Children love to cook breakfast, and sometimes mathematical situations arise.
Child: How many pieces of bacon can each person have? There are ten pieces of bacon and four people.
Child: 2-4-6-8-10 but that’s five people. There would be two pieces of bacon each if there were five people.
The parent sets out the white board and marker, neatly tucked beside the kitchen for impromptu math. The child draws ten tick marks and 4 circles representing bacon and plates. He puts one piece of bacon on each plate, and erases 4 tick marks. He repeats this process, so now there are two pieces of bacon on each plate, and two tick marks left (see picture).
Child: How can we share two pieces of bacon with four people?
Parent: You could break them.
Child: Well, we can’t do thirds, because there are not three people.... Fourths! We could do fourths…(long pause)...Could each person get two fourths?
Child: Each person can get two fourths. That’s fifty percent.
Parent: How much bacon will each person get?
Child: Half...two and a half!
The child proceeds to put the actual bacon in four piles, with 2 ½ strips per pile.
Parent: Let me show you how else you could do this.
The parent shows a division procedure on the white board, relating it to the child’s picture. The entire episode takes about 5 minutes, and it is time to eat breakfast!
It is common for children to use trial-and-error thinking in deciding what denominator to use, as this child did with thirds and fourths. Moreover, children often shift from less advanced strategies to more advanced, and back to less advanced throughout their learning process. This child has previously learned a division algorithm, but for a division situation in real life, he gravitated toward a pictorial solution strategy. The value of this episode was not in learning a long division procedure, but for the child to learn to model a real-world story problem with math, and without math anxiety.
Equivalent fractions review was also part of this episode as the parent prompted the child to convert two-fourths (2/4) or 50% into a half (½).
Making mathematical connections is one of the biggest things parents can do for their children’s mathematical understanding. The added connection to the division algorithm learned in school could have been left out, but the child was game, and the process was not belabored. Breakfast was on its way!
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