Let
A=[2324]B=[24−1130]C=[104−112013]A=left[begin{array}{ll}
2 & 3 \
2 & 4
end{array}right] quad B=left[begin{array}{rr}
2 & 4 \
-1 & 1 \
3 & 0
end{array}right] quad C=left[begin{array}{rrr}
1 & 0 & 4 \
-1 & 1 & 2 \
0 & 1 & 3
end{array}right]
Carry out the indicated operation, or explain why it cannot be performed.
B−1B^{-1}
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PowerPoint Practice CLUE WORDS FOR WORD PROBLEMS PowerPoint Presentation
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PowerPoint Practice CLUE WORDS FOR WORD PROBLEMS
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Presentation Transcript
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PowerPoint PracticeCLUE WORDS FOR WORD PROBLEMS
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Also ADD In all And between 2 numbers Sum More before the question Both Altogether Combined Plus Total Joined together Spend/spent
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SUBTRACT Change Difference Less Profit Left »er» words Minus More-in-question Off Not-in-question
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MULTIPLY Product One-before-question Twice Each-before-question Per-before-question A piece-before-question Every-before-question Times
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DIVIDE Quotient every-in-question Each-in-question Separate one-in-question per-in-question Equal half piece-in-question
Last Updated on May 26, 2022 by Thinkster
Math word problems are so frustrating that even parents dread seeing the mathematical paragraphs appear on their fourth grader’s homework assignments. If you hate doing word problems as an adult, then you know they’re no picnic for your 9-year-old child. Approach the task with enthusiasm so that your student will follow suit. Adopting a winning attitude is half the battle in math. You need to remember that math is all about logic—and numbers. Follow the numbers, and the word problem isn’t quite as confusing any longer.
1. Teach a Logical Process
If your child is struggling with 4th grade math word problems, teach him a logical process to go through to determine what needs to be done. These steps should be:
- Question – Read the problem to determine what the question is.
- Information – Determine what information you have.
- Clue words – What words tell you the math process to use.
- Equation – Use the information, question and clue words to write an equation.
- Check your work – Does your answer make sense compared to the given information and the question?
Once your child can learn to use this process on a regular basis, you will find that he has much more success with word problems.
2. Teach Common Clue Words
Many fourth graders read a word problem and have no idea what to do with it. Yet most word problems on this grade level have clue words in them. Teach your child to identify those clue words, to help ease the struggle. Here are the clue words:
- Addition – Combined, increased, total of, sum, added to, together, plus
- Subtraction – Minus, less than, less, fewer than, difference, decreased, take away, more than
- Multiplication – Multiplied, product of, times, of
- Division – Divided by, into, per, quotient of, percent, out of, ratio of
Students who can pair these clue words with the math process will be much more successful with 4th grade math word problems.
3. Provide Practice
In order for a child to gain mastery of word problems, he needs practice. Simply throwing a sheet of word problems at him is not going to do the job, however. He needs a way to practice that is engaging and enticing.
Thinkster Math, an iPad-based math tutoring program, is an excellent option for this. Thinkster provides personalized math tutoring covering all math topics, including word problems, and designated tutors provide instruction to ensure that students make adjustments as needed when practicing. Students who use Thinkster are engaged in their learning and enjoy excellent gains in difficult math concepts, such as 4th grade math word problems.
4. Use Manipulates or Diagrams
Sometimes visualizing the problem can give the student the tools needed to solve it. For problems with small amounts, you can use math manipulates to help your child picture what is happening. For larger amounts or measurements, draw a diagram. This action gets additional learning processes involved and helps make the word problem a visual concept for the child to consider.
The key to making fourth grade math word problems solvable for your child is to make them understandable and then provide the right practice and support. It can also be worthwhile to get your child a math tutor. By doing so, you will be able to help your child succeed in mathematics.
Summary
Article Name
Making Math Word Problems Accessible for Fourth Graders
Description
Is your child struggling with 4th grade math word problems? Here is what you can do to help.
Author
Pavithra Lakshminarayan
Publisher Name
Thinkster Math
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When you tell your students you will be working on word problems, do you hear a chorus of groans? If so, you are not alone! Teaching students how to solve math word problems tends to not be the most exciting math exercise in an elementary math curriculum (especially not learning about word problem key words and how they can be used to solve problems). They also tend to be very challenging for students. No wonder many students don’t like them!
In order for students to become proficient in mathematics, however, they need to apply their math learning to real life situations, which can be achieved through word problems. This experience should not be about following rote procedures and computing correct responses. When solving these types of problems, it is important for students to apply multiple strategies to make sense of the problem and solve it. These experiences should be grounded in strategy application and problem solving, rather than simply computation.
Identifying word problem key words is one of many strategies elementary students can use to help them solve single and multi-step word problems. Additionally, students need access to anchor charts, tools, and manipulatives that will equip them with the resources they need for these problem solving experiences. Using keywords for math word problems is just one piece of the puzzle!
This blog post will answer the following questions:
- What are word problem key words?
- What are some examples of keywords for addition word problems?
- Can you share some examples of keywords for subtraction word problems?
- What are some examples of keywords for multiplication word problems?
- Can you share some examples of keywords for division word problems?
- What are the limitations of using keywords to solve word problems?
- Is using word problem keywords an effective strategy?
What are Word Problem Key Words?
Word problem key words are words or phrases that signal which operations (addition, subtraction, multiplication, or division) are needed in order to solve a math word problem.
Using keywords for math word problems (often referred to as clue words and phrases) is a strategy to make sense of and solve word problems. It is the idea of training the brain to look for specific words and phrases to determine what mathematical operations are needed. Here is an example of this strategy in practice:
Erin reads the problem: Pat has 3 red shirts. He has 2 blue shirts. How many red and blue shirts does he have in all? After reading through the problem once, Erin rereads the problem but this time she is looking specifically for the clue words and phrases she has learned. She highlights or underlines the phrase “in all.” She has learned in class that “in all” signals to the reader that they need to add. This strategy has helped her make sense of the problem (which in this case means that the addition operation is needed), set up an equation (3 + 2 = ?), and solve for the answer (5 shirts).
Common Math Word Problem Key Words and Phrases
Below is a list of key words and phrases that students can use to solve addition, subtraction, multiplication, and division word problems. If you teach the younger grades, you’ll find the list of addition and subtraction key words helpful. If you teach the older grades, you’ll find those helpful, as well as the multiplication and division key words.
Addition Key Words
Here are some examples of addition key words:
- add
- altogether
- both
- combine
- in all
- increase
- increased by
- larger
- larger than
- longer
- longer than
- more
- more than
- perimeter
- plus
- sum
- together
- total
Subtraction Key Words
Here are some examples of subtraction key words:
- change
- decreased
- difference
- fewer
- gave away
- How many more…?
- How many less…?
- left
- left over
- less
- less than
- minus
- remain
- shorter than
- smaller than
- take away
Multiplication Key Words
Here are some examples of multiplication key words:
- area
- cubed
- double
- each
- groups
- per
- product
- quadruple
- rows
- squared
- times
- triple
Division Key Words
Here are some examples of division key words:
- average
- divide
- each
- equal group
- fourth
- half
- quarter
- quotient
- ratio
- share
- separate
- split
- third
Limitations of Using Keywords to Solve Word Problems
When students are learning how to solve word problems, it is beneficial for them to be exposed to, directly taught, and given practice with key words (also sometimes written as word problem keywords or keywords for math word problems). However, students need to understand that problems can be solved in many different ways. This is just one tool in their toolkit. It is not always the most effective strategy to solve a given word problem. For example, students should not be trained to always subtract when they see the word less because they could use a missing addend from addition to solve. This strategy should be used along with other strategies (e.g. visualization). As students progress through their math education and come across more challenging word problems, this strategy will become less effective. As a result, your students need to be equipped with an abundance of diverse strategies.
Math Resources for 1st-5th Grade Teachers
If you need printable and digital math resources for your classroom, then check out my time and money-saving math collections below!
Free Elementary Math Resources
We would love for you to try these word problem resources with your students. It offers them opportunities to practice applying word problem key words strategies, as well as other problem solving strategies. You can download word problem worksheets specific to your grade level (along with lots of other math freebies) in our free printable math resources bundle using this link: free printable math activities for elementary teachers.
Check out my monthly word problem resources!
- 1st Grade Word Problems
- 2nd Grade Word Problems
- 3rd Grade Word Problems
- 4th Grade Word Problems
- 5th Grade Word Problems
Lesson
2nd Grade Math — Word Problem Clues
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Clip 4/11: Word Clues Lesson — Part 2
Overview
During the processing of the first problem, Sarah notes that the second answer is incorrect. This puzzles other students. Together we take a critical look at the words in a word problem and see how those words connect to the symbols used in the number sentences provided.
I intended for students to not only look at how their peers decomposed numbers to come up with answers, but also look at how they documented it. Did they use a complete number sentence and words to clearly explain their thinking? If not, my goal here was for students to link the words in the problem to the symbols that would complete the number sentence. This resulted in the lesson taking a bit of a turn. I needed to know what my students were thinking in regards to this new dilemma presented by Sarah and supported by a few others (Aaryn and Nia). In this segment of the lesson Sarah is very quick to point out the error made by another student in how they understood the problem. She expresses very clearly where the mathematician went wrong in their understanding and how the answer they provided just does not make sense. She states her observations and conclusions very quickly.
During math lessons early in the year we spent a lot of time decomposing numbers to help answer questions and learn regrouping. While some students agree with Sarah’s position, others continue to be puzzled by how she knew to subtract. Aaryn points out that the words in the word problem «how many more» are a clue to subtract.
The key idea I wanted my students to gain was «DOES THIS MAKE SENSE, GIVEN WHAT YOU KNOW AND HAVE BEEN TAUGHT.» Iyanna who is a very strong reader, struggles in math and often shuts down. The process of re-engaging a task allows students like Iyanna time and space to make sense of a problem and get clarification.
After Sarah shares her thinking I am very careful about the statements and questions I use. «…but, you are thinking this should be a subtraction problem? Does anybody else think that? What are you thinking? I’m not sure. What do you think?» I am intentionally opening the door for students to also say exactly where they are in their process with this problem. There is no pressure. In fact Iyanna boldly states where she is in her thinking. It is the place where she is stuck. Keeping in mind that my goal here is to get struggling students to ask more questions and secure students in math to share their thinking. Through this process we can all learn more. As students speak up, and mumble on the carpet, I have a window into how they approached the problem. Now we can begin to attack misconception and break this poor habit of looking for number and just adding them together.
On way to break this habit is the use of thinking of certain phrases as code words. Nia speaks up and says, «How many more is the code!» D’wone, another struggling mathematician understand that it is a code for the number sentence. However, he is not 100% clear on what exactly it is supposed to tell him.
It is very tempting to jump in and make this a lesson about the words, «How many more» in a word problem. This group of students have found it useful to equate this phrase to subtraction, however I could have really taught this as a «comparison» or strategies for finding the difference by adding. I choose to maintain my course and allow student space and time to explore and discover errors, knowing that they will get to do this with their own work soon.
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Looking for clue words for multiplication when translating word problems? Wish you knew how to look at a word problem and immediately tell that it requires you to multiply?
Looking for clue words for multiplication when translating word problems? Wish you knew how to look at a word problem and immediately tell that it requires you to multiply?
After watching this video, you’ll be able to do just that as I show you common key words and phrases often used in multiplication word problems. You’ll learn words and phrases that come up when the problem shows repetition, comparisons, combinations, rates and much more.
Resources:
Download your «1-15 Multiplication Times Table» from the KOG Math Success Library here with your free account: kogmathsuccessacademy.org/libraryguides
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