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## Improve Critical Thinking with 3rd Grade Multiplication Word Problems

Last Updated on June 3, 2022 by Thinkster

When done well, 3rd grade multiplication word problems present an opportunity for teachers and parents to help kids improve their critical thinking skills. These problems require a significant amount of thought in order to decide which operation to use, figure out the answer, and then determine whether or not the answer makes sense.

Here are some strategies to help children practice the problem-solving process. They work well to fine-tune those critical thinking skills and help with 3rd grade multiplication word problems.

## Read the Problem to Find Meaningful Information

In order to solve 3rd grade multiplication word problems, students must learn in order to read the problem to locate critical information. The critical information includes the question asked, the clue word or words that indicate which operation to use, and the numbers that will be used to find that information. They might underline clue words and circle the question or highlight the numbers to help with this process.

3rd grade is an excellent time to introduce this process or to fine-tune it if it has been introduced earlier. Most third-graders have strong enough reading skills to be able to decode the words and start looking a little deeper into their meaning. As a result, they are better able to focus on honing their critical thinking skills.

Asking questions is one of the key components of critical thinking. After reading a word problem students need to ask themselves several questions, including:

• What am I trying to find?
• Will the answer be larger or smaller than the numbers given?
• What operation would work best to find this answer?
• What is my estimated answer?
• Does my estimated answer make sense?

These critical thinking processes will help them arrive at the right answer with less struggle.

## Visualizing the Problem

Many 3rd grade multiplication word problems work with numbers too large to draw a picture. Students must therefore solve the problem mentally, yet visualizing the process is still an important critical thinking skill. Teach children to draw mental pictures to visualize the word problems they are solving.

As you can see, 3rd grade multiplication word problems are an excellent way to begin developing those critical thinking skills. If you want to work on these skills at home, but lack the time or knowledge to sit down and work through word problems with your child, Thinkster Math can help. Thinkster’s innovative tablet-based math learning program will help your child focus on those critical thinking skills, then give them the tools they need to solve math word problems accurately with the help of knowledgeable math teachers. It’s fun to play and also  rewards children for their hard work , so your child will be motivated to learn.

If you’re looking for  online  math   tutoring  to help your child, you can try   Thinkster risk-free .

Thinkster provides a full-fledged  online  tutoring  platform (driven by AI, behavioral, and data science), as well as supplemental  math  worksheets ,  math   homework  help ,  test prep , and more. Our  Parent Insights App  allows you to monitor your  student ‘s work and  learning  improvements at any time.

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## Ditch the Timed Test! Alternative Ideas for Assessing Multiplication Facts

• September 18, 2023

Assessing multiplication facts gives some of us chills…and not the good kind! Do you have a childhood trauma story that starts with, “When I was in third grade we had to memorize our multiplication facts….” We all have experienced timed tests where we had to race against the clock to complete as many problems as possible or get a perfect score to climb our way up Multiplication Mountain. But as educators, it’s time to shift our focus away from these anxiety-inducing assessments and towards more engaging and effective ways of assessing multiplication facts.

First and foremost, make sure you’ve done a thorough job giving your students a solid foundation for understanding multiplication and strategies for different types of multiplication facts BEFORE you start assessing whether students have the facts memorized or not. The lessons in this multiplication unit are highly engaging and offer tons of strategies and practice activities.

Once you’ve taught all the factors, you can start assessing multiplication facts. Here are some fun and creative ideas to assess multiplication fluency in your classroom without resorting to the stress of timed tests.

## Goal Setting & Progress Tracking

Have your students set realistic goals for themselves and track their progress on a chart in the classroom. For example, their measurements could be to improve by one fact per week–if they got 5 out of 20 correct last week, celebrate when they get 6 out of 20 correct this week. As a teacher, you could use colored stickers or stars each time they achieve their weekly goal, leading to a sense of accomplishment and progress. Also, continuously communicating with each student about their progress helps to promote accountability and focus on specific areas of improvement.

## Technology-Based Assessment

Incorporating technology into students’ learning has become an increasingly common practice in recent years. Multiplication applications such as Math Duel, Prodigy, and Times Tables Rockstars are readily available on devices like mobile phones, tablets, and desktop computers. Websites like xtramath , Freckle , and 99Math are growth-promoting tools that students could use to take self-assessments and track progress in a gamified form of learning.

## Create a Multiplication Museum

What better way to show off multiplication mastery than to create a museum? Ask students to display their knowledge of multiplication by creating posters, models, and dioramas of their favorite multiplication facts or strategies. This activity encourages creativity, collaboration, and critical thinking, and students will take ownership of their learning.

## Peer Quizzing

Peer quizzing is a fantastic method of assessing multiplication facts without causing stress to the student. As students of a similar age group, they are bound to be more comfortable sharing with each other while still receiving valuable feedback. Take advantage of this by pairing students to answer multiplication questions for each other using these free flashcards and quiz pages . This method allows both students to work equally in a safe and relaxed learning environment.

## Create a Multiplication Book

Another fun way to assess multiplication facts is to have them create a multiplication facts pattern book. Students can show you they know their multiplication facts and explore the patterns that the facts create on a 0-100 number chart at the same time. This activity encourages creativity and critical thinking while also assessing multiplication facts in a subtle manner.

## Two-Tone Tables

Here’s a colorful idea for assessing multiplication facts! Give each student a blank multiplication chart and have them use two different colors of markers or colored pencils. Set a timer for using color #1 and have students fill in as much of the multiplication chart as possible. At the end of the timer, have students switch to color #2. Have students set an improvement goal for themselves to get more and more of the multiplication table done in color #1 each time you do the activity. Have students write the date on each table and keep them so students can easily see how much they have improved over time.

There are so many fun and engaging ways for assessing multiplication facts that don’t include timed tests. By incorporating creative projects and games you can keep your students motivated and engaged while ensuring they are mastering the essential skill of multiplication. Remember, education is not just about memorization but also about creativity, problem-solving, and critical thinking skills. By incorporating these fun ideas for assessing multiplication facts into your teaching, you can both challenge and engage your students while keeping the learning process enjoyable and stress-free.

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## Multiplication Word Problems 4th Grade

Welcome to our Multiplication Word Problems for 4th Grade. Here you will find our range of printable multiplication problems which will help your child apply and practice their multiplication and times tables skills to solve a range of 'real life' problems at a 4th grade level.

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• 4th Grade Multiplication Problems Worksheets
• Easier & Harder Multiplication Worksheets
• More related resources

## Multiplication Word Problems 4th Grade Online Quiz

Multiplication word problems, 4th grade multiplication problems.

Here you will find a range of problem solving worksheets involving multiplication.

Each sheet involves solving a range of written multiplication problems.

There are 3 levels of difficulty for each worksheet below: A,B and C.

Worksheet A is the easiest level, suitable for children at the beginning of their grade.

Worksheet B is a medium level worksheets for children who are working at the expected level in their grade.

Worksheet C is set at a harder level, suitable for children who are more able mathematicians.

The problems in each worksheet are similar in wording, but the numbers involved become trickier as the level gets harder.

To encourage careful checking and thinking skills, each sheet includes one 'trick' question which is not a multiplication problem. Children need to spot this word problem, and work out which operation they need to solve it.

• apply their multiplication and times tables skills at a 4th grade level;
• apply their times table knowledge to work out related facts;
• recognise multiplication problems, and try to spot 'trick' problems;
• solve a range of 'real life' problems.

Some of the sheets have a UK version with spelling and currency symbols set for the UK.

## 4th Grade Multiplication Word Problem Sheets

Series 4 sheet 1 set.

• Series 4 Sheet 1A (easier)
• Series 4 Sheet 1B (medium)
• Series 4 Sheet 1C (hard)

• PDF Series 4.1 (6 sheets)
• PDF Series 4.1 UK version (6 sheets)

## Series 4 Sheet 2 Set

• Series 4 Sheet 2A (easier)
• Series 4 Sheet 2B (medium)
• Series 4 Sheet 2C (hard)
• PDF Series 4.2 (6 sheets)
• PDF Series 4.2 UK version (6 sheets)

## Series 4 Sheet 3 Set

• Series 4 Sheet 3A (easier)
• Series 4 Sheet 3B (medium)
• Series 4 Sheet 3C (hard)

## Multiplication Word Problems Walkthrough Video

This short video walkthrough shows several problems from our Multiplication Problems Worksheet 4.3A being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

Looking for some easier Multiplication Problems?

In our 3rd Grade Multiplication word problem area, you will find a range of multiplication problems aimed at 3rd graders.

The following areas are covered:

• basic multiplication fact sheets;
• multiplication facts to 10x10;
• 2 digits x 1 digit
• Multiplication Word Problem Worksheets 3rd Grade

Looking for some harder Multiplication Problems?

In our 5th Grade Multiplication word problem area, you will find a range of multiplication problems aimed at 5th graders.

• multiplication fact sheets;
• multiplication related facts to 10x10 e.g. 6 x 70, 8 x 0.6, etc;
• problems needing written multiplication methods to solve e.g. 2 digits x 2 digits, decimal multiplication
• Multiplication Problems Printable 5th Grade

## More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Looking for more 4th Grade Word Problems?

Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.

Many of the problems are based around 'real-life' problems and data such as the world's heaviest animals.

• apply their addition, subtraction and problem solving skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems;
• attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

• 4th Grade Math Word Problems

## Multiplication Times Table Charts

Here you will find a selection of Multiplication Times Table Charts to 10x10 or 12x12 to support your child in learning their multiplication facts.

There is a wide selection of multiplication charts including both color and black and white, smaller charts, filled charts and blank charts.

• Learn their multiplication facts to 10x10 or 12x12;
• Practice their multiplication table.

All the free printable Math charts in this section are informed by the Elementary Math Benchmarks.

• Large Multiplication Chart
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• Multiplication Times Tables Chart to 10x10
• Times Table Grid to 12x12
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• Multiplication Math Games

Here you will find a range of Free Printable Multiplication Games.

The following games develop the Math skill of multiplying in a fun and motivating way.

• learn their multiplication facts;
• practice and improve their multiplication table recall;
• develop their strategic thinking skills.

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

This quick quiz tests your knowledge and skill at solving multiplication word problems by tens and hundreds.

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The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

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## 20 Math Critical Thinking Questions to Ask in Class Tomorrow

• November 20, 2023

The level of apathy towards math is only increasing as each year passes and it’s up to us as teachers to make math class more meaningful . This list of math critical thinking questions will give you a quick starting point for getting your students to think deeper about any concept or problem.

Since artificial intelligence has basically changed schooling as we once knew it, I’ve seen a lot of districts and teachers looking for ways to lean into AI rather than run from it.

The idea of memorizing formulas and regurgitating information for a test is becoming more obsolete. We can now teach our students how to use their resources to make educated decisions and solve more complex problems.

With that in mind, teachers have more opportunities to get their students thinking about the why rather than the how.

## Looking for more about critical thinking skills? Check out these blog posts:

• Why You Need to Be Teaching Writing in Math Class Today
• How to Teach Problem Solving for Mathematics
• Turn the Bloom’s Taxonomy Verbs into Engaging Math Activities

## What skills do we actually want to teach our students?

As professionals, we talk a lot about transferable skills that can be valuable in multiple jobs, such as leadership, event planning, or effective communication. The same can be said for high school students.

It’s important to think about the skills that we want them to have before they are catapulted into the adult world.

Do you want them to be able to collaborate and communicate effectively with their peers? Maybe you would prefer that they can articulate their thoughts in a way that makes sense to someone who knows nothing about the topic.

Whatever you decide are the most essential skills your students should learn, make sure to add them into your lesson objectives.

## When should I ask these math critical thinking questions?

Critical thinking doesn’t have to be complex or fill an entire lesson. There are simple ways that you can start adding these types of questions into your lessons daily!

## Start small

Add specific math critical thinking questions to your warm up or exit ticket routine. This is a great way to start or end your class because your students will be able to quickly show you what they understand.

## Add critical thinking questions to word problems

Word problems and real-life applications are the perfect place to add in critical thinking questions. Real-world applications offer a more choose-your-own-adventure style assignment where your students can expand on their thought processes.

They also allow your students to get creative and think outside of the box. These problem-solving skills play a critical role in helping your students develop critical thinking abilities.

## Keep reading for math critical thinking questions that can be applied to any subject or topic!

• Explain the steps you took to solve this problem
• Draw a diagram to prove your solution.
• Is there a different way to solve this problem besides the one you used?
• How would you explain _______________ to a student in the grade below you?
• Why does this strategy work?
• Use evidence from the problem/data to defend your answer in complete sentences.

## When you want your students to justify their opinions

• What do you think will happen when ______?
• Do you agree/disagree with _______?
• What are the similarities and differences between ________ and __________?
• What suggestions would you give to this student?
• What is the most efficient way to solve this problem?
• How did you decide on your first step for solving this problem?

## When you want your students to think outside of the box

• How can ______________ be used in the real world?
• What might be a common error that a student could make when solving this problem?
• How is _____________ topic similar to _______________ (previous topic)?
• What examples can you think of that would not work with this problem solving method?
• What would happen if __________ changed?
• Create your own problem that would give a solution of ______________.
• What other math skills did you need to use to solve this problem?

## Let’s Recap:

• Rather than running from AI, help your students use it as a tool to expand their thinking.
• Identify a few transferable skills that you want your students to learn and make a goal for how you can help them develop these skills.
• Add critical thinking questions to your daily warm ups or exit tickets.
• Ask your students to explain their thinking when solving a word problem.
• Get a free sample of my Algebra 1 critical thinking questions ↓

7 thoughts on “20 math critical thinking questions to ask in class tomorrow”.

I would love to see your free math writing prompts, but there is no place for me to sign up. thank you

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## 5 Ways to Stop Thinking for Your Students

Too often math students lean on teachers to think for them, but there are some simple ways to guide them to think for themselves.

Who is doing the thinking in your classroom? If you asked me that question a few years ago, I would have replied, “My kids are doing the thinking, of course!” But I was wrong. As I reflect back to my teaching style before I read Building Thinking Classrooms by Peter Liljedahl (an era in my career I like to call “pre-thinking classroom”), I now see that I was encouraging my students to mimic rather than think .

My lessons followed a formula that I knew from my own school experience as a student and what I had learned in college as a pre-service teacher. It looked like this: Students faced me stationed at the board; I demonstrated a few problems while students copied what I wrote in their notes. I would throw out a few questions to the class to assess understanding. If a few kids answered correctly, I felt confident that the lesson had gone well. Some educators might call this “ I do, we do, you do .”

What’s wrong with this formula? When it was time for them to work independently, which usually meant a homework assignment because I used most of class time for direct instruction, the students would come back to class and say, “The homework was so hard. I don’t get it. Can you go over questions 1–20?” Exhausted and frustrated, I would wonder, “But I taught it—why didn’t they get it?”

Now in the “peri-thinking classroom” era of my career, my students are often working at the whiteboards in random groups as outlined in Liljedahl’s book. The pendulum has shifted from the teacher doing the thinking to the students doing the thinking. Do they still say, “I don’t get it!”? Yes, of course! But I use the following strategies to put the thinking back onto them.

## 5 Ways to Get Your Students to Think

1. Answer questions with a refocus on the students’ point of view. Liljedahl found in his research that students ask three types of questions: “(1) proximity questions—asked when the teacher is close; (2) stop thinking questions—most often of the form ‘is this right’ or ‘will this be on the test’; and (3) keep thinking questions—questions that students ask so they can get back to work.” He suggests that teachers acknowledge “proximity” and “stop thinking questions” but not answer them.

Try these responses to questions that students ask to keep working:

• “What have you done so far?”
• “Where did you get that number?”
• “What information is given in the problem?”
• “Does that number seem reasonable in this situation?”

2. Don’t carry a pencil or marker. This is a hard rule to follow; however, if you hold the writing utensil, you’ll be tempted to write for them . Use verbal nudges and hints, but avoid writing out an explanation. If you need to refer to a visual, find a group that has worked out the problem, and point out their steps. Hearing and viewing other students’ work is more powerful .

3. We instead of I . When I assign a handful of problems for groups to work on at the whiteboards, they are tempted to divvy up the task. “You do #30, and I’ll do #31.” This becomes an issue when they get stuck. I inevitably hear, “Can you help me with #30? I forgot how to start.”

I now require questions to use “we” instead of “I.” This works wonders. As soon as they start to ask a question with “I,” they pause and ask their group mates. Then they can legitimately say, “ We tried #30, and we are stumped.” But, in reality, once they loop in their group mates, the struggling student becomes unstuck, and everyone in the group has to engage with the problem.

4. Stall your answer. If I hear a basic computation question such as, “What is 3 divided by 5?” I act like I am busy helping another student: “Hold on, I need to help Marisela. I’ll be right back.” By the time I return to them, they are way past their question. They will ask a classmate, work it out, or look it up. If the teacher is not available to think for them, they learn to find alternative resources.

5. Set boundaries. As mentioned before, students ask “proximity” questions because I am close to them. I might reply with “Are you asking me a thinking question? I’m glad to give you a hint or nudge, but I cannot take away your opportunity to think.” This type of response acknowledges that you are there to help them but not to do their thinking for them.

When you set boundaries of what questions will be answered, the students begin to more carefully craft their questions. At this point of the year, I am starting to hear questions such as, “We have tried solving this system by substitution, but we are getting an unreasonable solution. Can you look at our steps?” Yes!

Shifting the focus to students doing the thinking not only enhances their learning but can also have the effect of less frustration and fatigue for the teacher. As the class becomes student-centered, the teacher role shifts to guide or facilitator and away from “sage on the stage.”

As another added benefit, when you serve as guide or facilitator, the students are getting differentiated instruction and assessment. Maybe only a few students need assistance with adding fractions, while a few students need assistance on an entirely different concept. At first, you might feel like your head is spinning trying to address so many different requests; however, as you carefully sift through the types of questions you hear, you will soon be comfortable only answering the “keep thinking” questions.

## Practicing multiplication tables

Common Core Standards: Grade 3 Operations & Algebraic Thinking

CCSS.Math.Content.3.OA.C.7, CCSS.Math.Content.3.OA.D.8

This worksheet originally published in Math Made Easy for 3rd Grade by © Dorling Kindersley Limited .

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## Related Resources

• Chinook’s Edge Website

## Strategies vs Models

Strategy: How students solve the problem. (Examples: Decomposition, Compensation, Traditional Algorithm)

Model: How students notate their thinking. (Examples: Number line, Ten Frames, Base Ten Blocks)

## Important to Know:

One strategy can be explained using multiple models. One model can be used to explain multiple strategies.

Fluency with strategies evolves over time.

## The Development of Mathematical Reasoning

Pamela Harris' Development of Mathematical Reasoning:   Counting Strategies ⇒ Additive Thinking Strategies ⇒ Multiplicative Reasoning Strategies ⇒ Proportional Reasoning Strategies ⇒ Functional Reasoning Strategies

Students develop mathematical reasoning as they develop more sophisticated thinking. A student who solves 4 x 5 by using counting strategies or additive thinking strategies is not engaging in multiplicative reasoning. Although, this student will correctly determine the answer to 4 x 5 using other strategies, if they do not develop multiplicative reasoning, exploring more complex questions will be extremely challenging. For example, a student may use counting or additive thinking strategies as part of their process for solving 1.2 x 2.3 or (x + 2)(x - 1), but will be unable to solve it without using multiplicative thinking.

When a student develops fluency in multiple strategies and more sophisticated strategies, the student can confidently select the most appropriate strategy based on the numbers.

## Naming Strategies:

Mathematical strategies should be named using the math utilized in the strategy. It might be cute to name the strategy after the student who first demonstrates it in class but when a student moves to a different class or a different school, non-conventional naming is not helpful. A grade level team and, preferably, a school, should agree upon names for the strategies that will be explored in math class. There aren't that many of them. Decomposing, compensating, partitioning by place value, give and take, and the traditional algorithm will cover almost all possible strategies.

## Strategies for this concept:

Below you will find a short description for each of the most typically used strategies for multiplicative thinking. Each strategy will include one or two models to help notate the thinking within the strategy. When solving a question, a student might use a single strategy or apply two or more strategies. Note that, although the sample question provided below could be solved using other reasoning, only the reasoning appropriate to this concept has been included.

Examples have been included for each strategy.

Multiplication: 5 x 18

## Compensation

Adjust one of the numbers to make it easier to work with while keeping the other number the same. Solve the new question. Adjust the answer to account for (compensate for) the change made to the first number.

## Decomposition

Decompose (break apart) one or both of the numbers into more manageable values in order to make it easier to solve.

The Distributive Property:  Building Arrays and the Area Model: Explore the distributive property through arrays and the area model as it can be developed from Kindergarten to Grade 8.

Multiplication – Decomposition Strategy: These videos explore multiplication through decomposition.

Division- Decomposition Strategy : These videos explore division through decomposition while making connections to the traditional algorithm.

## “Doubles / Halving”

The name of this strategy is a misnomer as it is not limited to knowing doubles or halves. You might use triples, thirds, fourths, etc. The first example below focuses on “give and take” where you double the 5 at the same time that you are halving the 18. The second example could relate to compensation as it first doubles the 10, and then halves the result.

The traditional algorithm (often called the standard algorithm) is a standardized process for solving multiplication and division questions. It focuses on solving a question digit by digit. Caution: The Traditional Algorithm most often described by Canadians is the traditional algorithm for Canada. Other countries have their own traditional algorithms. Keep this in mind if using this phrasing with students. ( Source )

## Formative Assessment

Ways to show 4 x 3 – 4 questions. Students determine if the example shows a way to think about 4 x 3 and provide an explanation. Student exemplars included. <Original Website>

Encyclopedia of the Sciences of Learning pp 2389–2392 Cite as

## Multiplicative Thinking and Learning

• Parmjit Singh 2
• Reference work entry

578 Accesses

Multiplicative reasoning ; Multiplicative structures ; Multiplicative thinking

Multiplication (and division) is an arithmetic operator used on numbers while thinking is a cognitive process involving the mind of learners reacting to incoming information. Multiplicative thinking represents the learner’s mental adaptive processing of multiplication concepts by using different methods and approaches in various mathematical problem contexts. Considering the level of complexity inherent in the nature of multiplication, one requires a more complex approach when thinking about numbers and operations. Multiplicative thinkers are those who have understood the concept of multiplication and are able to apply the concepts and solve problems relationally.

## Theoretical Background

Multiplicative thinking has gained more recognition and interest in recent years, following the early work of Vergnaud in 1983 . The growth of multiplicative thinking is critical for a learner’s...

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Confrey, J. (1994). Splitting, similarity and rate of change: new approaches to multiplication and exponential functions. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 293–332). Albany, NY: State University of New York Press.

Dienes, Z. P. (1967). Building up mathematics . London: Hutchinson Educational Publishers.

Jacob, L., & Willis, S. (2001). Recognising the difference between additive and multiplicative thinking in young children. In J. Bobis, B. Perry & M. Mitchelmore. (Eds.), Numeracy and beyond (Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia, Sydney pp. 306–313). Sydney: MERGA.

Steffe, L. (1994). Children’s multiplying schemes. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3–40). Albany: State University of New York Press.

Susan, B. E., & Erin, T. (2006). The emergence of multiplicative thinking in children’s solutions to paper folding tasks. Journal of Mathematical Behavior, 25 , 46–56.

Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 141–161). Reston: National council of Teachers of Mathematics.

Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127–174). New York: Academic.

## Author information

Authors and affiliations.

University Technology MARA, Shah Alam, Selangor, Malaysia

Parmjit Singh ( Faculty of Education )

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## Corresponding author

Correspondence to Parmjit Singh .

## Editor information

Editors and affiliations.

Faculty of Economics and Behavioral Sciences, Department of Education, University of Freiburg, 79085, Freiburg, Germany

Norbert M. Seel

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Singh, P. (2012). Multiplicative Thinking and Learning. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_531

DOI : https://doi.org/10.1007/978-1-4419-1428-6_531

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## Critical Thinking: Test-taking Practice for Math Grade 3

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## Mathematics

Domain - operations and algebraic thinking, grade 3.

Represent and solve problems involving multiplication and division.

Math.3.OA.A.3 : Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Understand properties of multiplication and the relationship between multiplication and division.

Math.3.OA.B.5 : Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Math.3.OA.D.8 : Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.(This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order).

## Domain - Number and Operations in Base Ten, Grade 3

Use place value understanding and properties of operations to perform multi-digit arithmetic.4

Math.3.NBT.A.2 : Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Math.3.NBT.A.1 : Use place value understanding to round whole numbers to the nearest 10 or 100.

Math.3.NBT.A.3 : Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

## Domain - Number and Operations-Fractions, Grade 3

Develop understanding of fractions as numbers.

Math.3.NF.A.2 : Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Math.3.NF.A.3 : Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

## Domain - Develop understanding of fractions as numbers., Grade 3

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Math.3.NF.A.2a : Represent a fraction 1/ b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/ b and that the endpoint of the part based at 0 locates the number 1/ b on the number line.

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Math.3.NF.A.3b : Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Math.3.NF.A.3a : Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Math.3.NF.A.3c : Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram .

## Domain - Measurement and Data, Grade 3

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Math.3.MD.A.2 : Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).(Excludes compound units such as cm3 and finding the geometric volume of a container) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.(Excludes multiplicative comparison problems (problems involving notions of "times as much").

Math.3.MD.A.1 : Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Represent and interpret data.

Math.3.MD.B.3 : Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets .

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Math.3.MD.C.7 : Relate area to the operations of multiplication and addition.

Math.3.MD.C.5 : Recognize area as an attribute of plane figures and understand concepts of area measurement.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Math.3.MD.D.8 : Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

## Domain - Geometry, Grade 3

Reason with shapes and their attributes.

Math.3.G.A.1 : Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

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6. #maths |#logical questions|#thinking questions| #mattricks |#matchestricks

1. PDF Learning to Think Mathematically About Multiplication

This book is designed to help students develop a rich understanding of multiplication and division through a variety of problem contexts, models, and methods that elicit multiplicative thinking. Elementary level math textbooks have historically presented only one construct for multiplication: repeated addition.

2. Improve Critical Thinking with 3rd Grade Multiplication Word Problems

Visualizing the Problem. Many 3rd grade multiplication word problems work with numbers too large to draw a picture. Students must therefore solve the problem mentally, yet visualizing the process is still an important critical thinking skill. Teach children to draw mental pictures to visualize the word problems they are solving.

3. Ditch the Timed Test! Alternative Ideas for Assessing Multiplication

Take advantage of this by pairing students to answer multiplication questions for each other using these free flashcards and quiz pages. This method allows both students to work equally in a safe and relaxed learning environment. ... This activity encourages creativity and critical thinking while also assessing multiplication facts in a subtle ...

4. Multiplication Word Problems 4th Grade

4th Grade Multiplication Problems. Here you will find a range of problem solving worksheets involving multiplication. Each sheet involves solving a range of written multiplication problems. There are 3 levels of difficulty for each worksheet below: A,B and C. Worksheet A is the easiest level, suitable for children at the beginning of their grade.

5. 101 Great Higher-Order Thinking Questions for Math

The answer is by utilizing higher-order thinking questions for math. Higher-order thinking questions are critical thinking questions that require students to infer, apply, predict, connect, evaluate, and judge knowledge in new ways. The answers to these questions require prior knowledge and an expansive schema so that readers can see beyond the ...

6. Multiplication Worksheets

It encourages critical thinking in solving questions like '10 is 2 times as many as 5.' Customizable for specific learning needs, it can be converted into flash cards for interactive study or used in distance learning settings to accommodate different teaching modalities. ... Given the large number of problems in the worksheet, students are ...

7. Multiplication Critical Thinking

30 seconds. 1 pt. Which problems show the commutative property or the "flip-flop property" for multiplication? 4 x 5 = 20 5 x 4 = 20. 7 x 3 = 21 7 x 3 = 21. 6 x 6 = 36 6 x 6 = 36. 6 x 2 = 12 12 x 2 = 6.

8. What is multiplicative thinking?

Additive thinking is the ability to join and separate numbers. Subitizing, using manipulatives, story problems, balance equation activities, building numbers, and more are needed for additive thinking. Counting, even skip counting, is still additive thinking. Both early numeracy and additive thinking must be strong for students to build up to ...

9. Multiplication and Division Facts: Critical Thinking (Gr. 4)

Provided by Scott Foresman, an imprint of Pearson, the world's leading elementary educational publisher. Its line of educational resources supports teachers and helps schools and districts meet demands for adequate yearly progress and reporting.

10. Critical Thinking Math Problems: Examples and Activities

Cite this lesson. Critical thinking is an important factor in understanding math. Discover how critical thinking can help with real-world problem solving, using examples and activities like asking ...

11. Multiplication Critical Thinking

Multiplication Critical Thinking - Worksheets, Lessons, and Printables. Multiplication Worksheets. 2 Digit Multiplication. 2nd Grade Multiplication. 3rd Grade Multiplication. 4th Grade Multiplication. 5th Grade Multiplication. 6th Grade Multiplication.

12. 20 Math Critical Thinking Questions to Ask in Class Tomorrow

Start small. Add critical thinking questions to word problems. Keep reading for math critical thinking questions that can be applied to any subject or topic! When you want your students to defend their answers. When you want your students to justify their opinions. When you want your students to think outside of the box.

13. PDF Multiplicative thinking practice questions

Multiplicative Thinking Practice Questions. 1. Estimate the answer to 58790 ÷ 29, explaining your reasoning. 2. How would you demonstrate the multiplication 3 X 4 using arrays model. Use this model to show the commutative property of multiplication. 3. Solve 132 × 15 using two different methods. These two methods must be distinctly different.

14. Multiplication: Critical Thinking (Gr. 4)

Provided by Scott Foresman, an imprint of Pearson, the world's leading elementary educational publisher. Its line of educational resources supports teachers and helps schools and districts meet demands for adequate yearly progress and reporting.

15. Promoting Independent Critical Thinking in Math

5 Ways to Get Your Students to Think. 1. Answer questions with a refocus on the students' point of view. Liljedahl found in his research that students ask three types of questions: " (1) proximity questions—asked when the teacher is close; (2) stop thinking questions—most often of the form 'is this right' or 'will this be on the ...

16. Practicing multiplication tables

This math worksheet gives your third grader multiplication practice with equations and word problems involving shapes, volume, money, and logic. MATH | GRADE: 3rd. Print full size.

17. Multiplication and Division Concepts: Critical Thinking (Gr. 2)

Multiplication and Division Concepts: Critical Thinking (Gr. 2) Use these practice worksheets to accompany the initial teaching of multiplication and division. They provide varied strategies for solving problems with this topic that you can use them to differentiate your lessons, student assessments, and supplemental material.

18. Multiplicative Thinking

Below you will find a short description for each of the most typically used strategies for multiplicative thinking. Each strategy will include one or two models to help notate the thinking within the strategy. When solving a question, a student might use a single strategy or apply two or more strategies. Note that, although the sample question ...

19. PDF Critical Thinking Worksheet Grades 6-8: Mathematical Concepts

Engage student's critical thinking skills with the use of these worksheets in the classroom. Click here: critical_thinking_034-download.pdf to download the document. ... Students might create a special question mark symbol to post next to any item for which contradictory sources can be found Note: The Food Timeline is a resource that documents ...

20. Multiplication and Critical Thinking: Lesson Plan

For instance, they will need to represent "2+2+2+2" as "2∙4.". The second set of problems will include a set of multiplications for which the learners will have to provide answers (e.g., 3∙2=6). Finally, the third set will involve problems requiring the application of critical thinking.

21. Multiplicative Thinking and Learning

Definition. Multiplication (and division) is an arithmetic operator used on numbers while thinking is a cognitive process involving the mind of learners reacting to incoming information. Multiplicative thinking represents the learner's mental adaptive processing of multiplication concepts by using different methods and approaches in various ...

22. Critical Thinking: Test-taking Practice for Math Grade 3

Mathematics Domain - Operations and Algebraic Thinking, Grade 3. Represent and solve problems involving multiplication and division. Math.3.OA.A.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

23. Worksheet Library: Critical Thinking: Grades 3-5

Scratch Your Brain. Use addition and subtraction to figure out solutions to these brain benders. (Grades 3-5) From One Word to the Next. Change a letter in the previous word to make the word that completes each phrase. (Grades 3-5) Root Words. Complete this activity about words that have /capt/ or /tact/ as a root.