Open Middle®
Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create as many fractions as possible that are less than one half.
Hint
How can you tell if a fraction is less than one half?
What patterns do you notice?
How can you be certain you have all possible solutions?
What patterns do you notice?
How can you be certain you have all possible solutions?
Answer
16 fractions less than one half
1/9, 2/9, 3/9, 4/9, 1/8, 2/8, 3/8, 1/7, 2/7, 3/7, 1/6, 2/6, 1/5, 2/5, 1/4, 1/3
1/9, 2/9, 3/9, 4/9, 1/8, 2/8, 3/8, 1/7, 2/7, 3/7, 1/6, 2/6, 1/5, 2/5, 1/4, 1/3
Source: Christine Newell
I’m curious as to why you are counting equivalent fractions separately in your answer. Since 2/8 = 1/4 and 3/9 = 2/6 = 1/3, I initially found only 13 fractions.
Just seeing this. I would count them as separate answers because although they are equivalent, they have a “different number and size of parts” which is language that comes from a 4th grade standard. A question on the equivalent fractions students find would be a great follow-up question, though!
yea 4th grade can be a challenge and there is hard questions i’m still kinda stuck on whats something less than 1\2 i wish i did not have to do math the only math i’m really only good at addition subtraction and multiplication
I still wonder what this means lol
Christine Newell is right I am a 4th grader and I dont get these so I just wrote them down
Your answer uses the digits more than 1 time. Are they just meant to be possibilities?
WHAT are THREE fractions that are less than ½?
Nam
e THREE fractions that are greater than ½?
2\48 1\48
1/4, 1/3, 1/6, 2/6, 1/8, 2/8, 3/8, 1/5.
I love this one for exploring structure and patterns with my 5th graders. Used this with BTC & followed with “how can you be sure you have all the answers.” Fruitful discussions about how they organized their solutions to make patterns more visible. Some organize by numerator, others by denominator – and both also reinforce ordering fractions. Thanks for this very rich task!