Elementary Math is probably the single largest area of busywork, worksheets, and workbooks in a child's school experience. This need not be so.
When my older children were young I read a book called "Innumeracy: Mathematical Illiteracy" by John Allen Paulos. This made me aware that I needed to use rich descriptive language around my children. So, my children grew up in a home where mom used quantitative language and they had an opportunity to sing counting songs, learn counting rhymes, read analog clocks, find hymnbook page numbers, read numbered verses, read thermometers, learn oven settings, counting mile posts, watching the odometer, counting canning jars, setting the table, doubling recipes, figuring out how many ways the food got divided, and gauging life in so many ways.
When I taught my oldest three children, I used "Arithmetic Made Simple" (1960 Edition) by Abraham Paul Sperling; Samuel D Levison, as a road map to teaching Arithmetic. It covers basic math to the introduction of Algebra, is mastery based and is absent the busy work. We learned a new concept and then "played" with it on the blackboard by making up problems. Math was a game!
Then when I taught my younger four children, I developed the Power of an Hour: Gateway to a Classical Education, for them. The Power of an Hour includes Math History and Living Math every other week. This way they have two weeks to become comfortable with a new concept. I included math history because I wanted my children to understand the great ideas mathematicians struggled to solve. I wanted to give more context to Math. I also used Steve Slavin's book, "Math for your First and Second Grader: All You Need to Know to Be Your Child's Best Teacher," during our one-on-one learning time. This was easy to use, busywork free, hands on with items found in most homes, and it included short chapter tests, and end of year tests. We worked through the whole book and it gave a solid foundation. Then we went to the Arithmetic Made Simple book. Right now, if I come to a Math operation I am trying to teach my daughter and she is not getting it, I can do a google search on how to teach that concept and find several ways I can uses. Sometimes we just need to approach things differently. These two mentioned books are a road map of what to teach. (Since writing this post I have discovered that Steve Slavin has written several self-paced self-teaching math books for upper math, as well.
I have my students keep a Math Commonplace Book. One can use a simple Composition Book for a Commonplace Book. As they learn new concepts, they write the name of the concept, define the concept and give an example. They are building their own reference book.
Recently, I came across an article, Teaching of Arithmetic, by Louis Benezet, Superintendent of Public Schools in Manchester, New Hampshire in the 1930s. He did an experiment on teaching Math and Language Arts to elementary school students in his district. He delayed most of the formal Math and Language Arts until 7th and 8th grades. In place of formal instruction, he taught oral composition and no formal Math instruction, except as the children were exposed to Math in their reading. In 7th and 8th grade these non-traditional students were taught the formal Math and Language Arts their traditionally schooled peers had received in elementary school. At the end of 8th-grade both groups were tested. The non-formally instructed students out-performed the best formally trained students in the same district, both Math and Language Arts. Of course,his methods were nothing new. One year formal Math had been a success in one-room school houses in the United States.
When children learn and can demonstrate math, they like to show off. Dad will see their progress. A portfolio and the Math Commonplace Book should demonstrate what they are learning. As you can see, busywork, workbook pages, and worksheets are not needed.
In what ways do you teach your children or help them learn without using busy work, workbooks, and worksheets?