play more of the video
clip that reveals that we have to regroup one 10 and then add that
10 to the 1s column. Make sure students are following these transactions
on their own boards. Stop at each maneuver if necessary. Do not
play the video clip to the conclusion of the problem's solution.
Stop after the part of the video clip that subtracts the 7 from
the 10. (I do not like to introduce the concept of subtracting 20
from 60 at this point.) Have the students finish the problem on
their own and then hold up their boards for you to check for success.
Step 6: Show the first problem from your regrouping
PowerPoint presentation. Direct the students to use the adage that
you taught in the first step. Ask the children, "How does
our rap help us decide what to do here?" "Do we need
to stop or do we need to go next door?" etc. After a few of
these problems, you will be able to tell whether students have grasped
the concept of applying the adage to the problem at hand.
Learning Activities
Session 1
Step 1: Tell students we will be watching a video
clip about how to add two-digit numerals. As a Focus for
Media Interaction, ask them to pay attention to the steps
in the process and be prepared to discuss the similarities and/or
differences between subtraction and addition.
Step 2: Play the video clip, "Addition Using
100s, 10s, and 1s" (03:53), from the video, "Mathica's
Mathshop: Merry Band" (15:00).
Step 3: At the point where Mathica says, "This
calls for my trusty group of 10s," pause the clip. Prompt
students to be ready with their materials. As a Focus for Media
Interaction, instruct the students to follow after Mathica with
their own cubes using 58 and 64 as the addition problem we are working
on. Play the clip.
Step 4: Pause the clip when Mathica says, "There's
a group of 10 in there. I must make a trade." Watch that students
see the 10 cubes they have out of the 12 "1s" they have
gathered.
Step 5: Play the clip to the part where she exchanges
for a 10 rod and places it above the 10s column. Watch to see if
your students are following her action with the 10 rod (it is placed
above the 10s column).
Step 6: Let the video clip play out with the regrouping
to the 100s column. Talk to the students about the 100s column being
the same concept as carrying to the 10s column.
Step 7: Start the PowerPoint presentation that
you created with the addition and subtraction problems found at
http://www.rhlschool.com/worksheet.php4?option=add1
and http://www.rhlschool.com/worksheet.php4?option=sub1.
Have the students write on their individual boards whether or not
they have to regroup. Check their boards for accuracy as they hold
them in the air facing you.
Step 8: As you notice that the rate of success
is sufficient to move on from the regrouping concept, continue using
the PowerPoint presentation to help students practice regrouping
with the cubes. Make sure you are alternating from borrowing to
carrying as a regrouping strategy. Actively walk among the students
to advise them as they proceed and check for understanding.
Session 2
Step 1: (This session of the lesson could be organized
as a station in the classroom if that is a strategy you employ for
students' activities.) Take the students to the computer lab
or direct them to computers you may have set up in your room. As
a Focus for Media Interaction, have the students
use their individual marker boards to follow your steps as you demonstrate
so that students can see that each step in the operations must be
entered into the boxes and carrying positions for the train to leave
the station. Before you go on to the next step on the Internet site,
check their boards for the correct number that they will later put
in boxes online.
Step 2: On the presentation computer for the large
group, demonstrate an addition and subtraction problem from these
Internet sites: http://www.dositey.com/addsub/as85/add3r.htm
and http://www.dositey.com/addsub/subra4.htm.
Step 3: On their own computers, direct the students
to pull down to the Internet bookmarks you made ahead of time to
http://www.dositey.com/addsub/as85/add3r.htm
and
http://www.dositey.com/addsub/subra4.htm.
At these sites, students are to enter numbers into the blocks as
the problem progresses, step by step. Each student needs to practice
completing five subtraction problems and five addition problems.
Culminating Activity
Step 1: Students will practice their skills at
regrouping in this activity by acting as "bankers" and
"customers." One banker sits behind a table in the 1s
place and one banker sits behind the same table in the 10s place.
The rules for a banker are simple — they may not hold more
than 9 or less than 0 at a time. Bankers can accept deposits (addition)
or withdrawals (subtraction) of the place the banker is holding.
The banker must make trades with the other bankers that work to
solve the transaction. The 1s banker may group 10 "1s"
and "carry" them to the 10s banker or borrow from the
10s banker to make a withdrawal.
Step 2: The bankers are given 99 place value blocks
(manipulatives). As each customer approaches the bankers, they make
transactions using the deposit or withdrawal slip they have been
given by the teacher. Using the two-digit number on the slip, the
customers must decide whether they are to add or subtract and then
if they have to regroup from the banker's balance.
Step 3: Once the bank is broken (can no longer
make a transaction or you can declare a time limit), reverse roles
and have the bankers become customers and vice versa.
Cross-Curricular Extensions
English and Language Arts
- Read "Ten Sly Piranhas" by Victoria Chess. Have
students use the format of the story to create their own story
using equally sly creatures to portray two-digit subtraction problems.
"The Doorbell Rang" by Pat Hutchins is a picture book
title to use to teach addition.
Social Science - Geography
- Using maps from your county and/or state, ask students to locate
key places they would like to visit, plot a round trip route,
add up the distances between all the points and report on how
many miles their state or county vacation would cover.
Community Connections
- Bank representatives may visit your class with authentic withdrawal
and deposit slips and pose problems for the children to solve.
- Manufacturing workers or shelf stockers in retail may demonstrate
the packing of materials into sets of 1s and 10s.
Regrouping Examples for the PowerPoint Presentation (Introductory
Activity)
| 1. |
|
2. |
|
3. |
|
4. |
|
5. |
|
|
89
-14
|
|
17
- 7
|
|
60
- 2
|
|
11
- 9
|
|
98
-87
|
|
|
|
|
|
|
|
|
|
|
| 6. |
|
7. |
|
8. |
|
9. |
|
10. |
|
|
55
-15
|
|
33
-21
|
|
94
-64
|
|
13
-12
|
|
99
-15
|
|
