This unit is made of 4 lessons. Each lesson includes full explanations for teachers and activities for students including printable journal pages for practice and learning games; the entire unit is designed to help foster number sense, mathematical communication, and discovery-based learning.

Lesson 1 begins with number recognition from 1 – 10 focusing on building numbers in groups of 5. It then moves up to recognizing and building numbers up through 20.

Lesson 2 focuses on addition up through 20 with an emphasis on combinations of numbers that add to 10 and their associated fact families.

Lesson 3 goes on to more complex addition (up through 100) and teaches students to break numbers up into groups of 10’s and 5’s and re-arrange as needed to come up with the answer. The strategies explained here help to build a strong conceptual understanding of addition rather than emphasizing an algorithm (set of steps to follow).

Lesson 4 teaches students to subtract numbers (up through 100) by visualizing them in groups of 10’s (with sub-groups of 5’s).

Brief introduction to ten frames: 

Since our number system is built around groups of 10, it is essential for kids to learn from a young age how to identify and manipulate numbers within our base 10 system.
To provide a strong foundation for fluency in the language of numbers, students should be introduced first to visual representations of numbers. If they can recognize amounts at a glance based on groupings of 5’s and 10’s, this will pave a strong foundation for them to become comfortable and confident working with numbers. Once they can comfortably understand and explain how all single digit numbers relate to 10, it’s a simple matter to start adding or subtracting double digit numbers by re-arranging numbers into 10’s, 5’s, and 1’s.

Ten frame activities are a great way to introduce these topics. The activities in this lesson pack describe fun (and unconventional!) ways to use ten frames. You can purchase ten frames sold as sets with counting items, or you can simply draw ten frames on paper and use items you have around the house as the objects for counting (rocks, cheerios, marbles, legos, macaroni pieces, beads, etc.). I’ve also used an empty egg carton as a ten frame container after cutting it down to size.

For those of you who are familiar with base-10 blocks, some of these activities may look familiar. Although the same basic idea applies to base-10 blocks, the added value of breaking groups of 10 into sub-groups of 5’s makes this a viable strategy for mental math, even with large numbers. Students can instantly imagine “glance-able” amounts of objects, break apart and re-arrange numbers, and recombine the “leftovers” to figure out the final answer. And again, since amounts of objects up to 5 can be known at a glance, without counting, and since all numbers can be broken up into 10’s and 1’s (bigger numbers into 100’s and 10’s and 1’s, etc.), students can take this one step further (instantly, in their head) to see numbers as combinations of 5’s within groups of 10’s and solve larger addition or subtraction problems.

 Although the process explained in the following lessons may look elaborate and lengthy, once students have solidly grasped these foundational concepts they will be able to do higher level math problems nearly instantly in their heads. Learning math in this way will help them become confident and happy learners. The steps explained in this lesson pack are designed to lead children at their own pace to a solid understanding of the number system; each step builds on previous concepts so that children can extend ideas they’ve mastered to new situations without ever being forced into frightening new territory where they find themselves ill-equipped to answer questions.

Note: If you learned certain patterns of steps (an algorithm) for adding or subtracting large numbers and if you understood why those steps worked and you got pretty good at it, you may be able to do all the exercises mentioned here more quickly using your method than the method I will describe. Don’t let that deter you, however, from teaching your students how to count, add, and subtract using ten frames. Think of it as a language; if this is a second language for you, it may not be the fastest way for you to speak or think, but if you can teach your children this language of math from the beginning, it will become their default language and they will think of numbers in groups of 10’s that can be re-arranged as needed to help solve almost any problem.
This method is best when taught to young students who are just encountering the number system, because it presents numbers in an organized, mentally “re-arrangeable” way that will help them intuitively understand how addition and subtraction with large numbers works.

If older students have tried to learn certain algorithms but become frustrated because they don’t understand why a certain process works, or they can’t remember all the steps needed for things like re-grouping or borrowing, this method can be used to help them go back to the basics and lay a solid foundation. Then, based on a stronger sense of how numbers and operations work, they can advance quickly to more complex topics