July 2021
Welcome to EFM's July Newsletter!
Miscellaneous News
It's been fairly quiet around Early Family Math during this summer month. We hope you are enjoying the activities in the new Chapter 5.
In other news ...
Annotated Storybooks: The level of Beginning Story Lines is completed for now. The next level, Story Lines, has four books available so far, and more to come soon.
Translations: Chapter 2 for Traditional and Simplified Chinese is now available.
New Activities to Enjoy!
This month’s puzzles and investigations come from, or are inspired by, Open Middle. Their questions often have multiple answers and many ways of finding those answers. Rather than asking for simple, uninteresting calculations, these problems involve playing around and exploring mathematical relationships.
Each question has has some empty boxes and a range of numbers. Each number in the range is to be used at most once to fill the boxes. You can save a lot of erasing or crossing out by moving around Number Cards or Playing Cards on a piece of paper to find the solutions. These questions are similar to the Solitaire Shape Puzzles, Missing Number Puzzles, and Letter Substitution Puzzles of EFM Chapters 4 and 5.
Many of these questions involve an equal sign between two things neither of which is a simple number. Children often get used to seeing an equal sign as “producing a result,” as in 3 + 4 = 7. An equal sign can be used more generally — writing 1 + 6 = 2 + 5 = 3 + 4 says these three things have same value.
Play around with broadening or restricting the range of numbers to change the challenge level of many of these questions. You and your child can challenge each other by creating new versions of the questions as you play with solving the original ones.
Chapter 2
In these first two, the range of numbers is 1 to 6. Your child may notice that the answers to the second question are just the answers to the first one rearranged. That's great - they have discovered fact families!
□ + □ = □
□ – □ = □
In these next two, the range is 1 to 6 or 0 to 5. In addition to solving them, what are the largest values that you can create? What happens when you change the range?
□ + □ = □ + □
□ + □ = □ – □
Chapter 3
For the first two puzzles at this level, just use the last two puzzles, only use the range from 1 to 9.
For these next two, use 1 to 9.
□ = □ + □ = □ + □ + □
□ = □ + □ = □ + □ = □ + □
For this last one, use the range 0 to 9.
□ + □ = □ + □ = □ + □ = □ + □ = □ + □
Chapter 4
We'll now move into some double-digit problems. For this first one, the range is 1 to 9. For example, one solution is 24 + 7 = 36 - 5.
□□ + □ = □□ – □
The rest of the puzzles at this level involve putting double digit numbers in order using 0 to 9. You can do these two, three, four, or five at a time (we have shown the one that is five at a time). Put these on a number line if that helps your child visualize what is going on. The very last one livens things up a bit by putting in some explicit numbers.
□□ < □□ < □□ < □□ < □□
□□ < 35 < □□ < 41 < □□ < □□ < 88 < □□
Chapter 5
For these first two, use 1 to 7 (or 1 to 9 if you like). Once again, your child may realize that these two puzzles are really the same.
□□ + □□ = □□
□□ – □□ = □□
For the next two, use 0 to 9. As your child plays with this, they may notice that the two problems are actually very similar.
□□ + 53 = □□
□□ – □□ = 39
For these, use the range 0 to 9.
□□ + □□ = □□ + □□
□□ + □□ = □□ – □□
And finally in these last two, use 0 to 9 and get either sum as close to 100 as you can.
□□ + □□ + □□
□□ + □□ + □□ + □□
Chapter 6
For the final box challenge, use 0 to 9 and make these three expressions into three different odd numbers. You can only use each digit once throughout the three expressions.
□ / (□ – □); □ + (□ x □); □ – □ / (□ x □)
Bigger Challenge: For older children, here’s a challenge that extends some of the earlier questions. When can the numbers from 1 to n be broken into separate groups each of which has the same sum? For example, 1 + 2 = 3 breaks 1 to 3 into 2 groups with sum 3. Similarly, 1 + 4 = 2 + 3 = 5 breaks 1 to 5 into 3 groups with sum 5. This question will produce many hours of exploring!
If you have any questions or comments, please send them my way. I would enjoy the opportunity to chat with you.
- Chris Wright
July 18, 2021
chris@kitchentablemath.com