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.