Early Numeracy Slide Show from October 7th PD

Using Combinations of Ten to Increase Fluency

Applying known facts to figure out unknown facts results in efficiency, flexibility, and an understanding of number combinations in young students. A fluency approach to learning basic addition facts (such as using near doubles and tens) places a focus on developing and using mathematical strategies, with a goal on finding efficient, effective ways to apply known facts to derive unknown facts. (Kling, 2011)

Students who struggle to learn basic facts or who often forget certain facts should have an alternate plan to fall back on. This fall back plan allows for more complex mathematical thinking than simply counting.

Both speed and memorization play an important part in students learning of basic facts. Both are essential components of fluency. However, there is a difference between speed and efficiency: A student who can recall facts immediately is relying on speed and not on efficient use of strategies, whereas a student who needs a couple of seconds to mentally work through the fact is using a meaningful strategy is considered efficient (this does not mean simply counting up to the answer).

One such strategy that students should rely on is tens combinations. If a student is struggling with 6 + 5, for example, this students would rely on the known ten doubles fact 5 + 5 to get 10, then add 1 more to get 11. Or if a student has the problem 4 + 7, he can rely on the known fact 3 +7 = 10, then add one more to get 11.

In order to help students memorize these facts, it would be important to give them motivating experiences for them to engage in. Two games that can help with this in the younger grades are "Tens Go Fish" and "Turn Over Ten". Both of these games are based on two very favorite games that students in these grades tend to have: "Go Fish" and "Memory", respectively and are taken from the Investigations in Number, Data and Space (2008), Grade 2, but can be used in other grades to reinforce fluency.

Each of these games can be implemented into your math workshop in Grades 1 (beginning Unit 3) and 2 (Unit 1). Each game can be played with standard playing cards with the face cards taken out.

Here are the directions:

Tens Go Fish

(Played just like "Go Fish")

Purpose: Rather than looking for matching pairs, the students look for matching sets of 10. For 2 players.

Directions:

1) Each player draw 5 cards.

2) Player 1 asks for a needed card that can be added to another card in his deck so that the sum is 10. Example: If the student has a 3, he would ask for a 7.

3) If Player 2 does have this card, she hands it over and Player 1 lays the pair down. If not, she

says "Go Fish!" and Player 1 draws a new card from the pile and adds it to his hand. If Player 1 fishes his wish, he can then lay the two cards down.

4) Player 2 asks for a needed card that can be added to another card in her deck so that the

sum is 10.

5) Repeat step 3. Repeat.

6) The game is over once one student has laid down all of his cards in sums of 10 or there are

no more cards in the deck.

Turn Over Ten

(similar to Memory)

Purpose: To make pairs of 10 by playing a game similiar to Memory. For 2 players.

Directions:

1) Students set up 20 cards in a 4 x 5 array.

2) Player 1 turns over two cards, looking for a combination of 10. If a pair is found, the player

takes these cards and added to their pile. If not, the cards are turned back over and all players try to remember the previously turned over cards to help them find combinations of 10 in the future.

3) Place two more cards into the missing spots.

4) Player 2 takes a turn and repeats directions above. Play continues until all the pairs of 10 are found or all the cards run out.

Please refer to the article from Teaching Children Mathematics (source below) that was given to you for more information on addition fact fluency and other strategies to help with this important skill.

Information for this post was taken from Kling, Gina. "Fluency with Basic Addition." Teaching Children Mathematics Volume 18 (2011): 80-88.

Make Times Tables Fun? Yes You Can!

I came across a retweet of a blog post (Great Maths Teaching Ideas) I saw over this past summer that explains a fun game for practicing those tricky times tables! It also reinforces addition, order of operations and mental math. This can easily be made into a fun game that can be used during math workshop or as a game the students can play when they are finished with their classwork and need something to do!

It's called Damault Dice and an explanation of the game can also be found here on Math 4 Love's blog.

It's simple, really -no bells, no whistles. All you need are 3 standard dice. On your turn, you simply roll the three dice, add two of the them together and then multiply that sum by the last di. Piece of cake!

For example, I roll a 3, a 4, and a 6. I could either do (3+4) x 6 for 42 points, OR (3+6) x 4 for 36 points, OR (4+6) x 3 for 30 points. I’ll take the 42 points.

I spent some time playing this with my stepdaughter the other day and I saw that (1) it was genuinely fun, and (2) it gives you almost all the multiplication practice you could ask for. In fact, it gives even more, because the choice of which dice to add and which to multiply reveals some interesting structure of numbers. Seriously, get a kid (and an adult) hooked on this game, and it’s the equivalent of dozens or hundreds of times table practice sheets.

A couple other variations that I came up with:

• Use different sided dice (like 12 sided) to make it more challenging!

• To go past multiplying by sixes (and up to 12s) use four dice, taking the sum of each pair then multiplying that together? If I roll a 3, 4, 5, and 6, I can do (3+4) x (5+6) OR 12 x 11; (3 +5) x (4+6) or 8 x 10, and so on.

• To make it more interactive, allow a steal option. If a person makes a mistake in their computation, the next person can do a steal if he or she has the right answer! This way all players must be paying attention and also this reinforces their math fluency!

Or if you come up with any other variations, please post them! Talk about making math fun!

Math Professional Development Days!

We had our first math PD in years on August 25 and 26!

On August 25, we focused on the what, why and when of the Common Core State Standards. Teachers also learned about at the Mathematical Practices and applyed them into their first math unit of the year.

On August 26, K-5 Investigations teachers were introduced to the wonderful technology that Investigations offers. Teachers created log ins for successnet and saw the different teacher resources that were available on this website (including a complete FREE tie in to lessons and activities that teachers will need in order to teach to the CCSS). Teachers were also given Interactive Whiteboard Activities and Differentiation guides in order to be able teach Investigations effectively.

As we navigate through implementation of the Connecticut Standards (= CCSS) in grades K-2, and transitions 3-6, I will keep teachers up to date with all necessary resources and information through this blog and the Region #6 Elementary Math Wiki. Stay tuned!

It's a brand new school year and our little district is moving forward! Math's a priority!

There are many changes coming to math in the upcoming years as Connecticut has adopted the CCSS as our new frameworks. This means that by 2014-2015 we will be under a new grade specific standards for math. To make this transition easier on everyone, supports will be in place to help us move in the right direction.

This year's Kindegarten class will not take the CMT as we know it. A new test(s) will be in place, and as that information comes, it will be given to you. To start making a smooth transition, the district has decided to move forward with implementing the CCSS K-2 this school year. Grades 3-6 will begin implementing CCSS into their units.

This year it is important to learn and practice Math Standards for Mathematical Practice (this can be found on pages 6-8 on this link below). We will be learning about and discussing these on our first PD day.

For more information on the new math standards and practices check out the Mathematics Common Core State Standards.

It's going to be a great year for math!