Word Problem Wednesday – Farmer Fred

This month’s Word Problem Wednesday problem comes from Math in Focus Grade 3.

Farmer Fred makes 4 quarts of orange juice on Monday. He makes 2 quarts more orange juice on Tuesday than on Monday. He makes 2 more quarts on Wednesday than on Tuesday. He carries on making 2 more quarts of orange juice every day than the day before. In how many days will he make a total of 80 pints of orange juice?

Submit your solutions by the end of the month!

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Ask the Experts: What’s the best way to organize my math manipulatives?

The answer to this question is complicated. So much of how to organize materials is dependent upon personal preference with procedures and arrangement within your classroom. One thing that I can say is true in all cases is that they DO NOT belong in the closet!

I highly recommend that you dedicate a shelf or area of your classroom to math materials. It’s equally important for students to choose the most appropriate tool, as it is for them to use them. Having materials out for students at all times will allow for that.

One of the joys of my job is that I get to visit schools and classrooms across the country. So, I will share with you some organizational tips that I have gathered from my journeys.

There are three schools of thought (no pun intended) when it comes to organizing manipulatives; individual kits, group kits or community tubs. You may find it helpful to use a combination of the three, depending on the item.

I’ll mention a couple of manipulatives specifically here.

Place Value Discs

Student Kits

Many teachers prefer to organize discs into student kits. The idea being that students will have easy access to the discs for lessons with minimal time getting discs out and cleaning them up.

This option works great if you have enough discs for each student to have 20 of each place value; 20 ones, 20 tens, 20 hundreds, etc. Students are expected to keep these baggies or boxes of discs in their desks.

Pros: Easy access

Cons: Relies on students to maintain the correct number of discs in their kits. (I was that teacher who couldn’t stand the fact that there was one ten disc on the floor at the end of the lesson that seemed to belong to no one!)

Group Kits

Like student kits, you’ll need 20 of each place value in each kit. With group kits, you don’t need as many total discs. The idea here is that students will use discs with a partner or in small groups. These kits can be stored in a community tub and pulled out for use during lessons.

Pros: Easy access

Cons: See above. (Which kit does this disc belong to?!?)

Community Tubs

In this case, discs are organized by place value into tubs. So, you would have a tub of ones, a tub of tens, and so on. In each tub, you can keep a set of small cups (Dixie cups work well) for students to take a scoop of the discs when needed. Clean up is a snap. Students simply dump the cups of discs back into the correct place value tub.

Pros: No more mystery missing discs! Very quick set up. (No more evenings spent counting out discs while watching TV.)

Cons: Requires a bit more practice with the procedure of gathering and returning discs to the correct tub.

Linking cubes are a multi-functional manipulative that each classroom should have. For a class of about 20 students, you’ll want to have at least 400 individual cubes. That’s enough for each student to have a set of 20 when needed for instruction. If you’re using them for modeling area or multiplication arrays, you might want double that amount.

Student Kits or Group Kits

You’ll want to put at least 20 in each kit.

Pros: Ease of access.

Cons: Whose cube is this?!?

Community Tubs

If you are keeping your cubes in tubs, for ease of passing out and cleaning up, organize them in rods of 10, preferably by color. That way you can quickly pass out 2 rods (or more) to each student or partner group.

Pros: Fewer materials in student desks. No more mystery cubes.

Cons: Need to establish procedures for keeping cubes in rods of ten. (Easy, peasy!)

Other manipulatives should be in tubs on a shelf in the classroom available to all students at all times!

If you have any organizational tips from your classroom that you’d like to share, please send us a comment.

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Ask the Experts: What manipulatives do you suggest for my grade level?

Singapore Mathematics instruction – or, really, just good math instruction – will have students working through three phases of learning, referred to as the Concrete-Pictorial-Abstract approach. In order to teach following this approach, you need to start at the concrete level. Jean Piaget, a Swiss psychologist, believed that in order for students to be able to visualize and abstract mathematics they first must manipulate materials. He called this the concrete operational phase of learning.

So, what do you need to teach concretely? A complete list of recommended materials by grade level can be found here.

Really, though, with a few basic items you can get started…

Kindergarten – used for counting with one-to-one correspondence, measuring with non-standard units, and for modeling basic addition and subtraction situations.

1st – 2nd grade – used for place value understanding, to model story problems and mental math strategies, for measurement with non-standard units, building array models for multiplication, and for beginning bar modeling.

3rd grade – used to model part-whole and comparison word problems involving addition, subtraction, multiplication, and division, for building array models for multiplication and division, and for modeling area.

4th grade and up – used to model word problems for multiplication, division, and ratio, and to model area and volume.

Base-Ten Blocks and Place Value Discs

Find Base Ten Blocks here and Place Value Discs here.

1st grade – Base-Ten Blocks are used to model place value for numbers to 100

2nd grade and up – Place Value Discs are used as a more abstract (and manageable) model for place value understanding for numbers from thousandths to millions, and for modeling and developing a conceptual understanding of the four standard algorithms. Base-Ten blocks can continue to be used for those students needing a one-to-one representation.

Paper Strips and Squares of Equal Size

Cut them from paper found in the recycle bin.

1st and 2nd grade – used to model fractions of a whole.

2nd grade and up – used to model the four operations of fractions with the same size whole and for modeling part-whole and comparison word problems.

Number Cards (Playing Cards) and Dice

Find number cards on our resources page or pick up some playing cards at your local dollar store. Dice can be found here.

All grades – for playing games and making math fun!

Get creative and have fun building your inventory of math manipulatives!

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Word Problem Wednesday – Jason and Louis

This month’s Word Problem Wednesday problem comes from Primary Mathematics Challenging Word Problems 3.

Jason and Louis picked up a total of 30 cans. For every 2 cans that Jason picked up, Louis picked up 3 cans. How many cans did each boy pick up?

Submit your solutions by the end of the month!

Last month’s problem was from Dimensions Math 6A:

Here’s a solution from Reader Shirley Davis:

How did you do?

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Word Problem Wednesday – Laiza’s Dress

This month’s problem comes from Dimensions Math 6A and highlights the unitary method of solving problems:

Laiza spent 38% of her money on a dress and the rest on a purse. If she spent \$114 on the dress, how much did she spend on the purse?

Submit your solutions by the end of the month!

Last month’s problem was from the website TestPapersFree.com, which provides past copies of continual and semestral assessments from Singapore Primary Schools. This is a great resource if you’re looking to see questions directly from Singapore classrooms. The problem is from Raffles Girls School,  Grade 4, and is a Semester 2 assessment, which is the final term of the year.

Pei Ling had 3 times as many cards Zandy. Sulaiman had half the number of cards Zandy had. There were a total of 1278 cards. How many more cards did Pei Ling have than Zandy?

Here’s a solution from Reader Shirley Davis:

How did you do?

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