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How to Teach Counting and Problem-Solving Learning to Count in Early Childhood Part 5: Intermediate

Updated: Nov 26

Check out the other posts in this series! Emergent Part 1, Perceptual Part 2, Figurative Part 3, Initial Number Sequence Part 4, Facile Number Sequence Part 6.

Get the full overview in one place! Presented at the Making Math Moments Summit, you can get the full presentation here!

If a student is in the Intermediate Number Sequence stage of counting they can use a variety of strategies to solve subtraction problems. Students in this stage of counting are able to choose the most efficient count down from or count down to strategy.

A “count down from” strategy example is 18-5=, and a student would count 17,16,15,14,13, tracking in such a way they would know the answer is 13.

A “count down to” strategy example is when part of the problem is missing (subtrahend) and a student counts down to figure out the problem. Ex, 15- ___ =9. A student would count down from 15…14,13,13,11, 10, 9…6 are taken away.

This stage is similar initial counting stage, but their ability to solve missing subtrahend problems is indicative of this stage.

What do I look out for?

Students at this stage are similar to children in the previous counting stage

• Can keep track of their counts when solving problems, knowing they need to track and ability to accomplish it is a marker of this stage.

• Can count to forward to 100 by ones and beyond and tell you the number after without dropping back

• May be able to count backward from 30 but maybe not 100

• Recognize numbers to 100 but may make some reversal errors, calling 37 seventy-three

• May be able to name some 3-digit numbers like 527, but 502 may cause a mistake since there is no number in the tens place.

• They may be able to skip count by 10s on the decade (10, 20, 30) but not off the decade (14,24,34)

How can I help students in this stage of counting?

Whether through number talks with related number strings, or hands-on problem-solving, opportunities to make connections between problems and time for verbal processing will support students in this stage of counters focusing specifically on subtraction and missing subtrahend problems.

Number talks are an excellent way for students to hear other students thinking, and perhaps apply other students’ strategies. With opportunities for a variety of collaborative problem-solving, students can talk more deeply about the strategies they are using and through that, start to

Creating Problems for this Stage of Counting

This stage is more about applying their counting skills to solving problems. Students need opportunities to think creatively about problems, numbers, and their relationships to each other to develop their sense of number.

Regarding choosing numbers for word problems and number strings, choose numbers where the difference is in the range of 2-5 also known as the “count number.” The range of numbers is small so students can focus on developing strategies vs long strings of numbers to count.

While the counting range is 2-5, numbers can be any from 8- ___=3 or 78- __ =73. Students with a good understanding of finger patterns will use them to keep track of their counts in addition or subtraction tasks.

Activities for this stage of counting

Skip counting

Skip counting just like regular counting can be an abstract idea if students haven’t had a lot of practice with counting and why you might use it.

Abstract ideas need to be made concrete first for understanding. If students can see that there is value in a skill it makes more sense.

One way to bring skip counting to life is by a math task like dice skip counting. In this collection of math tasks, students are given an image of dice and they have to figure out how many pips (dots) are shown in the picture.