April 2024
Welcome to EFM's April Newsletter!
It is essential that every caregiver in the world reads books and does math with their young children!
EFM believes in every child’s mathematical right to equity, opportunity, and personal fulfillment.
News
Playing Cards Thousands of decks of EFM puzzle playing cards and family activity cards have just arrived in Melbourne and California. This time we have decks for grades K-3 and 2-5 in both English and Spanish. We look forward to distributing these in the coming weeks!
Make Focused Practice Playful Practice
I recently saw an announcement of an Australian symposium with the wonderful title “Inspiring Fluency Through Mathematical Curiosity.” Children need to develop fluency and number sense to be able to attend to the more advanced things one can do with mathematics, and we need to be careful how they learn those skills.
How do we help them develop fluency? The traditional method is to use flash cards, worksheets, and endless drilling. This results in fluency, but at the cost of creating a lifelong hatred for mathematics. It also creates missed opportunities for developing number sense and a sense of exploration and wonder. It certainly does not create fluency driven by curiosity, as that symposium would wish for.
This month I’d like to talk about examples of resources from EFM that provide enjoyable focused practice. They do it in a fun way that incorporates interesting connections that are made while developing fluency. One of our more straightforward resources is Math Games for Focused Practice. This has a list of math topics, and for each topic it has a list of games and puzzles that are particularly effective at providing fun and interesting practice.
Because they are so often abused, I’ll use learning multiplication facts as my example. This is a topic where adults too often succumb to using timed drilling that reduces many students to tears and feelings of inadequacy.
Learning Multiplication Math Facts
Before diving into the games and puzzles, here are some very brief learning steps for getting a child started, or unstuck, with single-digit multiplication. These steps emphasize a structured approach to learning multiplication – both because it is a lot more interesting than simple memorization, and also because it will lead to lasting insights. When a child stumbles recalling a multiplication fact, encourage them to figure it out using these steps.
1) Addition twins, doubling, and skip counting by 2’s. Children generally enjoy addition twins, and they provide a natural segue to these other two topics. It is also a good environment for a gentle introduction of talking about multiplying by 2.
2) Skip counting by 5’s and 10’s. This is connected with multiplying by 5 and 10, and multiplying other numbers times 5 and 10.
3) One more and one less. For example, 3 times something is doubling plus one more. 9 times something is 10 times something and then taking one less.
4) More doubling. For example, 6 times something is double 3 times something.
5) Skip counting by all numbers and multiplying by those numbers.
6) 3 x 4 = 4 x 3. Multiplication commutes – knowing this can save a lot of work.
7) Squares. Similar to addition twins, these can hold some fascination for children.
Let the Games (and Puzzles) Begin
Here are some activities to play with together. Each activity has a link to a PDF that describes it more thoroughly.
War with Multiplication
This version of the card game War barely deserves to be here. It is just a gamified version of flash cards and involves no choices or strategy. The only reason it’s here is that children seem to really enjoy playing it.
Turning the Tables and Revealing Products
Turning the Tables and Revealing Products are puzzles that take the boring and mundane task of filling in a multiplication table and turns it on its head. For example, Turning the Tables takes a multiplication table from 2 to 9 and asks the child to fill in all the missing squares, as in the table below.
To fill in this table, the child not only practices multiplication facts, but they also think about the ways that one or more numbers factor. The engagement is richer and far less predictable.
Should an adult wish to do some teaching along with the puzzle, there are many useful questions that can be asked. What made 9 and 49 good places to start? Why does the row with 20 and 36 have to be the “4” row – are there other possibilities? Encouraging introspection during puzzle solving can lead to some interesting mathematical places.
The Product Game
In The Product Game, children use multiplication facts to outmaneuver their opponent and be the first to get three-in-a-row on the board below.
Play starts with one player placing a marker on one of the numbers from 1 to 9 in the bottom row. The other player then places another marker on any of the numbers from 1 to 9, and claims the product of the two numbers on the big board. After that, the players alternate turns moving one of the two markers on the bottom row and claiming the product. The first player with 3 markers in a row in any direction wins.
There is a lot of thinking about numbers near existing markers on the board and which factors will be needed to put a marker where you want or to keep your opponent from doing so.
Two More Board Games
The games of Grabbing Factors (also Tax Collector) and Cover Factors / Multiples are similar to these first board games. They each involve thinking about what a number’s multiples and factors are.
Number Shapes
The investigation of Number Shapes is an activity that can be done with students in almost any grade. The older the grade, the more concepts that can come into play. A child is given a fixed number of markers (pebbles, coins, tokens) and asked which shapes they can make with them.
One of the simpler tasks is to make rectangles. For example, which rectangles can you make with 9, 10, 11, or 12 markers. Why are there only two flat rectangles for 11 markers? What other numbers only have flat rectangles? Why is there only one non-flat rectangle for 9 markers? What other numbers have that property? Lots of playing around and investigating can ensue and lead to interesting places. Among other things, this provides a very natural way to define prime numbers.
Nim With Factors
This is a verbal game that can be played anywhere. In Nim With Factors, a starting number is chosen and the player who moves first is agreed upon. Suppose the starting number is 20. On the first turn, that player can choose to subtract any factor of 20 (except for 20). Suppose they choose to subtract 5. Then the new number is 20 – 5 = 15, and the next player can subtract any factor of 15, and so on. The player forced to subtract to 0 loses.
Surprisingly, this game has a very simple strategy. However, until this strategy is discovered, this game provides lots of mental practice with factoring and subtracting. Even after the strategy is discovered, it is interesting to figure out and describe why the strategy works.
Mixed Operations with Number Scramble and Counting Neighbors
These last two games involve practice with all the operations. Even still, they provide excellent practice with multiplication. Number Scramble is one of my favorites, and it is a game I have played with children I tutored while waiting for their late parents to arrive. It is like the game of 24, but it has a lot more variety.
Use two dice to create a two-digit target number. Suppose the target is 19. Next take five dice (or one die used repeatedly), to create 5 digits to work with. Suppose the digits are 2, 3, 5, 5, and 6. The challenge is to use all five numbers to create the target. In this case, a possible answer is (5 x 5) – 6 x (3 – 2) = 19 and another is 3 x 6 + (2 – (5 / 5). If a particular puzzle proves to be impossible, the player who gets closest to the target wins.
Number Scramble can be modified in lots of ways. For example, the target can be less than 20 and only addition and subtraction are allowed. You can also mix in allowing combining some of the digits to make two-digit numbers.
The game of Counting Neighbors uses an 8 by 8 board with numbers from 1 to 64. On a move, a player rolls three dice and then claims one square whose value can be made using some combination of addition, subtraction, multiplication, and division. That player gets one point plus one more point for each square their square touches. After a preset number of rounds, the player with the most points wins.
Wrapping Up
I hope these examples have given you lots of ideas for more engaging and deeper ways you can have children build fluency with math facts. If you have some favorite activities that are not on the EFM lists, I’d love to hear about them – please write!
If you have any questions or comments, please send them our way! We would enjoy the opportunity to chat with you. Also, if you are interested in collaborating with us or supporting us in any fashion, we would love to talk with you about ways we can work together!
April 18, 2024
Chris Wright
Chris@EarlyFamilyMath.org
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Early Family Math is a California 501(c)(3) nonprofit corporation, #87-4441486.