Math Facts – An Easy Way to Learn Them

What is the best way to get students to understand number sense AND begin to do simple addition and subtraction problems?  Most math series that school districts contract with come with lots and lots of manipulatives! Unifix cubes,  counting bears, double-sided counters, place value blocks, geo shapes and so on until our shelves overflow with them!

 We are BIG advocates for using manipulatives with young children as these tools help develop a deep understanding of number and value and the concepts of More & Less and so much more. Even putting cubes on large charts of numbers help reinforce the value of each of the numbers (as seen here).

Once students have had an extensive amount of experience with cubes or small blocks to represent numbers up to 20 they are ready to start moving away from them.  They can start calculating with written numbers.  Since they haven’t memorized the addition and subtraction facts to 10 or beyond they often start to rely on using their fingers….those easy ‘manipulatives’ conveniently attached to their body! Unfortunately we only come equipped with 10 fingers so the problems they can solve are limited too. 

The solution is to move those cubes or small blocks ONTO the numbers and call them Tap ‘n’ Count places. There are specific spots on the numbers that correspond to each number’s value.  1 has one tapping spot, 2 has two, 3 gets three taps etc.  

How Do the Tapping Places work?

 By learning specific places to tap on each numeral, students can easily count UP (when adding) and count DOWN (when subtracting).  Each DOT on numbers 1-5 gets tapped once and each * on numbers 6-9 gets tapped 2 times.  Display the Colored Chart in the classroom or place it under a document camera. Print out the Black and white version and have students touch and count on their own copy to learn the proper way to tap ‘n count.

Practice “tapping ‘n counting” on each numeral over several days to familiarize the students with the “tap ‘n’ count” places. (Hints for remembering: 5 has a ‘belly button’ and 7 gets a ‘kiss on the nose’ to get that 7th spot counted!)  You must consistently tap in the same manner each time and soon the tapping places will become automatic.  Very quickly students will internalize these ‘places’ and be able to accurately complete math problems without using any dots in the numerals. That is the goal!

These  “Tap ‘n Count” spots serve as a scaffold for students when practicing early Addition and Subtraction skills. Tapping and counting accurately on the numbers in an equation will result in a correct answer every time.

Teaching the “Counting On” Strategy for Faster Addition

Once students have had lots of practice counting up with the tapping places on both numbers in the equation it is time to teach the “Counting On” strategy. Teach students to identify the larger of the two numbers in the problem, put that number in the head, and then “count on” the tapping places on the remaining number. Example: If the equation is 9 plus 4, students will say, “9”, then count on 4 more places saying, ” 10, 11, 12, 13. 13 is the sum!” This is the step that makes calculating a lot faster. Remind the students that the bigger number may be in any place in the equation. These tapping places work really well when calculating columns of numbers. Simply touch on the numbers in the correct tapplng places and count them up! Even Kindergartners are able to do column addition with several numbers! Talk with the students about identifying the larger addend in each problem, saying it, then “counting on” the other addend using the Tap ‘n Count places. Example: 7 + 3  say, “7, then touch the dots on the 3 and count up and say, “8, 9, 10”. This is the strategy called “Counting On” often taught in math textbooks. It is important students understand that the larger addend is not always on the top. Talk about the commutative property of addition (This property means that addends can be added in any order and the sum is always the same.) This is a precursor to algebra and young students can easily understand this property if it is shown using manipulatives a few times. Note: If both addends are the same, instruct the students to say either of the addends and “count on” while tapping on the second addend,  Ex 4+ 4  Say “4” and count on “5, 6, 7, 8”. 

Subtracting using Tap ‘n Count Places

Learning to count down (like NASA’s countdown to lift off!) is the way to teach students how to use the same tap ‘n count places to do Subtraction. When working on a subtraction problem the student says the top number and counts backwards on the tapping places on the other number. Children need practice counting down from any number under twenty. This can be practiced orally at numerous times of the day. Just call out, “Let’s count down from 15!” or “Let’s count down from 12!” Students are great at counting down from 10 but often get tripped up when counting down in the teen numbers. Stopping at a given number is essential to practice too! If the subtraction problem is “14 – 6” they must say “14, 13, 12, 11, 10, 9, 8 when tapping on the number 6! Also practice by counting down and stopping by writing the numbers as seen here.

There are no Tapping Places on the top number (the minuend) in a Subtraction problem as that is the number you say and then count down on the tapping places on the bottom number (the subtrahend).

The Final Step

The final step is to provide students practice doing problems with NO Tap ‘n Count scaffolds. Students should have progressed to doing addition problems fluently, having internalized the Tap ‘n Count places and relying on them as needed. They should also have practiced subtraction and counting down. The beauty of the Tap ‘n Count method is there is NO counting on your fingers AND if you can count correctly up or down you will achieve the correct answer every time! This will aid in memorizing addition and subtraction facts more quickly as “6 plus 7” will always equal “13” (and so on!)

Lots of Practice Pages!

We have created several Tap ‘n Count practice worksheets that are available at our TPT store. Click HERE to see them all under the math Activities category. Here is a FREE Sampler product to give you an idea of how the charts and practice sheets work.

We have created Tap ‘n Count packets for MANY themes. Here are just a few of them. Click on any cover to link to them at our TPT store.

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