Word Problem Wednesday – Apples

Summer’s here, but you’re missing your math? Don’t despair – we’ve got you covered. Check the site each week for one whopper of a word problem that’s sure to challenge!


This week’s problem comes from Primary Mathematics Intensive Practice 4A, published in 2004 by SingaporeMath.com

A grocer sold a carton of apples to some customers. The first customer tasted one apple and bought half the remaining apples. The second and third customers did the same. The fourth customer also tasted one apple and bought the remaining 23 apples. How many apples were there in the carton at first?

Submit your solutions and we’ll post all interesting strategies next week.


Last week’s problem and solution:

There are 3/5 as many cows as sheep on a farm. If there are 240 cows and sheep altogether, how many more sheep than cows are there?

Whew! How did you do?

Once again, astute reader Shirly Davis sent in a solution:

 

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Throwback Thursday – On the Topic of Math Sprints and Anxiety

Over the summer, we thought it would be fun to run some of the most popular posts from the past. When I re-read a post from the past I always take away something different because I am in a different place with my own experience. Perhaps you are as well!


On the Topic of Math Sprints and Anxiety

Originally published 4/30/15

Reflecting on my time at the two national math educator’s meetings, one interesting dichotomy appeared over timed fact tests. On the one side was Jo Boaler stating that timed tests are the root of math anxiety. Pushback came from others, most notably Greg Tang and Scott Baldridge pointing out that kids are timed in real life. They are put under pressure in real life. Students should learn from these experiences, not freak out over them.

It’s a powerful discussion: How do we get kids from fluency (I can use strategies to solve 7 x 8) to automaticity (I just know 7 x 8)? Do we need to get them to automaticity? Do timed tests create math anxiety? Is there spelling test anxiety? Should the key anxiety word be “test”, not “math”?

This conversation appeared recently on twitter after someone posted the “How to Give a Math Sprint” pdf from this site:


Yep, I’d be worried if kids who couldn’t make connections were timed, too.

I’m a proponent of Math Sprints; thoughtfully structured timed tests designed to practice one skill. Sprints are not your typical timed test. Students compete against themselves to improve the number of problems completed in one minute. Then the sprints are thrown away, not recorded in a grade book. They are practice. Period. And just one way to practice math facts.

Do Sprints harm students or cause math anxiety?

Not when administered correctly. I work with a school for students with ADHD and learning disabilities. Initially, teachers there said things like, “I can’t time my kids, they are slow processors”. It turns out that students at this school LOVE sprints. They can always improve by at least one problem on the second sprint. With all the content flying at them, practicing facts is one thing they can do and feel successful with.

Allison Coates runs the non-profit Math Walk Institute that works with schools and students to build a bridge to Algebra.

In every school we’ve ever worked, nearly all students enjoy sprints. They don’t see them as tests if the teacher doesn’t present them as tests. They see them as another fun game they can play against themselves (or against the teacher). Practice makes permanent their knowledge, and students love knowing they have knowledge. Knowledge is power.

Are Sprints from Singapore?

Nope. Sprints were created by Dr. Yoram Sagher as a fluency program to work with any curriculum. I’ve considered them a way to compensate for differences between Singapore and the U.S. In Singapore, parents drill fact fluency while schools teach the conceptual understanding. It’s not unusual for a first grader in Singapore to know all their math facts. It’s the school’s job to then get the understanding of multiplication into such a student. Contrast that with the U.S., where it is less likely that parents practice math facts at home with their child. Few American programs include a fluency component, often farming it out to the web or an iPad app.

Scott Baldridge has a great blog post on sprints: Fluency without Equivocation. I suggest you read it now.

My favorite Sprint books are Differentiated Math Sprints as they offer two difficulty levels with the same answers.

Eureka Math Sprints are aligned to Eureka Math (referenced in Scott Baldridge’s post above).

Wondering about the emphasis on math facts? Read: Why Mental Arithmetic Counts: Brain Activation during Single Digit Arithmetic Predicts High School Math Scores

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Word Problem Wednesday – Cows and Sheep

Summer’s here, but you’re missing your math? Don’t despair – we’ve got you covered. Check the site each week for one whopper of a word problem that’s sure to challenge!


This week’s problem comes from an oldie, but goodie: Mathematics Topical Worksheets 6A by Lawrence Loh, published in 2001 by SNP Education Pte Ltd.

There are 3/5 as many cows as sheep on a farm. If there are 240 cows and sheep altogether, how many more sheep than cows are there?

Submit your solutions and we’ll post all interesting strategies next week.


Last week’s problem and solution:

Rae bought 100 oranges and 46 apples. After she used an equal number of oranges and apples for making fruit juice. The ratio of her remaining oranges to apples became 5:2. Find the total number of oranges and apples she used.

Whew! How did you do?

Here’s a solution sent in by reader Shirley Davis:

 

 

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Throwback Thursday – Personal Whiteboards

Over the summer, we thought it would be fun to run some of the most popular posts from the past. When I re-read a post from the past I always take away something different because I am in a different place with my own experience. Perhaps you are as well!


Personal Whiteboards

Originally published 3/25/2009

whitebds

In the post about Number Strings, I referred to a student’s “personal whiteboard”.  I use whiteboards throughout the day as a way of informally assessing students.

Instead of a store bought whiteboard, I prefer to provide students with a customized version.

  1. Start with a glossy page protector, a box of which can be purchased inexpensively on eBay or at Sam’s Club or Costco.
  2. Insert a brightly colored sheet of card stock. Cardstock makes the whiteboard a little sturdier and by using color on one side, I can instantly tell when the entire group of students is ready.
  3. Add appropriate pages. In the first grade, I might have a pre-made number bond page ready to go. When I’m teaching a lesson on adding or subtracting, I’ll insert a place value chart.

By keeping a classroom set of these on the shelf with the student textbooks, they would last an entire school year. Here are some printables to get you started:

You can find information on Alexandria Jones’ Pharaoh’s Treasure in the picture at Let’s Play Math.

These are also great for games and learning centers…

Sudoku, Kenken, Contig or

The Hex game:

white-board

Or any of the international logic games on the handouts page of this site.

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Word Problem Wednesday – Rae’s Oranges and Apples

Summer’s here, but you’re missing your math? Don’t despair – we’ve got you covered. Check the site each week for one whopper of a word problem that’s sure to challenge!


This week’s problem comes from Fan-Math i-EXCEL Heuristic and Model Approach Primary 5 by Li Fanglan, published in 2008 by FAN Learning Publications.

Rae bought 100 oranges and 46 apples. After she used an equal number of oranges and apples for making fruit juice. The ratio of her remaining oranges to apples became 5:2. Find the total number of oranges and apples she used.

 

 

Submit your solutions and we’ll post all interesting strategies next week.


Last week’s problem and solution:

117 children took part in an art competition. 2/7 the number of girls is equal to 1/3 the number of boys. How many girls took part in the art competition?

How did you do?

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