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This activity idea was taken from the Mathercise series by Michael Serra.
Description
Needed Materials: Computation problems with missing parts. See Sample Warm Up questions
Directions:
Have the students complete the questions individually or in small groups, and then have a student lead a discussion of how to arrive at the correct answer.
My classes do a “warm up” as a regular part of the first class session of every week. It is a 10-minute activity during which the students answer 4 questions--1 reasoning, 1 computational, 1 sketch, and 1 review of current material. I was pleased to find that the materials I already use occasionally build in number sense questions in the “reasoning section”--we used them as springboards to discussions on place value and patterns in number facts.
Comment on the overall effectiveness of this activity. Then use the form below to reflect on the activity from the perspective of both the teacher and the student. Give the lesson points based on how well it went--each question is worth up to 4 points.
A few of my 8th
graders this year did have good number sense and could do these questions
quickly. My focus was to get them to
communicate their methods and knowledge with their classmates. That part was difficult for them as it is
becoming apparent to me that little or no emphasis is made on justifying
answers in our elementary classes. (I feel
another project coming on…) As the year progressed these students gained
confidence in explaining their reasoning and the entire class seemed to benefit
from the discussions. In particular,
about 1/3 of the students began to verbalize the kind of reasoning we used with
these puzzles while doing other computation-based problems.
I used similar questions in other classes besides Math 8. The tenth graders in particular were quick to pick up the speed advantage to thinking about problems this way rather than using rote computation. My Math Analysis class (grades 11-12) was particularly intrigued by a problem I found in More Thought Provokers by Doug Rohrer that used their understanding of place value to figure out the number system of an “alien” people.
_4_ Was the purpose of the activity clear to me?
_4_ Was the purpose of the activity clear to my students?
_3_ Did the activity support a range of learning styles?
_4_ Were the students engaged during this activity?
_15_ Total points (out of 16)
The purpose (objective) of the activity was…
I communicated to the students why we were doing the activity by…
The first time we encountered a number puzzle on a warm up, I explained my goal for them to improve their “sense of number” and reasoning skills as the year progressed. Each time we encountered such a problem or something similar in regular classroom discussions, I’d remind them this was another opportunity to sharpen their skills. With time, many students recognized the problems themselves and sometimes surprised me with their use of number sense skills rather than rote computation or use of a calculator.
The part of the lesson that was student-centered was…
…the student-led discussions. I tried always to keep my mouth shut unless the discussion got way off and no one questioned the results (that happened only once or twice).
Each of the three letters in the sum below represents a different digit. What is the value of A?
3 B
+ B 3
C A C
Each of the three letters in the sum below represents a different digit. What is the value of A - B?
A B
+ B A
1 B 6
Each of the three letters in the sum below represents a different digit. What is the value of A?
A 2 8
+ 8 4 B
C 5 A A
Each of the three letters in the product below represents a different digit. What is the value of B?
1 2 3
X A
A B 2
Each of the three letters in the product below represents a different digit. What is the value of A?
A 2 3
X B
A A C 7
Each of the four letters in the division product below represents a different digit. What is the value of D?
A C
7 | B A D
2 1
B D
B D
Each of the two letters in the sum below represents a different digit. What is the value of B?
A 2 A
+ 6 B 8
1 B 6 5
Each of the three letters in the sum below represents a different digit. What is the value of A + B + C?
A B C
B C A
+ C A B
2 4 4 2
Each of the three letters in the sum below represents a different digit. What is the value of A?
A 2 B
+ 8 C 9
C B D 2
Each of the four letters in the product below represents a different digit. What is the value of D?
A B
X 6 7
3 3 6
D B B _
3 D C 6
