Blockout!
Developed and Published
by
AIMS Education Foundation
This book contains materials developed by the AIMS Education Foundation. AIMS (Activities
Integrating Mathematics and Science) began in 1981 with a grant from the National Science
Foundation. The non-profit AIMS Education Foundation publishes hands-on instructional materials
that build conceptual understanding. The foundation also sponsors a national program of professional
development through which educators may gain expertise in teaching math and science.
Copyright © 2000 by the AIMS Education Foundation
All rights reserved. No part of this book or associated digital media may be reproduced or transmitted
in any form or by any means—including photocopying, taping, or information storage/retrieval
systems—except as noted below.
• A person or school purchasing this AIMS publication is hereby granted permission to make up to
200 copies of any portion of it (or the files on the accompanying disc), provided these copies will
be used for educational purposes and only at one school site.
• For a workshop or conference session, presenters may make one copy of any portion of a
purchased activity for each participant, with a limit of five activities or up to one-third of a book,
whichever is less.
• All copies must bear the AIMS Education Foundation copyright information.
• Modifications to AIMS pages (e.g., separating page elements for use on an interactive white board)
are permitted only within the classroom or school for which they were purchased, or by presenters
at conferences or workshops. Interactive white board files may not be uploaded to any thirdparty website or otherwise distributed. AIMS artwork and content may not be used on non-AIMS
materials.
AIMS users may purchase unlimited duplication rights for making more than 200 copies, for use at
more than one school site, or for use on the Internet. Contact us or visit the AIMS website for complete
details.
AIMS Education Foundation
P.O. Box 8120, Fresno, CA 93747-8120 • 888.733.2467 • aimsedu.org
ISBN 978-1-881431-87-9
Printed in the United States of America
BLOCKOUT!
1
© 2000 AIMS EDUCATION FOUNDATION
Blockout!
B
lockout! brings a problem-solving approach to intensive practice with basic addition facts at four
levels of difficulty. Students “block out” combinations of two or more addends whose sum
equals a target number. Target numbers range from 6 to 20. The four levels of difficulty are provided
by cards with 9, 16, 25, and 64 addends that need to be formed into sets.
Features
Blockout! possesses unique characteristics that are highly desirable
in practicing basis addition facts.
•Each problem is largely self-correcting. Self-correction
reduces need for teacher intervention. This feature results
from requiring that all squares on the game board must
be covered correctly to arrive at the desired sum.
•Practice extends finding the sum of two numbers to those
involving three and four addends.
•Mental rather than paper and pencil calculation is practiced.
Searching for appropriate addends builds facility with
“scanning,” a process in which sums are quickly determined
through mental calculation.
•Careful progression of difficulty allows the teacher to
prescribe practice at a specific level of difficulty or with
specific addends. More difficult combinations receive more
intensive practice.
•Emphasis on problem solving is built into the activity by
requiring specific combinations of addends to cover the
game board. Certain combinations, while correct in themselves, will not satisfy this requirement.
•The activity is versatile so that it can be used for individual,
small group, or total class practice.
•A positive attitude toward mathematics is facilitated in that
only the correct solution survives without trace of error. The
result is strong positive reinforcement and pride in one’s
work. Use of colored tiles permits the child to correct a
false move without leaving any record of the mistake.
BLOCKOUT!
3
© 2000 AIMS EDUCATION FOUNDATION
Rules and Procedures
The card number identifies the target sum. (The example below has a target sum of 19.) The
object is to identify sets of addends totaling this target sum in such a manner that all addends are
used. If any squares remain uncovered, the correct solution has not been achieved even though
each set of addends may total the target sum correctly.
Each addend in a set must have a common boundary with another addend; touching c orn e rs
does not fulfill this requirement. All the addends in a set will form a chain of some sort: I-shaped,
L-shaped, T-shaped, etc.
A set is composed of two or more addends. When a set of addends is identified, all members in
that set should be covered with tiles of a given color. The transparent tiles permit students to check
each set without removing any markers. No more than four colors are ever required to keep each
of the sets distinct from the others.
Problem solving is an integral part of this activity. As students move progressively through the
sequence of cards, their skill in identifying addends and fully covering the game board will
develop significantly.
The sum and difficulty level of each card is identified by its name. Thus, a card labeled “12a” will
have a target sum of 12 and will be the least difficult in the sequence; “12h” will be the most difficult.
Example: Card 19a
7
3
9
9
6
5
6
4
8
The target sum in this example is 19. The combinations of
the addends 7 + 3 + 9 equals 19, so it qualifies as a set.
However, the student must decide which 9 to combine with
the 7 and 3 since two 9s have a common boundary with
the 7 and 3 set and would qualify. If 9 in the second row is
used, it isolates the 9 in the first row by leaving it without
neighbors to form a sum of 19. So 7 + 3 + 9 in the top
row are covered with one color. Now begins the search for
another set of addends with a sum of 19. The set 9 + 6 + 4
qualifies because it equals 19, but should the 6 in the second
row or the 6 in the third row be used? The only choice that
will provide full covering of the game board is the 6 in the
third row. If the 6 in the second row is used, the 6 in the
third row is isolated. The final set consists of the addends 6,
5, and 8. The sense of satisfaction comes when adding the
final uncovered set, the target sum is achieved.
BLOCKOUT!
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7
3
9
9
6
5
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4
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© 2000 AIMS EDUCATION FOUNDATION
Suggestions for Use
T
o prepare the activities for classroom use, duplicate the masters on card stock. The cards can
then be laminated for longer life. Provide each student or group with sets of colored tiles as
required by the number of addends on the card. The activity can be used in the following ways.
Individual Prescription
A student diagnosed as having trouble with certain addends
is given an appropriate card with a suitable level of challenge on
which to practice alone. The difficulty level is gradually increased
until the desired level of competency is achieved.
Games in Pairs
The full page blocks are used in this activity. Each child is
supplied with tiles of a given color. Students take turns identifying
sets with the tiles. If a child makes a mistake, the incorrect set of
tiles must be removed and the turn is ended. Play ends when no
further sets can be covered. Because of the approach in placing
tiles under these rules, not all of the numbers will be covered.
The player who has placed the most tiles on the card is the winner.
Full Class
A transparency of a full-page card is prepared. In one variation,
two teams are formed. The two teams play competitively under the
same rules as under “Games in Pairs.” Teams alternate in forming
sets. If a team makes an error that is detected by the other team, the
turn is forfeited and the chips involved are removed.
One way to decide the winner is to award victory to the team
covering the most spaces. To emphasize the addition of more
difficult facts, however, the team having the most sets but covering
the fewest average number of spaces is the winner.
Under a second approach, the entire class works together to
find a way to cover all of the spaces on the board.
General Use of the Blockout Format
Practice with addition facts is only one of the many subjects for which the blockout format is useful. Any
subject in which classification of objects into three or more sets occurs can profit from the blockout format.
The components of each set would be arranged in a manner similar to that of the addends.
Here are some suggested other uses for teacher-made Blockout activities:
Language Arts: synonyms, parts of speech
History: events associated with a person, time span, or place
Geography: cities associated with states or states with regions of the country
Music: instrument classification such as reeds, horns, and strings
Science: animals in water, above ground, in the ground.
BLOCKOUT!
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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© 2000 AIMS EDUCATION FOUNDATION
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3
5
2
6
2
3
4
9
3
5
4
6
5
7
4
5
7
3
8
4
4
7
3
7
5
8
5
5
5
7
6
2
4
6
5
3
5
7
9
6
4
3
4
2
18h
BLOCKOUT!
47
© 2000 AIMS EDUCATION FOUNDATION
19a
19b
7
3
9
8
7
6
9
6
5
3
6
4
6
4
8
8
8
7
19c
19d
6
8
5
3
8
7
8
2
8
8
2
8
4
3
9
4
7
8
3
9
7
9
7
4
5
BLOCKOUT!
48
© 2000 AIMS EDUCATION FOUNDATION
19e
4
4
6
5
9
6
5
4
8
5
7
7
6
6
7
6
19f
BLOCKOUT!
2
4
9
3
7
4
8
7
6
9
7
4
7
3
7
8
49
© 2000 AIMS EDUCATION FOUNDATION
19g
19h
BLOCKOUT!
3
5
9
3
8
2
4
9
6
8
2
3
8
3
5
4
5
9
8
4
5
4
6
2
8
9
2
8
7
5
6
8
5
3
7
8
9
6
7
5
7
4
4
6
4
3
8
8
8
5
50
© 2000 AIMS EDUCATION FOUNDATION
20a
20b
6
4
9
7
6
8
5
8
7
5
6
8
9
8
4
8
3
9
20c
BLOCKOUT!
20d
9
2
9
7
6
7
8
6
7
5
6
2
7
5
7
7
8
9
5
6
7
5
6
8
6
51
© 2000 AIMS EDUCATION FOUNDATION
20e
7
4
3
3
6
7
6
9
4
7
9
8
8
8
5
6
20f
BLOCKOUT!
5
8
3
4
5
6
6
5
9
8
6
8
4
7
9
7
52
© 2000 AIMS EDUCATION FOUNDATION
20g
20h
BLOCKOUT!
2
9
9
5
8
2
4
5
3
7
3
4
6
4
6
3
8
5
8
7
9
6
5
8
4
3
9
2
6
3
7
5
6
9
6
4
4
5
7
7
7
6
6
7
4
7
2
7
6
5
53
© 2000 AIMS EDUCATION FOUNDATION
13
3
4
4
6
1
6
7
6
8
9
2
5
5
2
9
6
1
3
7
5
4
2
2
5
4
1
4
3
4
3
1
2
9
1
1
6
3
3
1
8
4
7
6
4
2
3
1
4
8
4
1
2
2
3
7
1
5
4
5
2
7
4
3
5
BLOCKOUT!
54
© 2000 AIMS EDUCATION FOUNDATION
14
7
2
1
9
7
6
1
5
8
3
4
3
3
6
3
4
5
2
1
1
4
6
6
4
1
6
8
5
2
2
5
1
2
1
3
3
5
8
7
6
5
2
1
2
2
4
5
4
4
7
7
4
9
5
2
4
5
8
6
5
9
4
3
7
BLOCKOUT!
55
© 2000 AIMS EDUCATION FOUNDATION
15
1
6
8
1
4
8
3
9
8
4
3
8
9
4
6
3
6
4
2
7
3
2
9
3
3
7
3
9
7
6
6
3
7
9
2
6
5
2
9
4
2
6
5
7
4
4
4
3
3
8
7
1
5
9
1
8
8
4
3
7
6
7
2
7
BLOCKOUT!
56
© 2000 AIMS EDUCATION FOUNDATION
16
4
8
8
3
4
7
2
5
4
3
7
4
3
3
6
5
5
2
1
6
9
9
8
6
3
3
9
8
2
4
2
4
7
1
6
5
1
4
9
8
2
9
6
5
3
5
2
4
7
7
7
3
2
5
6
7
7
6
3
6
9
2
2
7
BLOCKOUT!
57
© 2000 AIMS EDUCATION FOUNDATION
17
9
3
8
6
2
8
9
4
3
2
8
5
1
7
5
4
7
4
5
6
5
2
5
7
7
9
7
6
5
5
2
8
3
7
1
6
2
6
7
6
2
7
8
9
9
4
5
3
1
3
5
4
8
9
3
8
6
5
3
9
5
3
8
1
BLOCKOUT!
58
© 2000 AIMS EDUCATION FOUNDATION
18
7
6
4
1
7
9
8
5
3
3
6
3
7
5
4
5
8
6
6
8
4
7
6
3
6
8
8
4
5
2
5
6
4
8
2
2
3
7
8
9
9
1
8
7
7
7
9
9
2
9
1
9
2
2
8
4
3
4
7
2
8
9
9
6
BLOCKOUT!
59
© 2000 AIMS EDUCATION FOUNDATION
19
1
5
5
7
6
5
6
1
9
9
5
4
6
9
5
6
3
7
9
7
5
7
9
6
8
5
3
3
6
8
6
8
3
7
7
9
5
6
4
6
2
8
2
1
2
5
8
2
7
7
4
6
2
9
2
3
8
8
3
9
7
3
8
9
BLOCKOUT!
60
© 2000 AIMS EDUCATION FOUNDATION
20
9
7
6
4
9
5
5
5
6
7
8
8
8
2
6
5
2
3
9
2
9
1
9
9
8
8
6
5
3
6
5
1
2
7
8
1
7
4
9
1
2
5
3
8
9
8
3
6
8
7
4
6
7
9
2
6
2
7
8
6
7
3
3
6
BLOCKOUT!
61
© 2000 AIMS EDUCATION FOUNDATION
BLOCKOUT!
63
© 2000 AIMS EDUCATION FOUNDATION