The 6-year old had Fall Break last week, so no homework and no enVisionMATH-blogging for me. Tonight, however, she brought home a new worksheet for her weekly homework, and a couple of things caught my eye. I thought I’d throw those out there to you all, along with a question or two, as a two-part blog post.

For the first post, take a look at this (click to enlarge):

Questions:

- In your own words, preferably those that a smart 6-year old could understand, what is the basic principle that this page is trying to get across?
- What technique does this worksheet want kids to use when doing the Algebra problems?
- What’s your opinion about the principle/technique you think the worksheet is trying to communciate? Reasonable? Natural? Likely to be useful, or used frequently later on?

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Filed under Early education, Education, enVisionMATH, Math, Teaching

Tagged as algebra, Education, elementary education, envisionmath, Math, mathematics, Pearson

That 6 – 10 is like 1 – 5 all over again. That 5 + (a + b) = 10 iff a + b = 5. That you can get from Reading to Vermont in 2, so Vermont to Jail is 3.

As kids learn addition facts, before they have them down, the 5s relationships are valuable. Without context it is hard to tell what is going on, but from the level of abstraction I’m guessing that this is for kids who already know 1 digit facts. And that would make it fairly unimpressive.

Jonathan

Looks like getting 10-complements from knowing 5-complements. Actually fairly handy for doing mental math, but not a high-priority set of math facts.

Simple addition facts for numbers up to 20. gasstationwithoutpumps is right on target for those “5-complements” idea. What is missing from the uploaded page is how the teacher is treating this in the classroom, off-the-page. The teacher could point what is happening and at least some children may understand. On-the-page, those exercises by themselves, might not be as clear about this 5-complements situation for kids, other than just learning basic addition facts for numbers up to 20.

Common theme to both G’s and Jonathan’s comments: Missing context. I don’t know what that context is myself. I don’t what my kid’s teacher did, exactly, with this material in class, and I don’t know if she’s done other work that builds to this, and I don’t know if the connection to this material and previous material was made in a way that my daughter can understand.

How much context should parents have when their kids bring this home? I’m fortunate enough to be a mathematician who thinks about these kinds of questions and to have a blog where others help me think through it as well, but what about the average parent?

As was mentioned with past worksheets, the label “Algebra” on the extensions section is very strange. Missing addend problems are an introduction into algebraic thinking for young children, in a sense, but I think putting that label on a take-home sheet is more likely to confuse and stir up math anxiety in the parents. And it obscures rather than clarifies the connection between the first and second sections.

I think the worksheet is trying to do two things: use the 5-bonds (complements) as the others mentioned, and then extend the technique to two-digit numbers. In my opinion, the first goal is not worth spending homework time on. I would not bother with 5s (perhaps in class, but not in homework) and would instead go to the 10-bonds directly and practice them until they were mastered.

And the second goal, extension, is done poorly, without enough problems to let kids (and parents) see the pattern. My guess is that, no matter what the teacher did in class, most families will solve the “algebra” problems by counting-on.

In my mind, a much better homework assignment for this level of student would be for parent and child to play a game or two of Tens Concentration. It’s simple, fun, and focuses on the 10-bonds.

I’m not sure I was clear above, when I said there were not enough problems in the “algebra” section. What they should have done was something like this:

7 + ___ = 10

17 + ___ = 20

27 + ___ = 30

57 + ___ = 60

and

9 + ___ = 10

19 + ___ = 20

29 + ___ = 30

79 + ___ = 80

That should give enough data to the parents that they can see the point of the exercise, and it extends the pattern far enough for the child to understand that it applies to all numbers.

Of course, there isn’t room for that many problems if the book is going to insist on the silly “test-prep” format for the answers.

That is why knowing what is on the next page would be helpful. The two problems shown on the uploaded page, under the “Algebra” label, are just not enough.

G, the second page of the handout is shown in my second post in this series- the addition problems that turn out to be near-doubles activities. Those are the only two pages in the handout.

The next page really doesn’t matter for my argument. The parallel problems need to be right on top of each other, to make the pattern obvious. You cannot give as much space to a single problem as this worksheet does and then expect people to make the mental connection. As presented here, the test-prep bubble answers are a distraction from the mathematics.