Problem solving and reasoning are often some of the most difficult skills to teach to math students. With many states adopting the new Common Core Standards, effective ways to instruct students in these areas have an increased focus. The “Standards for Mathematical Practice” are required of all students K–12 in the Common Core plan and are aimed largely on problem solving and reasoning skills.
In my classroom, I use logic puzzles as extra practice to hone problem solving and reasoning. However, I have found that this activity is a “love or hate” one for many of my students. It tends to appeal to mathematical/logical learners while leaving many other types of learners, and often ELL students or struggling readers disinterested. Adopting a T-Chart graphic organizer used primarily to support literacy strategies in an ELA setting can provide scaffolding to help “hater” students find success in this activity. Using this literacy device also offers an interdisciplinary opportunity for students in math class to discuss concepts like “right there” and inferred information in text.
Use the links to download your own copy of the puzzle and the T-Chart graphic organizer and follow along as the process of incorporating this strategy is explained.
For those not able or interested in downloading, here is the puzzle:
“Take a Bow”
Five circus performers – Maya, Stephen, Hannah, Gabii, and Zaid – are trying to figure out the order they should take their bows at the end of the show. They decide to go in order of height, with the shortest performer going first. Use the clues below to figure out the order that the performers go.
1. Maya is 10 inches shorter than the Ringmaster.
2. The Clown and Gabii combined are as tall as the Stiltwalker.
3. Zaid gets to go first, the Acrobat third.
4. Hannah is shorter than Stephen by 50 inches.
... and this is the accompanying T-Chart:
Be sure to discuss the idea of inferred knowledge with your students. As students look at the first clue, “Maya is 10 inches shorter than the Ringmaster.” The “right there” information doesn’t help very much, but it can be used to infer several key bits of information:
- Maya can’t be the tallest person
- Maya can’t be the Ringmaster
- The Ringmaster can’t be the shortest/first
Have students represent this info on their T-Chart and Solution Grid:
Clue 2, “The Clown and Gabii combined are as tall as the Stiltwalker.” is similar. Here students can infer:
- Gabii can’t be the Clown
- Neither Gabii or the Clown can be the tallest / fifth
- Gabii is not the Stiltwalker
- The Stiltwalker must be the tallest (because the only sum possible out of two other heights is 90" – it can happen two ways: 30" + 60" and 40" + 50")
Discovering a solution for part of the puzzle is exciting! On the Solution Grid, there is a strong visual representation because students should not only be marking the solution (green), but also marking all the options that are no longer possible as a result (marked as red Xs):
At this point some students may also recognize that Maya cannot be the Stiltwalker (In order to keep students focused some may prefer to progress through all the clues one time before jumping around, but this can be adjusted based on student needs/styles.). Be sure to praise discoveries such as these!
Those with print-outs following along, try Clues 3 and 4 on your own and compare to the solutions presented here. Do not worry if your steps are not exactly the same! As with many solutions in mathematics, several routes can be taken in achieving the same outcome.
Some students may read Clue 3, “Zaid gets to go first, the Acrobat third.” and mark both parts of the clue as “right there.” However, there is some inferring happening here, Zaid is first, but an inference must be made that his height 30", the lowest. The Acrobat going third is the first instance of true “right there” information. This is a great example to reinforce these two types of information for students. Finally, an inference is made that Zaid cannot be the Acrobat.
The final clue, “Hannah is shorter than Stephen by 50 inches.” helps determine Hannah as 40" because it is the only solution that combines with 50" to make another height on the puzzle. This inference also requires Stephen’s height to be 90", which makes him the Stiltwalker. Lastly, we know that Hannah cannot be the Acrobat because her height requires her to go second, not third.
Notice the red Xs used on the Solution Grid to cancel out incorrect options once a match is determined. Only one spot in both Clue 3 (blue) and Clue 4 (purple) was not red. This practice of canceling out impossible options is a very useful tool as students progress and attempt more difficult puzzles.
Let’s finish!
- Maya must be 50” because Clue 1 tells us there must be a height 10" greater than hers. This also means that she is the Acrobat.
- Gabii has to be 60” because it is the only height left.
- Since Gabii is 60”, Clue 2 tells us that the Clown must be 30”. Zaid is the Clown.
- Clue 1 helps us determine that Gabii is the Ringmaster
- Which leaves Hannah as the lion.
To recap:
- Zaid the Clown is 30” and goes first.
- Hannah the Lion is 40” and goes second.
- Maya the Acrobat is 50” and goes third.
- Gabii the Ringmaster is 60” and goes fourth.
- Stephen the Stiltwalker is 90” and goes fifth.
The final product of the graphic organizers reveal a limited amount of writing that many students will be capable of doing, and the symbols used from the legend give students exposure to writing in a short-hand method that will help support note-taking. I believe the addition of this T-Chart strategy helps support linguistic learners as a connection to an area of strength; visual/spacial learners, ELL, and struggling learners as an alternative organizational tool with manageable amounts of text and writing.
This strategy is easy to accommodate to a multitude of learners by simply choosing easier or harder logic puzzles based on student ability. For students that really struggle with text, I could also see this activity adapted to be used with a puzzle like Sudoko, where the only text will come from student reasoning/inferences on the T-Chart. If needed, support staff could write that material as well.
For more information on connecting Literacy and numeracy, check out:
Marilyn Burn’s article 10 Big Math Ideas from Scholastic’s website.
Leslie Minton’s book What If Your ABCs Were Your 123s?: Building Connections Between Literacy and Numeracy is a great resource for those looking to learn more about using literacy strategies in the mathematics classroom.
Thank you for taking the time to explore this activity. I look forward to your feedback.
-Jay Harrington
