Multiplication Fact Fluency
A plan for intermediate classes
Our instructional time is precious, taking time out each day to learn and master multiplication facts may not seem like high priority work. In this situation, it’s a case of pay me now or pay me later. The sooner this work is accomplished, the easier it will be to get to the real work of mathematics. It helps to have children see math facts as simply a tool to do real work. We need tools. In the same way learning to use a stove is only necessary so you can cook food, or a saw so you can build something, math facts are a tool to do the real work of math, solving problems.
Fluency Multiplication 4/5
The process of acquiring math facts occurs over an extended time period. The process requires large amounts of time devoted to manipulating and working with objects and numbers. Working with some of the critical concepts in elementary mathematics :
counting and counting groups,
unitizing,
using strategies such as complements, doubling, halving etc.
building and modeling with
number lines,
arrays,
open arrays,
students should acquire much of their fact knowledge thru experience, strategy and relationships rather then rote memorization.
Math facts can be likened to sight words, they must be known so students can attend to higher order processes. Students will need some help securing their facts especially as we transition to the new Common Core Standards. Beginning this year the standard for multiplication fact fluency thru 10X10 is in third grade. Some of our fourth and fifth graders will have not yet met that standard. The following is presented to assist filling in fact knowledge NOT as the primary instructional tool.
The Math Fact Running Record
We need to assess where each student is with regards to aquiring their math facts. We often we try to do this by means of some sort of many problem fact test. There are many issues with using the timed or even the untimed version of a fact test. When a student does this independently we have no record of which facts they know or how automatically they know it. Did they recall, count, skip count, add, did some take 3 seconds and some 5 seconds? Is their handwriting or pencil grip causing a problem? The paper does not provide any detail. Additionally, wrong answers are being practiced and thereby reinforced. For some students the fact test can be a particularly discouraging experience. There are good uses and procedures for using the timed fact test but the process of acquiring facts needs to have structure and the students need to understand the process so we can maximize the results.
Begin by doing a one on one math fact running record for each student. (see appendix A) The student does not write, the administrator of the assessment does the writing. You need two copies. (see video #1) http://www.educreations.com/lesson/view/math-fact-running-record/1244714/. Select a confident student to do a class demonstration the first time to shorten the time needed to explain in depth to each student. Say this to the student:
“Today we are going to do a quick check to see where you are with learning your math facts. You and I need to know exactly which facts you know and which ones you need to work on so that’s what we are going to figure out. You are not going to have to do any writing.
You will look at each problem and just say the answer if you know it. (show the sheet). For example, this first one, you’ll just say 4 and go to the next one.
It’s fine if you don’t know it, you just say “skip”. If you don’t say the answer in a few seconds, I will say the answer and you go to the next problem. Remember we are looking to find which ones you know with no “figuring”. Please do not say the problem, just the answer. Do you have any questions?” (stop students who are repeating the problem, it’s a thinking/processing delay tactic- answers only)
The student places their finger on #1 and says the answer. You have three choices:
- It’s correct, you do nothing
- It’s incorrect , you write what they said and draw a line thru the incorrect answer
- They take longer then 3 or 4 seconds and you say the “ANSWER” and “NEXT”, you circle the problem number
The student continues down the page
When you get to the bottom of column one say, “The first column is a little easier then the second, they’ll get a little harder now.”
When they are done, take a highlighter and run a line through anything that was answered incorrectly. Those need to be addressed first. Next highlight anything that was skipped.
When you are done you have a record of what is known and what needs to be learned. Patterns are quickly visible, for ex. they have nines but no eights, they know everything thru time five but nothing higher etc.
Now you have a document to make a plan for each student. Keep this document. This is an excellent way to show students how much progress they have made as the year goes on.
I find it best to have students work on memorizing no more then two facts at a time per week. If possible they should contain four different numbers. For example when students work on two problems with a six in them, they often jumble them up. For this reason working on a fact family all at once can be confusing.
From the list choose some facts with small numbers first. If you choose 3 X 4 =12 and they learn this one, when they get to 6 x 4= 24 it’s easier to learn because it is a double of a fact they know. This is a very important strategy in acquiring math facts “Because I know …… I know …….”
Pick two incorrect problems for each week’s practice. Start with any problems with small numbers. In the margin of the See It ,Say It, sheet next to the first two problems you pick for practice, write #1 or week #1, pick two more and write week #2 in the margin. Assign a week number to every two facts they missed. Have the student make an index card for each of this week’s two problems with the problem on one side without an answer and write out the fact family on the back with answers. They should write large, fill the card. Students will accumulate a set of cards for continuing practice.
The first few times you do this, you probably want to decide on the order of problems on your own and then bring it back to the student to assign. You will very quickly get proficient at selecting the order of problems each student should work on.
Keeping in mind that a fact test is an assessment, it is not instruction, what can we do about learning the facts?
“See it, Say it, Write it”
Each student should now have two facts to work on. For homework you can provide a “See it, Say it, Write it” sheet. (see appendix B) . In the left column in class on Day One, the student writes out the fact family twice for each of the two facts. This page provides five days practice in 3 ways. Each evening the students are to rewrite the two fact families two times each while saying them aloud. Demonstrate this, don’t allow students to skip the oral recitation part, it’s like learning a song, the more you hear it, the deeper it is embedded. At week’s end they have written and said each family six times
Suggestion: demonstrate this for your whole class by picking two facts, say 3 X 4 and 5 X 7 and together do the first week entirely in class each day this week. This will assure everyone knows how to do this correctly and has a completed week’s work as a reference sheet. Send it home with the parent letter.
See Parent Letter Appendix C.
Circles and Stars
After completing the running record you have a pretty good idea of how you can pair up your students for some fact practice games. Students should play with an academic peer. (Some pairs may need a multiplication chart and or closer supervision to be sure we are not practicing incorrect facts). Students who have not mastered most of their facts by fourth and fifth grade may have not had the opportunity to see the numbers they are trying to manipulate. They may be struggling with 5 x 3 because they cannot mentally construct five groups of three and the abstract numbers 5 times 3 are meaningless. Backing up to a more visual flashcard is helpful. Circles and Stars is one method. (See Appendix D)
Each card contains a number of circles. In the example below, five circles. A student can quickly see the card is a “5”, five circles. Each circle contains stars, in this case, 2 stars per circle. When shown this card, the student response is “5 groups of 2 are 10” or “5 times 2 is 10”. Use both phrases often and interchangeably.
To Play ( see video #2) http://www.educreations.com/lesson/view/playing-circles-and-stars/1244801/
Start with the standard cards of 1 group of 1 thru 6 groups of 6.
Have students look at the patterns of the arrangements. It is the same for the circles and the stars. Even numbers are in two rows. Getting familiar with how each arrangement looks, helps students immediately recognize the number (subitize). They will quickly recognize what five etc. looks like and later a seven or eight etc.
Two students sit side by side with a set of cards, two pencils and a Circle and Stars recording sheet between them.
They turn over a card and the first one to correctly name the card “10” scores one point. The other scores 0. Both students write on line one on their side of the paper “5 x 2 = 10” No matter who gets the point they both write.
Ten cards is a round, if it is a tie, play one more. If it’s still a tie, both win. If they can’t decide who answered first, both score a point.
If students are well matched, some may be counting stars individually or skip counting, while other partners are flying. You can remove cards from teams if you want them to concentrate on certain facts or add higher number cards to teams who are ready.
After 3 or so days this becomes a 5 minute or less routine kids can easily manage on their own.
Suggestion: add only 2 or 3 new cards at a time
Suggestion: Make a chart of players by team, score a point for the winner each day. In an effort to discourage laggards, each day the team that finishes and is cleaned up last, scores no point.
Quick Practice – Dice or Cards (A,2-9 and Jack for 10) ( see video #3)
http://www.educreations.com/lesson/view/fact-practice-with-dice-or-cards/1244851/
- matched partners
- two (six , eight or ideally ten sided dice) (any math catalogue)
- eleven counters of some kind, poker chips work great
suggestion: small very clear Tupperware containers let you roll the dice without taking them out of the container, shake and place top down and you can see the dice otherwise use rubberized placemat or shoebox top to contain dice. Lose a coin if your dice hits the floor.
Keep a set of eleven counters and cards or dice in a basket or shoebox lid so they are always ready to go
To Play
- Students take turns rolling the pair of dice.
- The first student to respond correctly takes a counter and says the number sentence aloud, the other student repeats it. If the winner doesn’t say the sentence, he forfeits the counter.
- the students roll, recite and score until all the counters are gone
- ties, counter goes to both players
Suggestions:
- Some teams should have a number grid to check
- Make a chart of players by team, score a point for the winner each day. In an effort to discourage laggards, each day the team that finishes and is cleaned up last scores no point.
- If one player wins or loses by a large number each day, repartner some teams
After 3 or so days this becomes a 5 minute or less routine kids can easily manage on their own.
Other More Pictoral Flashcards
Also included in the appendix is a set of flashcards which have numbers, pictures and strategies right on the cards. Some teachers and students may prefer to use these. (See Appendix E)
The Timed Test
fact test is an assessment, it is not instruction
The timed test can be used more productively. When we ask students to complete one of these tests we need it to produce useful information for them and us. The key is getting students to recognize which facts they “know” and which ones they are still “figuring out”. Students have difficulty understanding why when they can use a strategy ( 8 x 3=? I know 4 x 3 = 12 so I know the answer is double, 24), which is how we construct and eventually memorize the facts, at the moment we count this as something they “don’t know yet”. The student is still “figuring” it out, it is not yet “automatic”.
It requires a lot of demonstration to get students to the place where they will take a fact test and answer the ones they know and skip the ones they don’t know “automatically”. We ask students to be thoughtful and tenacious and problem solve BUT NOT HERE. Here we want just data.
Suggestion: Have one or two confident student demonstrate this with you for the class. Be sure they are prepped for “know vs. don’t know”. If they are calculating say SKIP IT
Procedure:
Select a time appropriate to the number of problems
Year end goal for 100 facts - 3rd- 5 min., 4th- 4 min., 5th - 3 min. ( ½ to use 50 facts)
Project a timer like this one http://www.online-stopwatch.com
Students will begin in pencil and work left to right completing as many as they can (they should not be skipping around )
• turn over and begin,
• work until the goal time is called
• draw a line to show where they ended- call it the TIMELINE
• students switch to pen and keep working to completion including the problems they skipped over