Bar Fractions and Snowflake Fractions

1. Bar Fractions

This activity is adapted from Jo Boaler’s “Mindset Mathematics – Grade 5”, page 106. The only change we made is to use a bar rather than a square. We will use squares for a fraction activity later this week.

Step One (Concrete)

Pass out 5 blocks to each child: 2 Red, 2 Blue and 1 Green(or other color…) We use snap cubes, but any cubes will work. Alternatively, squares of construction paper will work.

Ask or write up this question: “Can you use some blocks to create a ‘train’ (‘bar’ if you prefer)? Red plus blue should be should be 3/4 of the train. The rest can be a different color.”

Some students will dive right in, others will show confusion, and ask “how many blocks can I use?” Don’t answer this except with the original (“I wonder, too….– the question says Red plus Blue should be should be 3/4 of the train. Is it possible?”)

Some students will hold up all 5 cubes. Say “hmmm… good start, but I don’t think Red + Blue is 3/4 of that…I think it’s 4/5…”

This reinforces (once again!) the crucial importance of the fact that 4 fourths make a whole, and 5 blocks are too many.

Soon someone will get it, and the solution will spread quickly. To keep them thinking, take 2 students’ trains, hold them up, and say. “It IS possible, look, these 2 students got different answers, so there’s not just one answer, there’s MORE than one!”


Screen Shot 2018-10-02 at 3.40.15 PM

Have someone verbalize what they see – both trains are 3/4 red+blue (and ¼ green) , but the order is different.  We say “Wow! I wonder if there are even more ways to arrange the cubes?'”

Step Two (Pictorial)

Pass out the CW assignment, (click here:  i CW redblue )  as well as red and blue pencils or crayons for each child. (or they can write “R” and “B” in the squares) Encourage each child to find the 4th’s on the CW sheet, and color it like their block ‘train’. Can they do the same with any of the other fractions? They should be getting used to using their fraction template, and seeing the equivalent markings of 4ths, 8ths and 12ths. If they have trouble with the equivalencies, lay a ruler (or piece of spaghetti) down at the 4ths markings, so they see that the 8ths and 12ths match.  (answer key: cw RB key)

For those students who work quickly, the last problem is challenging. Can they make an organized list? This is hugely important in later math classes, for example in probability.

2. Snowflake Fractions

This activity is also taken from Jo Boaler’s “Mindset Mathematics – Grade 5”, page 57.

We feel that 5th graders can never have too many concrete fraction experiences, and it’s great to find some that are enjoyable and teach the conceptual visualization of fractions well.

Process: We cut enough pieces of red (any color works) construction paper (6” by 6” ) so that each student can try this 3-5 times. The math is easier with a simple snowflake, but they might want to cut a more complex one, too.


Before cutting the snowflake, we had the students trace around the 6” square on a large piece of construction paper. (See photos below). After cutting a snowflake, they  then had to ESTIMATE the fraction of the missing paper in the snowflake, and finally try to find a way to support their estimate.

For example, the blue snowflake at right is IMG_1575missing eight small squares. The student estimated ¼ of the snowflake missing, and drew lines on the pink paper showing 4ths. The student then revised their estimate to 8ths, drew in new lines, and it fit very closely!

Students glue down the small cutout pieces onto their large construction paper square. We then play a guessing game where they hold up their snowflake, everyone guesses the fraction missing, and then the student holds up the large construction paper with the answer.

Finally, we display the snowflakes and the squares in the classroom.

1/9 : IMG_2481.jpg      5/9:IMG_5885

1/3:  IMG_8581   1/6:   IMG_7435

1/4:  IMG_6146         1/2?  IMG_1115




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