I begin today by holding up a set of red and blue markers. I say that I have a set of markers. I ask students what fraction of the markers are red? I ask a student to write that fraction on the board. I repeat the question with blue markers.
Next I hold up a set of construction paper. Some are yellow and some are green. I repeat identifying the fractional parts of my set. I ask students to record the fractions in their math journals. I circulate around to see if students understand how to write the fractions.
Students were introduced to fractions in first grade. They have also now had several lessons where they have seen fractions written, and where they have labeled fractional parts. They are familiar with writing fractions for halves, quarters and thirds which is a Common Core Expectation.
I start today by inviting students to the rug. I turn their attention to the fractions we have just written for the markers and paper. I show them a castle dungeon on the bottom of the fraction and an arrow pointing North at the top. I introduce the terms numerator (escaping north), and denominator (the dungeon is at the bottom of the castle). I tell students that the dungeon (denominator) always has all the parts locked in so they can't escape or change in any way, but sometimes at the top the numbers try to escape north (we have been studying slavery so this terminology makes sense) and those that might escape are know as the numerator (and the N for north is like the N for the term numerator which is the top of the fraction while the D for the locked dungeon is like the D for denominator which is the term for the bottom of a fraction. I make sure students are comfortable with this new terminology.
I tell students that today they will create a treasure map with clues. The clues will be fractions of the treasure along the way. They will create a map and on the map they will draw places where part of the treasure is hidden. They need to remember that the bottom of the fraction is like the dungeon and it tells the total treasure of that kind that they have.
I hand them a sheet and ask them to decide on a number less than 12 for 4 kinds of treasure they will hide. They need to draw a picture of each type of treasure (it can be a symbol for it), along with the total number of pieces of that treasure they will hide. They will hide several pieces of treasure in the dungeon with no number attached so that their partners can figure out what fraction of the treasure is in the dungeon.
The treasure map will have hidden treasure for partners to find. When they have gathered all the treasure, they will need to figure out how many pieces of each are still in the dungeon.
I explain that they should decide how many pieces of gold, or jewels, or crowns or whatever they want to have and then hide part of that on the map and write the fraction of it. So if I decide to have 12 pieces of gold and I hide 3 pieces behind a tree what would I write? (3/12) In the dungeon of my fraction or denominator there are 12 pieces in all so I write 12. To the north of my fraction I have 3 pieces hidden so I write 3. Now I have 3/12 hidden behind the tree. If I want to hide more gold, I have to remember that I already hid 3 of the 12 pieces so I can only hide how many more? (9).
I make sure students understand that they are going to hide their treasure along the way, with a few pieces left hidden in the dungeon and not drawn or labeled. They need to draw the other pieces they hide, and write the fraction that is hidden there. I tell students they can use flaps to hide the treasure under so their partners have to look under the flap to gather the treasure. (See sample picture)dungeon picture sample.pdf
I ask students to draw a path with a castle at one end where they can hide the remaining treasure. Along the path they are to add trees, bushes, etc. with flaps to cover the treasure.
I know that the treasure is not really hidden in the real sense of the word, but students can enjoy creating the treasure map and pretending to hide things along the way. Students may even put "dummy" flaps along the way so their partners open the flap and nothing is there.
I tell them that later we will work in small teams to find the treasures and figure out how many pieces are still in the castle.
I give students time to complete their castles and then we share them. I start by asking for the class to bring their castles to the rug and lay them on the floor in front of them. Next I ask for a volunteer to show us his/her castle. We look for the hidden treasures and try to find all of each kind of treasure. We have to figure out what is left in the castle.
I give students time to figure it out and then I have students break up in teams of 4 to share their castles and find the hidden treasure.