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We recently received feedback from our 7 year old daugther's school teacher. One of the things mentioned was that our daughter still counts her fingers when she does addition and subtraction. The teacher said that it is important to find other strategies which will save time and effort.

She doesn't have any trouble identifying ones, tens, hundreds, thousands, and she does addition and subtraction on paper when we stack the numbers on top of each other. So, the understanding of numbers and positions are in place.

Although I understand that counting fingers may not be the fastest way to do addition or subtraction, I'm not quite sure which / if other strategies are available to her / us?

Answers to a similar post on this site, although about younger children, seems to agree that using fingers are perfectly fine.

However, I'm curious to know if there are any "standard" ways out there to teach our daughter to do subtraction and addition in her head - without inventing our own system for that.

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  • $\begingroup$ "The teacher said that it is important to find other strategies which will save time and effort." "I'm not quite sure which / if other strategies are available to her / us." Did the teacher only identify a "problem" and offer no possible solutions? $\endgroup$ – Nick C Jun 4 at 13:59
  • $\begingroup$ @Nick C, no alternative strategies were offered in the written feedback. I haven't responded to that feedback, but wanted to be a little prepared and investigate some on my own as well before i did that. $\endgroup$ – sbrattla Jun 4 at 16:21
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    $\begingroup$ For numbers, written or imagined visually, can count points on the numbers, up for addition and down for subtraction. I saw this for numbers 1 - 4 in the 60's. A reference is touchmath.com/index.cfm?fuseaction=about.how $\endgroup$ – Tom Jun 7 at 21:09
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I have no problem with her counting on her fingers but here are 2 other strategies that she may find useful. These 2 strategies assume she can add 1 or subtract 1 without her fingers. If not she should learn that adding or subtracting 1 is just counting up or down.

  1. If she knows her doubles e.g. 3 + 3 or 8 + 8, then when she adds 3 + 4 or 8 + 9, she could realize that the new equations are just doubles plus one. Even if she doesn't know a lot of doubles, she probably knows that 5 + 5 is 10.
  2. When adding 10 + 7, she should recognize that you just have to put 7 in the ones place (although) she may not call it that) to get 17. Once she knows the trick for adding 10's, she can add 9's by adding 10 and taking away 1.

There may be other strategies listed in her book - it is worth looking or asking the teacher to suggest strategies. She should also know some of her facts by heart. In particular it is good to learn doubles and sums to 10 by heart.

When counting on her fingers, encourage her to start from one of the numbers and count up, so that if she is adding 3 + 9, she shouldn't count 3 and then another 9. Instead she should start at 9 and then count up 3 more using her fingers (10, 11, 12). This is faster and shows a greater understanding.

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In short: a standard expectation is that children of about your daughter's age should have memorized all sums of one-digit numbers. For example, here's the language from the Common Core Standards for Grade 2:

Add and subtract within 20.

CCSS.Math.Content.2.OA.B.2

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Nowadays this memorized, instant-recall knowledge is often referred to as "addition facts". It's a fundamental expectation to how our base-10 number system is designed to support operations like adding and multiplying large numbers.

When I was your daughter's age, the customary way of learning this was to get a set of flash cards with all of the combinations of one-digits addends and practice with those daily. Nowadays there are many more options (such as online games, phone apps, etc.) Here's one site with suggestions. You can internet search for the phrase "learn addition facts" for many more.

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Typical strategies include:

  • Memorizing sums to 10, e.g. $7 + 3 = 10$, then using that equation to determine $6 + 3 = \_\_$ or $7+4=\_\_$
  • Memorizing the doubles, e.g. $7 + 7 = 14$, then using that to determine $8+7=\_\_$
  • Decomposing/Recomposing. e.g. $9+8=10+7=17$
  • Using single digit facts to determine sums within 20. e.g. Since $3+6=9$, then we can easily figure out $13+6=\_\_$.

If these strategies do not seem obvious to your daughter after seeing them in symbolic form, then you should use ten-frames, linking cubes, and number tracks to help her visualize them.

Auction games are a fun way to practice a lot of this.

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    $\begingroup$ Small addition to this: Switching up the format makes the student learn subtraction without them knowing that they are learning something new, e.g. $7 + ___ = 10$ $\endgroup$ – Chris Cunningham Jun 12 at 14:15
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Play games: dice, board games, card games. So many of them include counting and "adding on". Or an online game like this one.

Play store, where you pretend to buy things.

Draw a circle numbered 1 to 10, and draw lines between the pairs that add to 10. Then decorate it. If she likes this, do a circle numbered 1 to 12, and connect the pairs that add to 12. Make up your own rules.

The idea is to make friends with the numbers, so it's not tedious. As Montessori said, "Play is children's work."

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    $\begingroup$ Nice drawing! A similar one gets rainbows on the number line. For a seven color version, draw arcs joining pairs of numbers that add to 14. $\endgroup$ – Jaume Oliver Lafont Jun 15 at 6:26

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