MATH: Transitioning to the "Partial Products" Multiplication Strategy

On homelink 9-4, students have their first opportunity to practice the Partial Products Strategy at home. We've been transitioning to this multiplication strategy over the last two class periods, as this strategy will give us more "room to grow" so to speak, when we get to two digit x two digit problems.

So far, we've used Partial Products to solve one digit x two digit problems, as well as one digit x three digit problems.

I wanted to give a step by step example of the strategy, as it is quite different from the traditional algorithm we parents learned growing up.

I'll use the same problem we used from the earlier post: 6 x 23.

First, we record the problem vertically.

We still break apart the two-digit number into it's basic parts: 20 and 3, and we show that we will multiply both by the other factor, 6.

Then we solve both parts, lining up our products along the ones-place so it's easy to add together.

Last, we add up our products for our final answer.

Let me know if you have any questions!

Math: Beginning One Digit x Two Digit Multiplication

We can solve multiplication facts, like 6 x 3 = 18.

And recently, we've been working to solve extended facts, like 6 x 20 = 120. In extended facts, we use our knowledge of facts to solve problems using multiples of 10, 100, and 100.

Now we are taking it one step further, to solve a one digit x two digit problem, but where the two digit number is not a multiple of 10.

Here’s an example of the type of problem I’m talking about: 6 x 23.

In class today, we learned how to solve this problem by applying what we already know. We showed our work in a concrete way, as follows.

First, we broke apart the two-digit number into 20 and 3. If we multiply each of these parts by 6, and then put the parts back together, we’ll get our answer.

Next, we record our work of multiplying each part by 6. We use our fact power to multiply 3x6 and our knowledge of fact extensions to multiply 20x6.

Finally, we take our two parts, 120 and 18, and add them back together to come to our final answer.

We start out with this visual strategy as a bridge towards the "Partial Products" algorithm, which will eventually become our main strategy for multi-digit multiplication. I hope this helps on the home-front as your child is moving into some new territory.

MATH: Decimal Booklets

Students have been using these place-value booklets to work on decimal skills. Hopefully you've seen this little tool come home.

There are lots of things you can do with it to practice. Here are a few suggestions:

• Counting: Start at a number like 0.1, and practice counting out loud by tenths, as the student flips the numbers in the book. Count by hundredths starting at 0.01, or by thousandths starting at 0.001.
• Counting through transitions: Pay special attention to transitions when counting with decimals, like what happens if you count from 0.7 to 1.4, or from 0.09 to 0.15.
• Dictating decimals: Say a decimal number and have your child make it on the booklet.
• Reading decimals: Make a decimal number and have your child read it aloud properly
• Putting digits in certain places: Ask your child to put a certain number in each place and then read the decimal aloud. Like, put a 0 in the ones place, a 5 in the hundredths place, and a 4 in the tenths place. "0.45"
• More or less: Have your child make a decimal on the booklet. Then give a second number and ask your child which number is greater.

MATH: Unit 4's "Last Problem"

On the test review for Unit 4, the last problem (#12), which will be similar to the "Open Response" question on the test, asks students to find the difference between two multiplication problems without doing any multiplication.

That's tricky.

I wanted to show a strategy for how to do this with an array. We used this strategy in an example problem today. So here's a similar problem we'll use for our example:

Mrs. Smith told her class that they could calculate the difference between 11x6 and 11x7 without doing any multiplication. Make sure to include the answer to the problem in your explanation.

Here is what a student might draw/write/record to receive a strong score on this problem:

In the image above, you can see how drawing an array for 11x6, and then adding a row to create 11x7, can show the "difference" between the two problems. The difference is just one row of eleven.

After doing several of these types of problems, students may see a pattern. Like, if I asked what the difference is between 4x13 and 5x13, they might start to see the answer would just be 13, which is right. However, it is still important that students be able to show or explain how to get the difference. And you know how much we like arrays in third grade!

This array strategy certainly isn't the only route to get to a correct answer and explanation, but it is definitely an option for students to use.

MATH: Using Arrays to Represent Division

In Lesson 4-3, we worked hard on using arrays to represent division stories. Here was our learning target:

We worked on two types of division stories: equal sharing (where a number of items are shared equally between a given number of people) and equal grouping (where a number of items are put into a groups of a given amount).

I wanted to show how students worked through these two types of division stories. While these aren't the only strategies that will get to a correct answer, I know sometimes it's helpful to see how your children are practicing in class.

Equal Sharing
Here's an example of an equal sharing number story, and the steps we would go through, along with exactly what we would record:

First we made a "tick mark" to represent how many people we had (or how many groups we would need.)

Then we started distributing our 14 counters by drawing circles (or Xs), in an equal way. (We had to give each person one before we gave any person a second one.) We kept track of how many counters we were giving out.

As we gave out the counters by drawing the circles, we made sure to keep the array organized. We stopped after our 14th circle.

We then drew a line to separate the "leftovers," since we know that each person has to have an equal number. Then we counted how many each person received.

We counted up our leftovers, and recorded our answer: "4 counters each, with 2 remaining."

Equal Grouping
Here's an example of an equal grouping number story, and the steps we would go through, along with exactly what we would record:

This time, we don't know how many groups (or people) we need: that's what we're trying to figure out. But we do know that each person will get 5, so we go ahead and make the first row of 5 in our array:

We continue to make groups of 5, keeping track of how many counters we have given out. We stop after 16.

Then we draw our line horizontally, to show that the 16th counter would be a leftover. Now we can draw the "tick marks" as we count how many people we would have.

We count up our remainder, and can write our answer as: 3 people with 1 counter remaining.

While working on homelink 4-3, encourage your child to record their arrays on the opposite page. Let me know if you have any questions!

MATH: Measuring with Inches

We have been working hard on measuring with rulers this week. We've focused most of our time on measuring with inches.

Students have gone through a progression, starting with measuring a line to the nearest inch, then measuring a line to the nearest half-inch, and then measuring a line to the nearest quarter-inch, which is clearly the trickiest.

To help identify the quarter-inch "system" (which is tricky because it also involves all the whole-inch marks as well as the half-inch marks), we've been using the analogy of a cricket hopping by quarter-inches. Like this:
Then, when we go to measure a line to the nearest quarter-inch, we first see how many WHOLE inches we've passed, then look closely to the remaining quarter-inches:

We have to decide which quarter-inch mark the line comes closest to, and record the measurement correctly, which also takes some skill.

A relevant discussion we had today was the idea that sometimes your "answer" might change, depending on if you are asked to measure to the nearest whole, half, or quarter inch.

We've also been practicing measurement to the nearest whole centimeter, nearest half-centimeter, and nearest millimeter.

Please take some time at home to do some "real-life" measuring situations with inches and centimeters. Thanks!

MATH: Using "Plickers" to Help Review

We have our Unit One math test coming up on Friday. In class today, we used a program called "Plickers" to make reviewing a little more fun. Each student gets a card with a code, and they use these cards to answer multiple choice questions I show up on the screen. To answer a question, they hold their card up, turning it to a specific position to match their individual answer.

Then I use the "Plickers" app to scan all the codes, which gives us real-time data on how the class performed on that question. We can show the results up on the screen as a bar graph, and then help explain why the answer was right.

Here's a picture of me using my phone to scan the code cards.

We'll need to fine-tune our "card-holding" skills a little, but overall, it was a great piece of technology to help us out today!

MATH: Data Landmarks

Our lesson today (1-5) was all about data. We collected some data from our class into a tally table, and then we found important "landmarks" of the data: maximum, minimum, range, mode, and median. We made a little note card memory device to help us remember what these terms mean.

Maximum is the greatest value.
Minimum is the smallest value.
Range is the difference between the minimum and maximum.
Mode is the value that happens the most often.
Median is the middle value, after putting the data in order.

Hello Math Class!

We are waist deep in Unit One! The first math unit is all about numbers and number routines. We've been working a lot with counting patterns and number grids. Today, students got to know their student reference book a little better too. Here's a look at what their "first job" was:

Did you know the student reference book is available online, too? When your child logs in to the Everyday Math website, he or she can access it there. It can even read the text out loud!

Lots of great math games, similar to ones we play in class, are also available on the site. All students received a log in card this week, so have fun trying it out!