Next, I had table partners push their single recipes together to show how to double the recipe. "How many cups of trail mix do we have now?" I asked. Everyone thought for a moment and then delightedly answered, "Three cups!"
We drew the recipe on graph paper showing one recipe, then doubled it for three cups, and doubled it again to represent six cups.
Leslie and Cristal show 3 cups.
Cesar's paper shows the solution for 6 cups of trail mix, which can also be written as:
4 x 3/4 cup of peanuts
4 x 1/2 cup of raisins
4 x 1/4 cup of chocolate chips
Galilea drew 4 times the recipe correctly, but added 4 cups plus 1/2 + 1/2 + 1/2 + 1/2 = 4 4/8, even though she multiplied 4 x 1/2 correctly.
All of the children struggled with how to fill in the table and ESPECIALLY with how to find the correct ratios for 3/4 cup of the recipe.
Alexis knew that fractions always have equal parts, so "all you have to do is put 1/4 plus 1/4 plus 1/4 and that equals 3/4." He also confused other parts of his table, even though his graph paper illustrations were correct.
Oh dear! I knew I had to think about this one tonight. How will I approach helping the children understand the step of finding 3/4 cup of the recipe?
Days 2 and 3 of trying to solve the Trail Mix problem
How can we find 3/4 of a cup of the recipe?
Everyone jumped into thinking about how to solved this. I was delighted to watch the culture of the classroom change as they began debating and challenging each other's ideas in trying to make sense of the problem.
Finally, Rigoberto said we could just cut the recipe in half and this would be 3/4 of a cup!
Rigoberto shows the class how 3/4 can also be written as 6/8.
Patricio exclaimed, "I see it! It's 1/8 cup of chocolate chips, 3/8 cup of peanuts, and 2/8 cups of raisins."
Although most of the children are still struggling with fraction concepts, I was so proud of their determination to make sense of the problem and find the correct solution!
Day 4 of Trail Mix
Collaboration and excitement filled the room all four days of this lesson, which is why I love the Common Core standards. Teaching this way takes much more effort, but is worth it, so take heart!
New friendships were being forged and new levels of trust developed as the children kept sharing their ideas with each other.
Jonathan and Jessi share ideas together.
To close the lesson, each group had a chance to present their ideas to the class. This is another important skill my bilingual students need to develop, and it helps build their confidence.
This time, several showed understanding of how to correctly fill in the table. Jessi saw that he only had to double the numbers again to go from 6 cups to 12 cups of trail mix. Galilea showed her work by multiplying each ingredient by a whole number to show how many times she increased the recipe.
I was also excited about Gabriela's work (shown below). She told me that you could not simplify 18/4 so I asked, "But how many fourths are in one whole?" Her face brightened. "I get it!" she beamed and circled each of the 4/4 in 18/4. Then she totaled this all up and wrote 4 1/2.
Whew!! We are starting to make progress!