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### Flower Petal Puzzles

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#### Overview

Materials: Worksheets, pencil and scratch paper
Common Core: 1.OA.A.2, 1.OA.C.6, 1.OA.D.8, 2.OA.B.2, MP1, MP7

Put each number in a “petal” so each line of three numbers in a row has the same sum.

#### Why We Love Flower Petal Puzzles

This is a simple but thought-provoking puzzle.
It’s a great way to encourage students to make mistakes and learn from them in order to arrive at a right answer in the end.
A fun structure to explore and build on, this is skills practice embedded in a more rigorous and interesting puzzle.

#### The Launch

Draw the “flower” drawing and explain that it is possible to put the numbers 1 through 7 into each “petal,” using each number exactly once, so that each straight line adds up to 10. Take suggestions from students about which number could do where, making sure that a “1” does NOT go in the center. With student input, get as far as you can until you are stuck. Then distribute the template and let students try on their own.

Example Conversation

Teacher: I’ve heard that it is possible to put the numbers 1 to 7 into the petals of this flower to make every line of three petals add up to 10. How can we do it, I wonder? What number could we put in the middle?
Student: Three?
Teacher: Let’s try it. I’ll cross the “3” off my list of
numbers, since I want to use each number only once. Now what could I put in this next petal?
Student: I don’t know.
Teacher: I don’t either. But let’s try something and see if it will work. We can always erase later.
Teacher (writing in 6, and crossing it out from the list of
numbers): Ok, now we have a 6 and a 3 in one row. What should we put in the last petal to make 10? In other words, if we add up 6 and 3, what more do we need to add to make 10? Think about it, then pair and share.

[Kids think and discuss]
Student: It has to be 1.
Teacher: How do you know?
Student: Because 6 + 3 is 9, and then we need one more to make 10.
Teacher: Aha! I’ll put that in too, then. So what can go here?

[Teacher continues until it becomes clear that the flower petal puzzle CANNOT be solved.]
Teacher: Hmmmm… it looks like this isn’t going to work. Maybe we should have put a different number in the middle.

What number would you try? [Students give suggestions.] You know what, let’s go ahead and try it out on our own. I’ve got empty flower petal pictures right here (passes out the empty template). Try out different numbers in the petals and see if you can get each row to add up to 10. When you can solve that, I’ve got some followup challenges for you too.

• Challenge 1: All lines add to 10.
• Challenge 2: All lines add to 12.
• Challenge 3: All lines add to 14.
• Challenge 4: Students make their own Flower Petal Puzzles.

#### Tips for the Classroom

1. Hints: put a 1 in the middle to make each row add up to 10. To make 12s, put a 4 in the middle. To make 14s, put a 7 in the middle. Start with the entirely blank templates. If kids need extra help, you can pass out the partially filled in templates.
2. Students can use counters to try moving numbers around if they need a more concrete look at the puzzle.
3. If students don’t know what to try when they make up their own puzzles, encourage them to try drawing a flower with more petals, or give them the template with more petals and ask them what puzzle they can make from it.
4. If you can motivate students to create their own puzzles, this can be the start of an even richer exploration.