The Road the Fluency

Recently I've been doing a bit of research on the best way to help our students become fluent in addition and subtraction. I know many of you reading this are probably saying,

"Hey Elizabeth, that's easy! Make them MEMORIZE their facts. That's how I learned them. It's hard at first, but they'll get it eventually."

While you may be right, I stumbled upon this lovely statistic while reading up on different studies done on memorization and the effectiveness of memorization as a strategy. In a study conducted by Henry and Brown in 2008 showed that only 11% of students made progress toward the memorization standard that was equivalent to their progress in the school year. That means 1 in 10 students didn't memorize as many facts as they should have in comparison to the progress they made overall. What's more is that this study was conducted in some of the highest performing schools in the nation.

So if only 11% of kids in these high-performing schools are able to adequately memorize information, how can we expect our "average" student to do the same? Instead, I propose we teach our students to THINK for themselves rather than memorize information. Sounds great right? So where do we start?

After reading many MANY more articles and several soul-baring discussions with other educators, my answer to that question is actually pretty simple. Use tens frames.

Yes. The simply array of 5 x  2 squares can help lay the foundation for fact fluency if implemented correctly! Kind of makes you think that the person who came up with the K.I.S.S acronym may not have been too far of the mark, huh?

According to Van de Walle (2003) we should begin to teach students about numbers and number relationships with a five frame (a tens frame cut in half). With the five frame, students work within 5 to discover the relationships of the numbers 0-5 and 5.

For example, if you asked a child to put three counters on their frame, they would have two empty spaces. The relationship between three and five is two ( 3 + 2 = 5, 5 - 2 = 3). Instead of giving you these equations students might say something like "well I have three counters. I have two empty spaces. So if I put two more down, I would have five counters." These are the connections that we want students to start making. After a fair amount of practice with a five frame, students can then progress to using a tens frame. Students need to continue to look for the relationships between the number given by the teacher (say 7) and the numbers 5 and 10 ( 7 is 2 more than 5 but 3 less than 10). These are the building blocks for fact fluency.

Figure 1: Example of a tens frame that may be used by students in the lower elementary grades to build fact fluency and a basic understanding of the concept that ten units is the same as one “ten”.

Try the following activities with your students. Make sure to have your students talk or write (even better: talk AND write) about the connections they see between numbers. Once students are fluent in the relationships between numbers 0-10, then we can start talking about introducing equations into the picture. Keep in mind that familiarity with the tens frame and numerical relationships are KEY!

Activity 1: Five-Frame Tell About

·          Standards Addressed:

o    K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5

·         Materials: five-frame (a halved tens frame), 10 manipulatives (cubes or coins)

·         Tell students that they are only allowed to put one manipulative in each square on the five-frame.

·         Ask the students to show the number 3 on their five-frame. Ask students to share what they can learn about the number 3 from their mat. After hearing responses from several students, guide the discussion on to other numbers 0-5.

·         Any response is correct. For example, a student may put two manipulatives on each side of the five-frame, leaving a space in the middle. This may result in a response such as “there is a space in the middle” or “four is two plus two”. (Van de Walle, 2003).

Activity 2: Ten-Frame Tell About

·         Standards Addressed:

o   K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5

·         Materials: tens frame, manipuatilves (cubes or coins)

·         Students are told that only one manipulative may be used in each space.

·         The teacher asks students to create numbers 1-10 on their tens frame, and guides students in discussing the relationships between the number shown and 10. For example, if students are working with the number 6, a student may respond that “6 is 4 less than ten” or that “4 more than 6 is 10.”

·         Students may also relate numbers to five. For example “6 is 1 more than 5” is also an appropriate response. By relating numbers back to five, students increase the number of connections between numbers and their fluency in those relationships. (Van de Walle, 2003).

Activity 3: Crazy Mixed-Up Numbers

·         Standards addressed:

o   K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5

·         Materials: tens frames, manipulatives (cubes or coins)

·         The teacher calls out numbers 0-10. Students make the number on their tens frames using the manipulatives.

·         This activity may be adapted to for lower-level students by working with a five-frame. Students may also play the game independently. Prior to playing independently, each child makes a list of 10-15 numbers to call out to their peers. One child acts as “teacher” calling out numbers. After their list is exhausted, another child may take the place of “teacher” and continue to call out numbers (Baratta-Lorton, 1976). 

Activity 4: Tens Frame Flash

·         Standards addressed:

o   K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5

·         Materials: playing card-sized tens frames showing numbers 1-10

·         Students take turn flashing the cards to their partners. The partner states the number shown on the card as quickly as possible.

·         If the student is correct, he or she keeps the card. If the student is incorrect, the card is returned to the deck. The game is played until the student has earned all the cards. Partners then switch  (Van de Walle, 2003).

Activity 5: Interactive Tens Frame and Fives Frame

·         Standards addressed:

o   K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5, K.NBT.A.1

o   1.OA.B.3, 1.OA.B4

·         Website: http://illuminations.nctm.org/Activity.aspx?id=3565

·         On this website, students interact with a digital tens frame or five frame. The website prompts students with instructions or questions such as “How many circles are there?” or “How many boxes are empty?” The student responds with his or her answer by either clicking numbers at the bottom of the screen or by typing in the number.

·         Other variations on the game include building numbers, adding manipulatives to make a larger number, and adding two numbers together.

Activity 6: Interactive Tens Frame

·         Standards addressed:

o   K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5, K.NBT.A.1

o   1.OA.B.3, 1.OA.B4

·        Website:http://www.curriculumsupport.education.nsw.gov.au/countmein/children_butterfly_ten_frame.html

·         On this website, students see a tens frame filled with colorful butterflies. Some of the butterflies fly away. The student must name how many butterflies fly away and how many are left over.

Thanks for reading, and thanks for being a mover, a shaker, and a difference-maker!
-Liz


To read the Henry and Brown article in its entirety, click here: http://www.jstor.org/stable/30034895