Take the digits 5, 4, 3, 2 and 1, in that order. Using those digits and the four arithmetic signs — plus, minus, times and divided by — you can get 1 with the sequence 5 – 4 + 3 – 2 – 1. You can get 2 with the sequence (5 – 4 + 3 – 2) x 1.
The question is … how many numbers from 1 to 40 can you get using the digits 5, 4, 3, 2, and 1 in that order along with the four arithmetic signs?
You can group digits with parentheses, as in the example. There are no tricks to this, though. It’s a straightforward puzzle. How many numbers from 1 to 40 can you get — and, specifically, what number or numbers can you not get?
If the letter a= 1 cent, b= 2 cents, c= 3 cents, and so on up to z= 26
cents, how many $1.00 words can you make
Arrange all the integers from 1 to 9 in such a way that the numbers total
Here's an example:
12 + 3 + 4 + 5 - 6 - 7 + 89 = 100
You don't have to keep the numbers in order and you can use any
operations to get your answer.
How many combinations can you find?
The third graders have been hard at work. After learning about Chinese Numerals, Egyptian Numbers, Roman Numerals, and a variety of base systems, the third graders are ready to create their very own number system. They are working in pairs to develop a number system in a base other than 10. They are designing their digits, converting between systems, and computing addition and subtraction problems! They cannot wait to share their ideas with the class!
The third grade Navigate students have been busy exploring ancient number systems. They have learned to write in Egyptian and Roman Numerals. Both of these systems had their positives and negatives. The students found that Egyptians had a number system in base ten so it was easier to understand, but writing out numbers proved to be time consuming. During our discussions on Roman Numerals, the students realized that they needed to be very quick at mental math in order to figure out the values of the numbers. We discussed expanded form as well as the similarities and differences of our Hindu Arabic number system!
The first unit in third grade math Navigate will introduce students to a variety of number systems. To start the year off, we learned about and created Quipus. Quipus were used by the Incas to represent numbers at a time when a written number system did not exist. A series of strings and knots allowed the trained Camayos to read numbers and stories using the Quipus. This number system is similar to our own because it uses a base ten system. Each student created their own quipu, which proved to be a lot more challenging than writing out the digits in our number system! We used these quipus to answer the questions in the number stories that the students wrote to accompany their quipus.