SWBAT identify relationships among different combinations of a number. SWBAT find a solution that fits the clues given in a story context.

Calling all Sleuths! Take out your magnifying glasses and get ready to solve some mathematical mysteries. Your young mathematicians will need to use the clues to try and solve each task. Good look Jr. Detectives and get to work!

5 minutes

You will need to make two copies of the ten frame cards that are in the section resource before you start this part of the lesson.

"I would like each of you to sit and face the smart board. Today, I am going to flash two ten frame cards at the same time. I will turn them over for three seconds and then cover them. I will give you a few seconds and then show you the same two cards again (for three seconds). Your job is to figure out how many dots there were in all. I will then display the cards (until finished with this round) and allow you to check your work. I would like you to explain how you figured out how many dots you saw. I will call on students to share ether thinking. You can then decide if it is who you solved it or if you used a different approach."

I will do this for cards that make ten (i.e. 6 +4). Repeat this several times. I am doing this so that the students ar practicing using their complements of ten and work on their fluency within ten (CCSS.MATH.CONTENT.1.OA.C.6).

15 minutes

I like to start this lesson with a magnifying glass (a big one) to capture the students attention and gain their interests in the lesson.

**"What is a detective? Have you ever seen a detective use one of these (pull out magnifying glass)? Why do detectives use this tool? Yes, it is to look for clues. Well today, you are all going to become math detectives. You will be solving story problems in which you will have to use clues to find the correct solutions. We will be finding combinations of Apples and Bananas (yesterday's lesson), however you will have to make sure that each combination that you create fits the clues given. **

**Let's try one together. I am going to team you up and give each of you 10 red cubes (apples) and 10 yellow cubes (bananas). I will then read the problem to you. Remember, I want you to visualize what is going on before you do anything else, so please focus on the information first.**

**I have 5 apples and bananas. There are more apples than bananas. How many of each could I have?"**

I will reread the problem and then ask students to explain what is going on in the problem (through the use of their visualization). I want them to understand that there are specific clues that they need to pay attention to (the total and the fact that there are more apples).

*"Did anyone notice the two clues that were given? Yes, there is a total of 5 and there are more apples than bananas. I am going to write those two clues on the whiteboard. *

*Now, your job is to work with your partner and figure out how many combination there can be. Remember it has to equal 5 but have more apples."*

I then give the students a few minutes to work together to solve the problem.

**"Who can give me one of the combinations that they found?"**

I will take each example suggested and then write it on the whiteboard. We will check each combination with the clues, to make sure that they fit. There is an example in the section resource of this chart.

30 minutes

I then hand out the 4 Fruit Mystery problems that are int he section resource. You will need to make enough copies for each student. I read the first problem out loud to the class, so that everyone is clear on the first one and can get right to work. I read the other problems to students as needed.

I will ask most of my class to work not his by themselves. I will put two of my students in a group and work with them as they try to work with this concept and task. First graders differ widely in how readily they can solve these kinds of problems. You will have to know your own group and manage the breakup accordingly.

**"I now want you to go and solve the 4 mysteries that are on your paper. Remember to underline the clues and check your answers to make sure they fit."**

As I was working with my group of two (these students need a lot of modification and individualized attention), one of the girls noticed that she could start with all of one type of fruit and then just add more of the other. I have included a video of her thinking in the section resource.

This student was able to generalize a structure/rule and apply it to her thinking. This allowed her to quickly solve the problem and to systematically create the combinations.

The students are meeting the CCSS practice standards by using quantitative reasoning by "creating a representation of the problem, considering the units involved, attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. (CCSS.MATH.PRACTICE.MP2)"

15 minutes

I gather the students back on the carpet and have them face the easel once again. I want to go over the first mystery.

"I want to reread the first mystery. I have 9 pieces of fruit. Some are apples and some are bananas. I have more apples. How many of each could I have?

Who can tell me a way they found a combination. Hannah said that she used cubes and that she used 5 red cubes and 4 yellow cubes. Let's see if that answer fits are clues. Does it equal 9? Are there more apples than bananas. Emma wrote the equation 5A+4B=9. Does this equation match what Hannah did?" In this case students are able to analyze the situation and can recognize and use counterexamples. They are justifying their conclusions, communicating them to others, and responding to the statements of others (CCSS.MATH.PRACTICE.MP3).

I continue to write examples given, connect them to other students' thinking and then check them with the given clues. There is a photo in the section resource of this chart.

5 minutes

During the last trimester of our school year, I want to really focus on fact fluency and build upon the students ability to solve within ten fluently (CCSS.MATH.CONTENT.1.OA.C.6). I am going touse the Mad Minute Routine. This is a very "old school" routine that some may question. However, I truly feel students need practice in performing task for fluency in a timed fashion.

You will need to purchase for own copy of the book in order to have permission to print this sheet and have copies of the additional sheets. It is a very cheap buy online.

**"Today we are going to start a new routine. It will involve you solving addition equations in a set amount of time. We will try and do this each and everyday that we have math class. I would like each of you to find a spot in the room where you can work by yourself. Once I give you your paper, I will need you to put your name on it. When I say go you will all start at the same time. I will give you 1 minute to solve as many problems as you can."**

To see a video of this in action or a sample fact sheet click here. This link will bring you to the lesson that I introduced this in. If you go to the Continued Practice section, you will find the resources in that section.

It is important that students obtain fact fluency for two reasons. In order for students to complete more complex tasks, they must have this fact knowledge in place. This way the focus is in the higher level skills and not on the basic computation. This fluency also allows for connection to additive reasoning. The other importance of fluency is that students who enter third grade lacking addition fact fluency, tend to struggle with the multiplication and learning those facts.