Day: March 19, 2015

Squishy Circuits

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Brought to you by the Alameda County Library:

Squishy circuits at the Newark Library!

Squishy Circuits in action at the Newark Library

Squishy circuits are a neat way to have students learn about some of the basic properties of electricity through tinkering and problem solving.

But where is the math?

Besides problem solving to troubleshoot their design, students have a chance to engage in some measurement and data.  In each of the 2nd through 5th grade CCSS standards, students have to measure something and put it on a line graph.  The difference has to do with the scale on the line graph, 2nd is to the nearest whole number, 3rd includes halves and fourths, and 4th adds eighths.

So after your students engage in problem solving to test and make their squishy circuits, they’ll measure the distance between the LED and the battery and add that to the class graph.  After all groups add their data, they identify the longest distance.  Then ask them to make a conjecture about the longest possible distance and build it to see if it works.  All the circuits that work should be added to the class graph.  If time and interest, repeat until you’ve found the maximum distance.  An example student lab sheet can be found here.

Come play with this and more at the Making Math Expo on March 28th!

-Jim Town, Mathematics Specialist at ACOE

Aiding a Confused Parent with Arrays

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Found on Twitter with the caption: “kids can’t learn 6×8= 48 anymore its now 6×8=(5+1)x8 Why the confusing work”

Dear Confused Parent,

The picture you posted comes from a Powerpoint made by EngageNY to help teachers teach Grade 3, Module 3, Lesson 10.  Lesson 10’s objective is to “use the distributive property as a strategy to multiply and divide.”  So the question “How does topic C use the array model to move learning forward?”  is for teachers to consider as they think about the lesson.  The answer EngageNY gives is: “The array model helps students understand division as both a quantity divided into equal groups, as well as an unknown factor problem.”  Which provides important background, but does not directly answer your question.
To get back to the first part of your statement, “kids can’t learn 6×8 = 48 anymore.”  In fact, the Common Core State Standards state that by the end of third grade students should “know from memory all products of two one-digit numbers.”  So they can and should learn 6×8 = 48.  At the same time, they are learning why 6×8 = 48 and how to figure out that 6×8 = 48.
That finally leads us to your question, “Why the confusing work?”  The answer boils down to two main reasons, 1) the distributive property and 2) helping students figure out why 6×8 is 48, based in facts they already know and might be able to do in their head.  The distributive property states that a(b+c) = ab + ac.  The property is important for understanding elementary ideas such as how multiplication and addition are related

5 x 3 = 5(1+1+1) = 5 + 5 + 5

to secondary concepts such as multiplying binomials

(x + 4)(x – 5) = x(x – 5) + 4(x – 5) = x2 – 5x + 4x – 20 = x2 – x – 20.

In the problem you posted, students can break up the array of 48 dots into

(5 + 1)8 = 5 x 8 + 1 x 8 or 6(5 + 3) = 6 x 5 + 6 x 3 to show that they both equal the same number of dots.

This is also a strategy for figuring out 6×8 = 48 if students have forgotten the fact.  They may know 6×5 is 30 and 6×3 is 18 and can add to find 48.  Similarly, they may know 5×8 is 40 and 1×8 is 8 which together make 48 again.  An important part of the Common Core is building fluency through practice and conceptual understanding.  So by the end of third grade they should know

6×8 = 48, but if they don’t we should make sure they have the tools to figure it out.

I hope this makes you feel less confused,

Jim Town – Mathematics Specialist at ACOE Core Learning
Need more Common Core Math help?  Visit our Common Core Math Help page and get your answers today!

Actually Helping Jack with his Subtraction Problem

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You may have seen this purported parent response to a homework question on Facebook or even the Colbert Report.

I thought it was time to help Jack and explain what the teacher was probably thinking when he or she assigned this problem.


Dear Jack,

You did a great job using the number line to figure out this subtraction problem.  It looks to me like you forgot about the tens jump.  Remember 316 means 3 hundreds, 1 ten,  and 6 ones.  I see you took away 3 hundreds jumps and 6 jumps of one, but missed the 1 jump of ten.

I hope this helps.

A Math Teacher

The Frustrated Parent is exactly right about this being an inefficient method of subtracting.  Procedural fluency is an important part of the Common Core State Standards (CCSS), so the teacher wants the student to be able subtract those two numbers quickly and efficiently.  However, another important part of the CCSS is building conceptual understanding.   One of the reasons we need the Common Core State Standards is because for many years students were only taught procedural fluency without any understanding of the concept behind it.  That is to say, the trouble Frustrated Parent had figuring out the problem is exactly the reason it was assigned.  The math teacher wanted the student to understand what subtraction and place value mean so that they can do the problem and understand the problem.  This new shift will require parents and teachers to relearn many of the mathematics they thought they knew.
Another aspect of the Common Core this teacher was working towards was Mathematical Practice 4: Construct viable arguments and critique the reasoning of others.  Whether or not you agree with Jack’s method, being able look at someone else’s work, figure it out, and help them fix the errors, is an important skill.
While many of us are not familiar with the particular models that are being used to develop students’ conceptual understanding, those of us who have seen the shift in student comprehension of mathematics agree that these models can serve as a very important bridge between just “doing” math and actually understanding it.


Need more Common Core Math help?  Visit our Common Core Math Help page and get your answers today!

By Jim Town – Mathematics Specialist at ACOE Core Learning