MATH WORD PROBLEMS at home

Closed- & Open-Ended Problem Solving

What’s the difference?

Close-ended: Many of the questions we traditionally ask students call for a single number, figure, or mathematical object. These kinds of questions are closed-ended because the expected answers are predetermined and specific. There are many examples of closed-ended problems online. These can be very valuable practice, and excellent homework support.

Examples of closed-ended questions:

1) Jennie wanted to buy some flowers for her mom. Each flower costs $3. If Jennie buys 15 flowers, how much money will she have spent?

2) The total number of people at Monday’s football game was
50,000 + 9,000 + 300 + 1. What is this number, written in standard form?

In contrast, Open-ended questions allow a variety of correct responses and elicit a different kind of student thinking. The open-ended nature of the question allows students to demonstrate their own ways of solving the problem.

Examples of open-ended questions:

Type 1: Ask Students to Explain Who Is Correct and Why: These types of items present two or more views of some mathematical concept or principle and the student has to decide which of the positions is correct and why. Example: Ian says that when you find the sum, you have a lot of choices for a common denominator. Frank says there is only one choice for the common denominator. Who is correct and why?

Type 2: Ask Students to Create a Situation or an Example That Satisfies Certain Conditions Questions of this type require students to recognize the defining characteristics of the underlying concept. Students must take what they know about a concept and apply it to create an example. Example: At Friday’s game, there were more people than there were at Monday’s game and fewer people than at Saturday’s game. How many people could have been at Friday’s game? Explain how you know your answer is right.

I’d like some more sample problems!

There are many math problems online - and many are close-ended. You can easily convert a close-ended problem into an open ended problem (and visa versa). Both are excellent practice, and we use both open- and close-ended problems in our math classroom.

Original Closed-Ended Item	Revised Open-Ended Item
Find the Lowest Common Multiple of 18 and 24.	Why can't 48 be the LCM of 18 and 24?
What are the next three numbers in the following sequence? 1, 4, 7, 10, 13, ___, ____, ____	Consider the following sequence: 1, 4, 7, 10, 13, ... . Is 100 a member of this sequence? Explain your reasoning.
Round 37.67 to the nearest 10th.	Generate three different numbers that when rounded to the nearest 10th give 37.7.

The following sites have great close-ended word problems organized by grade or strand

http://ca.ixl.com/math/grade-4 http://math.about.com/od/wordproblem1/Worksheets_for_Word_Problems_Various_grades.htm

http://www.dadsworksheets.com/v1/Worksheets/Word%20Problems.html

http://www.mathplayground.com/wpdatabase/wpindex.html

Some open-ended (others closed):

http://math.wiki.cvsd.k12.pa.us/Open-Ended+Questions

Pinterest drives my instruction: Math games

Some of the newest math games in my classroom. Inspired by this user and this user (and upon further inspection from that nutty and amazing Teacher Tipster.)



I altered a Guess Who? game. I replaced all of the heads with 3 or 4 or 5 digit numbers. The rules are the same, as kiddos are trying to guess their opponent's number. Is it s 3-digit number? Is it greater than ___? Does it have a 5 in it's tens column? Is it an odd number?



I altered a Jenga game with multiplication facts. The tower gets set up (like in normal Jenga), and as kids take out a Jenga block (and it doesn't fall) they have to answer the multiplication fact. If they get it right, they are safe. If not, they have to pull another block.



DOMO. (So the game is really called SNAKE, but I teach French Immersion and our class pet is my stuffed DOMO-kun, so we renamed the game DOMO.) This is a whole-class game. Each kid draws a tableau on some scrap paper with each column a letter in the word you are spelling (DOMO). Round 1 is round D. All students stand up and I roll two dice. Once I roll I ask if they want to stay in the game. If they stay, they write down the total of the dice on their table and I move on. I roll the dice again, and before i tell them the total, I ask if they are in or out. If they are out, they keep all the points that they've accumulated so far. If they stay in, they are facing risky business. You see, if I roll  a 1, they lose all the points. If I roll a double 1 (snake eyes) they lose all points from the current round and any round before. Once I roll a 1, students add all the points from column D and we move on to Round 2:Round O and all kids stand up again. They love it. We also have a (first to 100) bébé DOMO version that kids play in pairs.

**More games to come soon. Also I want to share the crazy-ness that is my triple-grade numeracy block! Until then - try some of these games.

*Note: Pinterest doesn't really drive my instruction. The data (is the roadmap that) drives my instruction and student interests, but there are so many amazing resources for teachers waiting to be pinned. And since I have over 200 pins on my schooled board (that I am actually doing!) I thought I should share them with the world.

mathy valentines.

Today we wrote some math (thomas) valentines. Here are some of my favourites translated. These kids are hilarious.

"Dear Area - You fill my heart with love and make me feel all warm and cozy inside. Love, Rectangle"
"Dear Mode - You are beautiful and smart. You'll always be my favourite. Love, a data set."
"Dear 536 - Things are not working out. We need to break up and go our own ways. I've found someone new. From, Division"
"Dear numbers, I love you in my life. Our love keeps growing and growing. Love, ascending pattern."
"Dear addition - We belong together and will be together forever. You are my match. Love, subtraction."



These valentines were part of some voice trait learning. We've been talking about adding voice to our writing with some quick-write mini lessons. One of the ways we can add voice is to change the point of view of the author.  Above is a picture of my hallway bulletin board devoted to the voice trait. Included with the valentines are some "Show, don't tell" paragraphs and some voice-embedded opinion grocery lists. I also put some self-portrait collages - because if they aren't full of voice, I don't know what is.

Subtraction strategies!

We are working on subtraction strategies. It is very important to realize as a parent (and a teacher!) that the traditional North American algorithm (columns with regrouping) is NOT the only or best or fasted way to solve large-digit subtraction. It may seem that way because for many adults, it was the only strategy that we learned in school.

Some of the other strategies that we'll be exploring at school include: Base 10 blocks, Decomposing, Number Line (why subtract when you can add?), friendly numbers and anything else that students come up with that works every time!

I was taught in school the traditional algorithm (cross out the number, borrow from the next), but after learning so many new strategies, I'm never going back!

Check out this video of a teacher explaining 16 different ways to subtract!