# Ten Frames Part 2: Addition and subtraction

Last week’s focus was on using ten frames to help with students’ number sense and conceptual development of number bonds for amounts 1-10. This post will feature ways to use ten frames to enhance students’ understanding of addition and subtraction. Look for freebies and a video!

There are many addition and subtraction strategies to help students memorize the basic facts such as these below. The ten frame is a very good tool for students of all grade levels to make these strategies more concrete and visual. I will focus on some of these today.

• add or take away 1 (or 2)
• doubles, near doubles
• facts of 10
• make a ten
• add or sub. tens and ones

Doubles and near doubles (doubles +1, -1, +2, or -2): If the doubles are memorized, then problems near doubles can be solved strategically.

• Show a doubles fact on a single ten frame (for up to 5 + 5).  Use a double ten-frame template for 6 + 6 and beyond.
• With the same doubles fact showing, show a near doubles problem.  This should help students see that the answer is just one or two more or less.
• Repeat with other examples.
• Help student identify what a doubles + 1 more (or less) problem looks like. They often have a misconception there should be a 1 in the problem. Make sure they can explain where the “1” does come from. Examples:  7 + 8, 10+11, 24+25, 15 +16, etc.
• For subtraction, start with the doubles problem showing and turn over the 2-color counters or remove them.

Facts of 10: These are important to grasp for higher level addition / subtraction problems as well as rounding concepts.

• Place counters on the ten frame. Determine how many more are needed to fill in the ten frame. This also helps with missing addends.  Example:  3 + ___ = 10.  Ask, “What goes with 3 to make 10?”
• Using 2-color counters, fill the 10 frame with 1 color. Then turn over some to reveal a number bond of 10 (such as 4 and 6).

Shake and Spill

• Play “Shake and Spill” with 10 two-color counters.  Click on these links for Shake and Spill Directions and a Shake and Spill recording page. Basically, the student puts 10 of these counters in a cup, shakes it, and spills it out (gently). Count how many red and how many yellow. Repeat 10 or more times. Keep track of the spills on a recording sheet. Which combination came up most often? Which combination never came up? What is really nice to observe is if a student spills counters and sees  6 are red, do they know automatically there are 4 yellow, or do they still have to count them?
• Since number bonds enable a student to see addition and subtraction problems, the second bullet above will serve subtraction problems very well.  Start with 10, turn over 7 to the yellow side. How many counters are red?

Make a Ten: This strategy builds on the above (facts of 10) to help with problems with sums between 10 and 20. Students should readily be able to solve a problem such as 10 + 4 mentally first.

• Use 2 ten frames (see Ten Frames part 1 for a link for templates)
• Let’s say the problem was 8 + 5.  Place 8 counters on one ten frame, place 5 on the other.
• Move counters from one ten frame to fill up the other.  8 + 5 is the same as 10 + 3. The problem 10 + 3 should be a mental math problem. Students will need to see that counters were not added, but shifted from one ten frame to the other.
• Repeated practice with this concrete activity helps children think more deeply about the relationship of numbers.

Continued practice with these strategies:

1. During your daily math meeting, flash ten frame dot cards to students in which they must use the above strategies. Use it as a # Talk sessions so students can verbally explain how they solved it.
2. Try this from NMCT Illuminations sight (National Council for Teachers of Mathematics): Interactive ten frame
3. Watch this video of a teacher modeling the Make-a-Ten strategy: Make a ten video using ten frames
4. Learning stations:
• With a blank ten frame, create doubles and near doubles problems. Or look at flash cards and make those problems.
• Show a partially filled in ten frame. Student must tell their partner how many more are needed to fill it in.
• Give students flash cards for problems with answers between 10 and 20. Show each addend on a ten frame and use the make-a-ten strategy.

Share your experiences with ten frames!

# Addition and Subtraction Part 3: Facts Strategies KG-3rd

This is part three in a series of strategies regarding addition and subtraction strategies.  This part will focus on a variety of strategies to help toward memorization of facts, meaning automatic computation. While children are learning their number bonds (building up to 5 in KG, to 10 in first grade, and to 20 in second grade), there are other facts which cross several number bonds that students can work towards. These strategies to build mental math automaticity are highlighted below. Get some freebies in the section on doubles / near doubles.

Identity (or Zero) Property:

• The value of the number does not change when zero is added or subtracted.
• 3 + 0 = 3
• 9 – 0 = 9

Subtracting All:

• The answer is always zero when you take away / subtract all.
• 9 – 9 = 0
• 50 – 50 = 0

• Adding 1 results in the next number in the counting sequence.
• Subtracting 1 means naming the number that comes right before it in the counting sequence.
• With manipulatives, lay out an amount for student to count.  Slide one more and see if he/she can name the amount without recounting.
• Do the same as above, but take one away from the group to see if he/she can name the amount without recounting.
• Show this concept using a number line.
• 6 + 1 = 7;    26 + 1 = 27
• 7 – 1 = 6;     37 – 1 = 36
• After +1 or -1 strategies are in place, then go for +2 or -2 for automatic processing.

Next-Door Neighbor Numbers:

• If subtracting two sequential numbers (ie 7 subtract 6), the answer is always one because you are taking away almost all of the original amount.
• Help students identify these types of problems:  8-7;   10-9;   98-97;  158-157
• Guide students to writing these types of problems.
• Relate these to subtracting 1 problems.  If 10-1 = 9;   then 10 – 9 = 1.
• Show on a number line.