Patterns in a Calendar

 Most classrooms have a Calendar hanging somewhere on the walls, but I wonder how often we use it for a mathematics Investigation?

After seeing the date 22 2 22 (and making the previous blog) in made me think I should share more calendar ideas

There are many investigations we can encourage our students to do, from the very young 

            skip counting, Counting in Ones, 2's 3's etc

            Odds, Evens, 

            What do you notice about Monday 4th and Monday 11th? Is it the same for other days of                 the week?    Why?

To older students who may be able to add and multiply to find various other number patterns.

        7 times table

        Adding Seven

Depending on whether the students are working individually, in pairs or small groups, they should have a blank calendar in front of them.  

I encourage a THINK, PAIR, SHARE approach.  Each student has time to think, investigate on their own, then with a partner or the group discuss their findings and if necessary come up with a consensus, finally share with the larger class.  In my experience too many "quick thinkers" are the first to be asked for an observation, while the shy, plodders are never asked to share and they are are often embarrassed to share.  By discussing in a pair, small group it empowers all the group and they all own what will be shared with the class.!

Activity 1            Adding 4 Adjacent Numbers

Draw a square around the four numbers  4, 5, 11, 12. Now ask the students to add each of the numbers together 4 + 5, 4 + 11,  ... (they should get 6 number pairs) and see if they notice any patterns in the sums(answers)?

Try it with other adjacent sets of 4 numbers. Do you get similar patterns?

Extension:             a. Repeat for Multiplication       

                                b. I have just realised we could move into some Combinations and Probabilities (If                                 2 adjacent numbers give us 1 number pair, 3 adjacent numbers give us 3 number                                     pairs and 4 adjacent gives us 6, I wonder how many we get for 5, 6, 7  etc... (might                                 lead into generalisation of a rule- Algebra)

Activity 2            A Box around 9 adjacent Numbers on a Calendar

 Start with the question, "What patterns do you see in this set of 9 Adjacent numbers?" 

Possible answers might be:         Diagonals added together have the same sum

                                                    Diagonals and the Middle row and column have the same sum

            Please accept all answers and allow the groups to check the observations.

                                        "What do you notice about the middle number?" 

                            Its the average (Mean) of each row, column, and diagonal 

                                        "What do you think we might find in a box of 16 numbers? 

                    There could be a place for listing predictions and then checking these

Now the Clincher  

                            Just to show that you, the teacher, have some magic tricks up your sleeve!

 

1. On a piece of paper write the number 64 now put in to an envelope and tape it under a student's desk or chair (best done before school so know one sees you)

2. Put a box around the 16 numbers on the Calendar (as above) if you choose a different set of numbers then you will need to have a different number in the envelope

3.  Say to the class:  "I am going to ask you to do some things to this square of numbers so that we                                     leave just 4 numbers, which we will add together"

                                "I have Magic Power (or a Sixth Sense) and I will predict the sum of the                                             numbers you choose!!  Ready?

 

4.  Ask a child to put a circle around one of the numbers in the square (say 4)

        Now cross out the other numbers in the same row and column (If 4 is chosen then 11,18,25, 5, 6, 7 are crossed out

 

5.  Ask another child(or the same one) to put a circle around a number that is not crossed out

        (There are 9 to choose from)

          Now cross out the other numbers in the same row and column 

 

6.  Ask another child to put a circle around one of the last uncrossed numbers

          Now cross out the other numbers in the same row and column  - this should leave 3 numbers with         circles around them and one last number. Put a circle around this one

7. Ask the class to find the Sum of the 4 circled numbers

        Should be 64

 

8.   With a Magician's flourish or Abracadabra ask the student to look under the desk with the             envelope to open it and read out the number

    You will be inundated with Wow's and how did you do it.... Like all good Magicians dont tell them(if you know) how it was done 

 

Word of warning: Try it out with another staff member or your partner at home and prepare you Magician's lines.  I usually have a Cape, Pointed Hat, and a special Wand!!!