Home School Life Journal

Home School Life Journal
"Let us strive to make each moment beautiful."
Saint Francis DeSales
painting by Katie Bergenholtz

Math Games: Connecting the Concrete to the Abstract

Numerical and mathematical symbols are introduced at the connecting level. Mathematical symbols(e.g., +, –, =) are even more abstract than the mathematical language they represent. Both vertical and horizontal equations should be experienced. Children visualize symbols as they solve number problems using manipulatives. They show their understanding at this level by building concrete models with various types of manipulatives to match written equations and relating equations to manipulatives or to a word problem they have created. The student or teacher records the mathematical symbols.

Recording Number Stations
Remember when we learned how to do the Number Stations? The next step is to record the results of this game. Take cups of any fixed number or beans, for example 8 white beans and 8 red/brown beans. You could also use white beans that have been spray painted a color on one side. (In that case you would only use 8 beans, instead of 16 total.) To play the game, the student pulls out 8 beans without looking at them and using a worksheet with shapes of beans colors the red/brown beans, leaving the white beans alone. Write the ratios on a white board and then add the symbols "+" and "=."

Recording explorations with Unifix cubes can also be recorded. Take whatever number you wish and have them make patterns using that amount of unifix cubes in two colors They then recorded them by coloring them on a worksheet.

Unifix Trains
Again pick out a number of Unifix Cubes connected together into one stack. I then asked them to divide the stack evenly into two. "Did it break evenly into two's?" "Are there any left over?" "Does that make 9 an even or an odd number?" "How about if we break it into three's?"...

Lift the Bowl-Connecting Level
Remember when we learned the "Lift the Bowl" game? When we first played it, we only used counters. Now we begin connecting the counters to numbers but they are not yet asked to write the numerals. Using cards with numbers on them, and the bowl template, they work out simple addition and subtraction problems.

Recording Toothpick Number Station
Remember when we made patterns with pasta? Well, this time you can "record" toothpick patterns by gluing toothpicks to pieces of cardstock.

The Cave Game
You can play the cave game initially with just counters of your choice and your child's hand. Have him up a number of counters out and then have him put some of the counters in a "cave" made by your child cupping his hand into a backwards "C" shape. Once he can both say what the problem he made can be (such as 4 minus 1 equals 3 or 3 plus 1 equals 4) then he can move onto the connecting level. You can then lay out the counters and then have him put the numeral cards under the counters. Once this becomes comfortable, then he can look at problems on a worksheet that laid out just like the cave game. Lastly, he can use flashcard problems and can work them out himself using his cave game skills.


  • Math Their Way, Robert Baretta


  1. I think I have some Unifix-like cubes stuffed away somewhere - I'll have to pull them out, and try these.

  2. Thanks for reminding me to use unifix cubes. I've been using it for patterning but not addition yet.


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