math problem solving strategies 4th grade examples

$Mr. Mathematica gave his class these digits: 1, 5, 7, 9, 2, 8, and 5. He asked them to make the smallest number possible using every digit once. What would that number be?$

4. The detectives found this number pattern as part of the code on a keypad to unlock a vault. 27, 26, 24, 23, 21, , . What are the last two numbers they should punch in?

$The detectives found this number pattern as part of the code on a keypad to unlock a vault. 27, 26, 24, 23, 21, __, __. What are the last two numbers they should punch in?$

5. Tom’s bicycle cost $50 more than Bob’s bicycle. Bob’s bicycle cost $180. How much did Tom’s bicycle cost?

$Tom’s bicycle cost $50 more than Bob’s bicycle. Bob’s bicycle cost $180. How much did Tom’s bicycle cost?$

6. Randy bought 2 baseball hats for $5.25 each. He also bought 2 wrist bands for $2.50 each. How much money did he spend?

$Randy bought 2 baseball hats for $5.25 each. He also bought 2 wrist bands for $2.50 each. How much money did he spend?$

7. Lots of birds were spotted at the new bird feeder. There were 12 sparrows, 15 crows, 8 orioles, 3 squirrels, and 9 cardinals. How many birds were there in all?

$Lots of birds were spotted at the new bird feeder. There were 12 sparrows, 15 crows, 8 orioles, 3 squirrels, and 9 cardinals. How many birds were there in all?$

8. There were lots of visitors to the town history museum this past winter. There were 75 in December, 98 in January, and 69 in February. How many visitors did the museum have this past winter in total?

$There were lots of visitors to the town history museum this past winter. There were 75 in December, 98 in January, and 69 in February. How many visitors did the museum have this past winter in total?$

9. Luis was setting up his new office. He bought a new computer for $350. He also bought a printer for $99 and two ink cartridges for $37 each. How much did he spend?

$Luis was setting up his new office. He bought a new computer for $350. He also bought a printer for $99 and two ink cartridges for $37 each. How much did he spend?$

10. There was a big sale at the Super Duper Shoe Store for 3 days. They sold 87 pairs of shoes on Friday, 95 pairs of shoes on Saturday, and 83 pairs of shoes on Sunday. How many pairs of shoes were sold all together?

$There was a big sale at the Super Duper Shoe Store for 3 days. They sold 87 pairs of shoes on Friday, 95 pairs of shoes on Saturday, and 83 pairs of shoes on Sunday. How many pairs of shoes were sold all together?$

11. Pia had a huge sticker collection. She had 280 stickers. Her friend, Jen, had 155 stickers in her collection. How many more stickers did Pia have than Jen?

$math problem solving strategies 4th grade examples$

12. Robyn scored a total of 155 points in basketball this season for the Tarrytown Tigers. She had 30 rebounds as well. Last season she scored 106 points. How many more points did she score this season than last season?

$Robyn scored a total of 155 points in basketball this season for the Tarrytown Tigers. She had 30 rebounds as well. Last season she scored 106 points. How many more points did she score this season than last season?$

13. John went to lunch at the Cool Cat Cafe. He spent $1.25 on a juice drink and $5.50 on a sandwich. He also bought a brownie for 99 cents. He gave the cashier a $20 bill. How much change did he get?

$John went to lunch at the Cool Cat Cafe. He spent $1.25 on a juice drink and $5.50 on a sandwich. He also bought a brownie for 99 cents. He gave the cashier a $20 bill. How much change did he get?$

14. Race Car Ralph drove 1,000 miles in the big cross-country auto race. 775 of those miles were with his dog, Speedy, in the car. The rest of the way, he drove alone. How many miles did Ralph drive without Speedy?

$Race Car Ralph drove 1,000 miles in the big cross-country auto race. 775 of those miles were with his dog, Speedy, in the car. The rest of the way, he drove alone. How many miles did Ralph drive without Speedy?$

15. Best Baked Bakery baked 10,250 holiday cookies. They sold almost all of them. Only 56 were left. How many holiday cookies did they sell?

$Best Baked Bakery baked 10,250 holiday cookies. They sold almost all of them. Only 56 were left. How many holiday cookies did they sell?$

16. There were 3 cats and 4 geese in the barnyard. How many total legs were there?

$There were 3 cats and 4 geese in the barnyard. How many total legs were there?$

17. Donna picks 5 apples every minute in the orchard. How many apples does she pick in 20 minutes?

$Donna picks 5 apples every minute in the orchard. How many apples does she pick in 20 minutes?$

18. Morris the magician pulled 2 doves out of his hat, twice as many rabbits as doves, and 4 times as many mice as rabbits. How many animals did he pull out of his hat?

$Morris the magician pulled 2 doves out of his hat, twice as many rabbits as doves, and 4 times as many mice as rabbits. How many animals did he pull out of his hat?$

19. Tina is making pizzas for 15 guests. If each person (including Tina) is expected to eat 2 slices, how many 8-slice pizzas should Tina make?

$Tina is making pizzas for 15 guests. If each person (including Tina) is expected to eat 2 slices, how many 8-slice pizzas should Tina make?$

20. Chef Charlie is decorating a birthday cake with a circle of berries. He has 6 strawberries and would like to put 5 blueberries between each strawberry. How many blueberries does he need?

$Chef Charlie is decorating a birthday cake with a circle of berries. He has 6 strawberries and would like to put 5 blueberries between each strawberry. How many blueberries does he need?$

22. To make a winter stew, Jamal needs 3 pounds of sweet potatoes. If they cost $1.29 per pound, what will it cost to buy enough sweet potatoes?

$To make a winter stew, Jamal needs 3 pounds of sweet potatoes. If they cost $1.29 per pound, what will it cost to buy enough sweet potatoes?$

22. The Hotel Swanky has 10 floors. Each floor has 16 guest rooms. There is also a ballroom, two meeting rooms, and a restaurant. How many guest rooms are in the hotel?

$The Hotel Swanky has 10 floors. Each floor has 16 guest rooms. There is also a ballroom, two meeting rooms, and a restaurant. How many guest rooms are in the hotel?$

23. Mrs. Mason got a new bookcase for the library and filled it with books. There were 6 shelves. The top two shelves had 50 books on each shelf. The bottom four shelves had 75 books on each shelf. How many books were there in the new bookcase?

$Mrs. Mason got a new bookcase for the library and filled it with books. There were 6 shelves. The top two shelves had 50 books on each shelf. The bottom four shelves had 75 books on each shelf. How many books were there in the new bookcase?$

24. The cafeteria ordered 6 packs of jumbo chocolate chip cookies and 3 packs of brownies. Each pack of cookies had 12 cookies in it. They sold 45 cookies and 30 brownies. How many cookies are left?

$The cafeteria ordered 6 packs of jumbo chocolate chip cookies and 3 packs of brownies. Each pack of cookies had 12 cookies in it. They sold 45 cookies and 30 brownies. How many cookies are left?$

25. The new elementary school has 30 desks in each classroom. There are four classrooms for each grade. There are 5 grades in the school. How many desks are there in the school?

$The new elementary school has 30 desks in each classroom. There are four classrooms for each grade. There are 5 grades in the school. How many desks are there in the school?$

26. Gina planted six rows of carrots in her garden. Each row had 30 carrots. Rabbits ate half of her carrots. How many carrots did she have left?

$Gina planted six rows of carrots in her garden. Each row had 30 carrots. Rabbits ate half of her carrots. How many carrots did she have left?$

27. Jack planted a magic bean. The bean plant that grew was 1 foot tall on the first day. Then it doubled in height each day. How tall was the plant on the fifth day?

$Jack planted a magic bean. The bean plant that grew was 1 foot tall on the first day. Then it doubled in height each day. How tall was the plant on the fifth day?$

28. Big Brain University bought 15 new supercomputers and 50 printers. Each supercomputer cost $5,300. A printer cost $100. How much did the university spend buying new computers?

$Big Brain University bought 15 new supercomputers and 50 printers. Each supercomputer cost $5,300. A printer cost $100. How much did the university spend buying new computers?$

29. The new golf course had 3 tournaments every month this year. The course is open 12 months a year. Each tournament was limited to 101 golfers and was full. How many golfers played in the tournaments all together this year?

$The new golf course had 3 tournaments every month this year. The course is open 12 months a year. Each tournament was limited to 101 golfers and was full. How many golfers played in the tournaments all together this year?$

30. The school office printer can print 200 pages every 10 minutes. If the printer runs for an hour straight, how many pages can it print?

$The school office printer can print 200 pages every 10 minutes. If the printer runs for an hour straight, how many pages can it print?$

31. Lucia makes beaded bracelets. Each bracelet has 12 beads on it. She made 55 bracelets for each of the school fairs. The school had 3 fairs. How many bracelets did Lucia make?

$Lucia makes beaded bracelets. Each bracelet has 12 beads on it. She made 55 bracelets for each of the school fairs. The school had 3 fairs. How many bracelets did Lucia make?$

32. Sammy Speedball is a pitcher for the Boogaloo Bearcats. He practiced his pitching on Saturday for an hour in the morning and an hour after dinner. He threw 20 pitches every 30 minutes. How many practice pitches did Sammy throw on Saturday?

$Sammy Speedball is a pitcher for the Boogaloo Bearcats. He practiced his pitching on Saturday for an hour in the morning and an hour after dinner. He threw 20 pitches every 30 minutes. How many practice pitches did Sammy throw on Saturday?$

33. Serena had 35 cherries. She gave 8 to each of her sisters. She still has 3 left over. How many sisters does Serena have?

$Serena had 35 cherries. She gave 8 to each of her sisters. She still has 3 left over. How many sisters does Serena have?$

34. The new teacher was giving out pencils to her class for the year. She wanted to give them out evenly. She had 15 packs of pencils with 10 pencils in each pack. She had 20 students. How many pencils should each student get? How many pencils would be left over?

$The new teacher was giving out pencils to her class for the year. She wanted to give them out evenly. She had 15 packs of pencils with 10 pencils in each pack. She had 20 students. How many pencils should each student get? How many pencils would be left over?$

35. 150 kids signed up for the summer soccer league. There are going to be ten teams, and the Dragons are one of the teams. Each team has 3 coaches and they want an equal number of players on each team. How many players should be on the Dragons?

36. the wonderful widget company produces 480 widgets every day. they have 6 widget making machines running every day, with each machine making equal amounts of widgets. the company runs six days a week. how many widgets does each machine make.

$The Wonderful Widget Company produces 480 widgets every day. They have 6 widget making machines running every day, with each machine making equal amounts of widgets. The company runs six days a week. How many widgets does each machine make?$

37. Farmer Fran has 35 hens. Each hen lays a dozen eggs a day. Fran packs the eggs into packs of ten. How many packs of eggs does she pack per day?

$Farmer Fran has 35 hens. Each hen lays a dozen eggs a day. Fran packs the eggs into packs of ten. How many packs of eggs does she pack per day?$

38. ReadOn Publishers gives free books to schools every year on the last day of the year. They have 900 books for this year’s giveaway. 18 schools have applied for the free books. How many should each school get if they are evenly distributed?

$ReadOn Publishers gives free books to schools every year on the last day of the year. They have 900 books for this year’s giveaway. 18 schools have applied for the free books. How many should each school get if they are evenly distributed?$

39. Coach Cindy is meeting with each player for practice individually. Each player will get 15 minutes with the coach. Coach Cindy has 2 hours for this on Saturday. How many players can she meet with?

$Coach Cindy is meeting with each player for practice individually. Each player will get 15 minutes with the coach. Coach Cindy has 2 hours for this on Saturday. How many players can she meet with?$

40. Dr. Bea Well has 120 patients. ¼ of them wear glasses. How many of her patients don’t wear glasses?

$Dr. Bea Well has 120 patients. ¼ of them wear glasses. How many of her patients don’t wear glasses?$

41. Lucy has 24 stuffed animals. She loves elephants, and one-third of her stuffed animals are elephants. Half of the elephants are gray. How many elephants does she have?

$Lucy has 24 stuffed animals. She loves elephants, and one-third of her stuffed animals are elephants. Half of the elephants are gray. How many elephants does she have?$

42. Annie collects seashells. She has 120 shells in her collection. They are from both the Atlantic Ocean and the Pacific Ocean. ¾ of the shells are from the Atlantic Ocean. How many shells are from the Pacific Ocean?

$Annie collects seashells. She has 120 shells in her collection. They are from both the Atlantic Ocean and the Pacific Ocean. ¾ of the shells are from the Atlantic Ocean. How many shells are from the Pacific Ocean?$

43. Bill has 7/8 of his homework done. Andy has 9/10 of his homework done. They have the same amount of homework. Who has more homework done?

$Bill has 7/8 of his homework done. Andy has 9/10 of his homework done. They have the same amount of homework. Who has more homework done?$

44. Jose was offered 2/5 of a jumbo chocolate bar or 3/6 of the same bar. He loves chocolate. Which should he choose if he wants the most chocolate?

$Jose was offered 2/5 of a jumbo chocolate bar or 3/6 of the same bar. He loves chocolate. Which should he choose if he wants the most chocolate?$

45. Janelle has 6 notebooks for school. Donnie has 1/3 more than Janelle. How many notebooks do Janelle and Donnie have all together?

$Janelle has 6 notebooks for school. Donnie has 1/3 more than Janelle. How many notebooks do Janelle and Donnie have all together?$

46. Tonya found two small interesting stones. The black one weighs 0.3 of an ounce. The red one weighs 0.09 of an ounce. Which stone weighs more?

$Tonya found two small interesting stones. The black one weighs 0.3 of an ounce. The red one weighs 0.09 of an ounce. Which stone weighs more?$

47. Leah has a baseball bat that is 2 and a half feet long. Bryson has a bat that is 28 inches long and another one that is 2 feet and 5 inches long. Who has the longest bat?

$Leah has a baseball bat that is 2 and a half feet long. Bryson has a bat that is 28 inches long and another one that is 2 feet and 5 inches long. Who has the longest bat?$

48. Mr. Smith’s class collected coins in a big jar for 6 months. Their coins weighed 2 pounds and 8 ounces. Ms. Smith’s class did the same thing. Their coins weighed 2 ½ pounds. Whose coins weighed more?

$Mr. Smith’s class collected coins in a big jar for 6 months. Their coins weighed 2 pounds and 8 ounces. Ms. Smith’s class did the same thing. Their coins weighed 2 ½ pounds. Whose coins weighed more?$

49. The track team was practicing for the big meet. Tim ran for 25 minutes every day for 5 days. Tom ran an hour every day for 3 days. Who spent the most time running?

$The track team was practicing for the big meet. Tim ran for 25 minutes every day for 5 days. Tom ran an hour every day for 3 days. Who spent the most time running?$

50. The Jones family left for the airport at 10:00 a.m. for vacation. Their flight leaves at 12:30 p.m. They stopped twice for 10 minutes each time. They got to the airport at 11:30 p.m. How much time did they spend driving?

$The Jones family left for the airport at 10:00 a.m. for vacation. Their flight leaves at 12:30 p.m. They stopped twice for 10 minutes each time. They got to the airport at 11:30 p.m. How much time did they spend driving?$

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Classroom Q&A

With larry ferlazzo.

In this EdWeek blog, an experiment in knowledge-gathering, Ferlazzo will address readers’ questions on classroom management, ELL instruction, lesson planning, and other issues facing teachers. Send your questions to [email protected]. Read more from this blog.

Four Teacher-Recommended Instructional Strategies for Math

(This is the first post in a two-part series.)

The new question-of-the-week is:

What is the single most effective instructional strategy you have used to teach math?

This post is part of a longer series of questions and answers inviting educators from various disciplines to share their “single most effective instructional strategy.”

Two weeks ago, educators shared their recommendations when it came to teaching writing.

Last month , it was about teaching English-language learners.

There are many more to come!

Today, Cindy Garcia, Danielle Ngo, Patrick Brown, and Andrea Clark share their favorite math instructional strategies.

‘Concrete Representational Abstract’

Cindy Garcia has been a bilingual educator for 14 years and is currently a district instructional specialist for PK-6 bilingual/ESL mathematics. She is active on Twitter @CindyGarciaTX and on her blog:

The single most effective strategy that I have used to teach mathematics is the Concrete Representational Abstract (CRA) approach.

During the concrete step, students use physical materials (real-life objects or models) to explore a concept. Using physical materials allows the students to see and touch abstract concepts such as place value. Students are able to manipulate these materials and make sense of what works and what does not work. For example, students can represent 102, 120, and 201 with base 10 blocks and count each model to see the difference of the value of the digit 2 in each number.

During the representational step, students use pictures, images, or virtual manipulatives to represent concrete materials and complete math tasks. Students are making connections and gaining a deeper understanding of the concept by creating or drawing representations.

During the abstract step, students are now primarily using numbers and symbols. Students working at the abstract stage have a solid understanding of the concept.

The CRA approach is appropriate and applicable to all grade levels. It is not about the age of the student but rather the concept being taught. In 3rd grade, it is beneficial to students to have them use base 10 blocks to create an open-area model, then draw an open-area model, and finally use the multiplication algorithm. In algebra, it is STILL beneficial to practice using algebra tiles to multiply polynomials using an open-area model.

The CRA approach provides students P-12 to have multiple opportunities to explore concepts and make connections with prior concepts. Some teachers try to start teaching a concept at the abstract level, for example, the standard algorithm for multiplication. However, they soon find out that students have difficulty remembering the steps, don’t regroup, or don’t line up digits correctly. One of the main reasons is that students don’t understand this shortcut and they have not had the concrete & representational experiences to see how the shortcuts in the standard algorithm work.

‘Encouraging Discourse’

Danielle Ngo is a 3rd grade teacher and Lower School math coordinator at The Windward School . She has been a teacher for 10 years and works primarily with students who have language-based learning disabilities:

Growing up, so many of us were taught that there is one right answer to every math problem, and that there is one efficient way to arrive at that conclusion. The impetus to return to this framework when teaching math is a tempting one and one I’ve found myself having to fight actively against during my own classroom instruction. In my experience, the most effective way to counter this impulse is to mindfully increase the discourse present during my math lessons. Encouraging discourse benefits our students in several ways, all of which solidify crucial math concepts and sharpen higher-order thinking and reasoning skills:

Distributes math authority in the classroom: Allowing discourse between students—not just between the students and their teacher—establishes a classroom environment in which all contributions are respected and valued. Not only does this type of environment encourage students to advocate for themselves, to ask clarifying questions, and to assess their understanding of material, it also incentivizes students to actively engage in lessons by giving them agency and ownership over their knowledge. Learning becomes a collaborative effort, one in which each student can and should participate.

Promotes a deeper understanding of mathematical concepts: While the rote memorization of a process allows many students to pass their tests, this superficial grasp of math skills does not build a solid foundation for more complex concepts. Through the requisite explanation and justification of their thought processes, discourse pushes students to move beyond an understanding of math as a set of procedural tasks. Rather, rich classroom discussion gives students the freedom to explore the “why’s and how’s” of math—to engage with the concepts at hand, think critically about them, and connect new topics to previous knowledge. These connections allow students to develop a meaningful understanding of mathematical concepts and to use prior knowledge to solve unfamiliar problems.

Develops mathematical-language skills: Students internalize vocabulary words—both their definitions and correct usage—through repeated exposures to the words in meaningful contexts. Appropriately facilitated classroom discourse provides the perfect opportunity for students to practice using new vocabulary terms, as well as to restate definitions in their own words. Additionally, since many math concepts build on prior knowledge, classroom discussions allow students to revisit vocabulary words; use them in multiple, varied contexts; and thus keep the terms current.

‘Explore-Before-Explain’

Patrick Brown is the executive director of STEM and CTE for the Fort Zumwalt school district,in Missouri, an experienced educator, and a noted author :

The current COVID-19 pandemic is a sobering reminder that we are educating today’s students for a world that is increasingly complex and unpredictable. The sequence that we use in mathematics education can be pivotal in developing students’ understanding and ability to apply ideas to their lives.

An explore-before-explain mindset to mathematics teaching means situating learning in real-life situations and problems and using those circumstances as a context for learning. Explore-before-explain teaching is all about creating conceptual coherence for learners and students’ experiences must occur before explanations and practice-type activities.

Distance learning reaffirmed these ideas when I was faced with the challenge of teaching area and perimeter for the first-time to a 3 rd grade learner. I quickly realized that rather than viewing area and perimeter as topics to be explained and then practiced, situating learning in problem-solving scenarios and using household items as manipulatives can illustrate ideas and derive the mathematical formulas and relationships.

Using Lego bricks, we quickly transformed equations and word problems into problem-solving situations that could be built. Student Lego constructions were used as evidence for comparing and contrasting physically how area and perimeter are similar and different as well as mathematical ways to calculate these concepts (e.g., students quickly learned by using Legos that perimeter is the distance around a shape while area is the total shape of an object). Thus, situating learning and having students use data as evidence for mathematical understanding have been critical for motivating and engaging students in distance learning environments.

Using an explore-before-explain sequence of mathematics instruction helps transform traditional mathematics lessons into activities that promote the development of deeper conceptual understanding and transfer learning.

A ‘Whiteboard Wall’

Andrea Clark is a grade 5-7 math and language arts teacher in Austin, Texas. She has a master’s in STEM education and has been teaching for over 10 years:

If you want to increase motivation, persistence, and participation in your math classroom, I recommend a whiteboard wall. Or some reusable dry erase flipcharts to hang on the wall. Or some dry erase paint. Anything to get your students standing up and working on math together on a nonpermanent surface.

The idea of using “vertical nonpermanent surfaces” in the math classroom comes from Peter Liljedahl’s work with the best conditions for encouraging and supporting problem-solving in the math classroom. He found that students who worked on whiteboards (nonpermanent surfaces) started writing much sooner than students who worked on paper. He also found that students who worked on whiteboards discussed more, participated more, and persisted for longer than students working on paper. Working on a vertical whiteboard (hung on the wall) increased all of these factors, even compared with working on horizontal whiteboards.

Adding additional whiteboard space for my students to write on the walls has changed my math classroom (I have a few moveable whiteboard walls covered in dry erase paint as well as one wall with large whiteboards from end to end). My students spent less time sitting down, more time collaborating, and more time doing high-quality math. They were more willing to take risks, even willing to erase everything they had done and start over if necessary. They were able to solve problems that were complex and challenging, covering the whiteboards with their thinking and drawing.

And my students loved it. They were excited to work together on the whiteboards. They were excited to come to math and work through difficult problems together. They moved around the room, talking to other groups and sharing ideas. The fact that the boards were on the wall meant that everyone could see what other groups were doing. I could see where every group was just by looking around the room. I could see who needed help and who needed more time to work through something. But my students could see everything, too. They could get ideas from classmates outside of their group, using others’ ideas to get them through a disagreement or a sticking point. It made formally presenting their ideas easier, too; everyone could just turn and look at the board of the students who were sharing.

I loved ending the math class with whiteboards covered in writing. It reminded me of all of the thinking and talking and collaborating that had just happened. And that was a good feeling at the end of the day. Use nonpermanent vertical surfaces and watch your math class come alive.

Thanks to Cindy, Danielle, Patrick, and Andrea for their contributions!

Please feel free to leave a comment with your reactions to the topic or directly to anything that has been said in this post.

Consider contributing a question to be answered in a future post. You can send one to me at [email protected] . When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.

You can also contact me on Twitter at @Larryferlazzo .

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Because differences are our greatest strength

Skills kids need going into fourth grade

By Amanda Morin

At a glance

In preparation for fourth grade, third graders focus on using language and writing in all subjects.

Most kids who are ready for fourth grade understand why and how multiplication works.

Fourth graders have to support their statements about a text with facts and details.

Getting ready for fourth grade involves focusing on using language and writing in all subjects. Math skills include using more than one step or operation to solve a problem.

To see if your child is ready for fourth grade, take a look at your state’s academic standards . Not all states use the same standards, but many of them have similar expectations for students. Here are some of the key skills kids are expected to master by the end of third grade in preparation for fourth grade.

Skills to get ready for grade 4: English language arts and literacy

To prepare for fourth grade, students are exposed to a variety of reading material, including fiction, nonfiction, charts, and maps. They’re expected to understand these new materials and write about what they’ve read . As writers, kids are expected to start organizing information and ideas more effectively and support their statements or observations with facts and details.

Rising fourth graders are also expected to know how to:

Read many types of stories and describe what happened, how the characters were affected, and what lessons they learned
Answer questions about reading material that covers history, social studies, and science; also use information in illustrations, maps, and charts to help answer questions
Give a class presentation on a topic using facts, details, and specific vocabulary
Participate in discussions by speaking clearly, listening, sharing opinions, building on other people’s ideas, and asking questions
Use dialogue and description to write about what a character is thinking and feeling
Gather information from online sources in addition to books and articles; use that information to write research papers

Is your child struggling with reading? Learn ways to help your child build phonological awareness in grade school, along with other ways to improve reading skills at home .

Skills to get ready for grade 4: Mathematics

By the end of third grade, children need to be familiar with fractions and start to understand the “whys” of multiplication and division. In fourth grade, students begin to calculate the area of shapes and use different problem-solving strategies to solve word problems. To work on these skill areas, they’re expected to be able to:

Explain what multiplication and division are
Know the times tables up to 12 and multiply numbers by 10
Use addition, subtraction, multiplication, and division to solve word problems involving more than one step
Understand the concept of area and how it relates to multiplication
Understand and identify fractions as numbers that can be placed on a number line; compare two fractions (like knowing that 2/3 is bigger than 3/5)
Express whole numbers as fractions and recognize fractions that are whole numbers (like knowing that 8/2 is the same as 4)
Measure weights and volumes
Read charts and graphs and show data as a graph or chart

See how learning and thinking differences can affect math skills . And explore a list of questions to ask about the school’s math instruction .

How to help your rising fourth grader

Kids learn at different rates. Don’t worry if your child hasn’t mastered all of these skills before starting fourth grade. But if your child is having trouble with many of these skills, you may want to consider talking with the teacher . Together you can come up with a plan to figure out what’s making learning harder.

Read about fourth-grade learning challenges for kids who learn and think differently. And explore ways to help your child prepare for fourth grade at home. Here are some ideas:

Practice word problems with more than one step or operation.
Talk about the characters and ideas in books you read together.
Expose your child to informational text like charts, brochures, and newspapers.
Role-play social situations .
Use multisensory techniques to build reading skills .
Try multisensory techniques to build math skills , too.

Key takeaways

In fourth grade, kids are expected to understand many types of stories and write research papers.

Consider talking to the teacher if your child is having trouble keeping up with schoolwork.

There are lots of ways to help your child prepare for fourth grade at home.

Tell us what interests you

About the author.

Amanda Morin is the author of “The Everything Parent’s Guide to Special Education” and the former director of thought leadership at Understood. As an expert and writer, she helped build Understood from its earliest days.

Reviewed by

Kristen L. Hodnett, MSEd is a clinical professor in the department of special education at Hunter College in New York City.

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Top 9 Math Strategies for Successful Learning (2021 and Beyond)

Why are effective Math strategies so important for students?

Getting students excited about math problems, top 9 math strategies for engaging lessons.

How teachers can refine math strategies

Math is an essential life skill. You use problem-solving every day. The math strategies you teach are needed, but many students have a difficult time making that connection between math and life.

Math isn’t just done with a pencil and paper. It’s not just solving word problems in a textbook. As an educator, you need fresh ways for math skills to stick while also keeping your students engaged.

In this article, we’re sharing 9 engaging math strategies to boost your students’ learning . Show your students how fun math can be, and let’s freshen up those lesson plans!

Unlike other subjects, math builds on itself. You can’t successfully move forward without a strong understanding of previous materials. And this makes math instruction difficult.

To succeed in math, students need to do more than memorize formulas or drill times tables. They need to develop a full understanding of what their math lessons mean , and how they translate into the real world. To reach that level of understanding, you need a variety of teaching strategies.

Conceptual understanding doesn’t just happen at the whiteboard. But it can be achieved by incorporating fun math activities into your lessons, including

Hands-on practice
Collaborative projects
Gamified or game-based learning

Repetition and homework are important. But for these lessons to really stick, your students need to find the excitement and wonder in math.

Creating excitement around math can be an uphill battle. But it’s one you and your students can win!

Math is a challenging subject — both to teach and to learn. But it’s also one of the most rewarding. Finding the right mix of fun and learning can bring a lot of excitement to the classroom.

Think about what your students already love doing. Video games? Legos? Use these passions to create exciting math lesson plans your students can relate to.

Hands-on math practice can engage students that have disconnected from math. Putting away the pencils and textbooks and moving students out of their desks can re-energize your classroom.

If you’re teaching elementary or middle school math, find ways for your students to work together. Kids this age crave peer interaction. So don’t fight it — provide it!

Play a variety of math games or puzzles . Give them a chance to problem-solve together. Build real-world skills in the classroom while also boosting student confidence.

And be sure to celebrate all the wins! It is easy to get bogged down with instruction and testing. But even the smallest accomplishments are worth celebrating. And these rewarding moments will keep your students motivated and pushing forward.

Keep reading to uncover all of our top math strategies for keeping your students excited about math.

1. Explicit instruction

You can’t always jump straight into the fun. Explicit instruction still provides the best foundation for the activities to come.

Set up your lesson for the day at the whiteboard, along with materials to demonstrate the coming activities. Make sure to also focus on any new vocabulary and concepts.

Tip: don't stay here for too long. Once the lesson is introduced, move on to the next fun strategy for the day!

2. Conceptual understanding

Helping your students understand the concept behind the lesson is crucial, but not always easy. Even your highest performing students may only be following a pattern to solve problems, without grasping the “why.”

Visual aids and math manipulatives are some of your best tools to increase conceptual understanding. Math is not a two dimensional subject. Even the best drawing of a cone isn’t going to provide the same experience as holding one. Find ways to let your students examine math from all sides.

Math manipulatives don’t need to be anything fancy. Basic wooden blocks, magnets, molding clay and other toys can create great hands-on lessons. No need to invest in expensive or hard-to-find materials.

Math word problems are also a great time to break out a full-fledged demo. Hot Wheels cars can demonstrate velocity and acceleration. A tape measure is an interactive way to teach area and volume. These materials give your students a chance to bring math off the page and into real life.

3. Using concepts in Math vocabulary

There’s more than one way to say something. And the more ways you can describe a mathematical concept, the better. Subtraction can also be described as taking away or removing. Memorizing multiplication facts is useful, but seeing these numbers used to calculate area gives them new meaning.

Some math words are going to be unfamiliar. So to help students get comfortable with these concepts, demonstrate and label math ideas throughout your classroom . Understanding comes more easily when students are surrounded by new ideas.

For example, create a division corner in your station rotations , with blocks to demonstrate the concept of one number going into another. Use baskets and labels to have students separate the blocks into each part of the division problem: dividend, divisor, quotient and remainder.

Give students time to explore, and teach them big ideas with both academic and everyday terms. Demystify math and watch their confidence build!

$Teacher sitting in front of her class of students with their arms raised$

4. Cooperative learning strategies

When students work together, it benefits everyone. More advanced students can lead, helping them solidify their knowledge. And they may have just the right words to describe an idea to others who are struggling.

It is rare in real-life situations for big problems to be solved alone. Cooperative learning allows students to view a problem from various angles. This can lead to more flexible, out-of-the-box thinking.

After reviewing a word problem together as a class, ask small student groups to create their own problems. What is something they care about that they can solve with these skills? Involve them as much as possible in both the planning and solving. Encourage each student to think about what they bring to the group. There’s no better preparation for the future than learning to work as a team.

5. Meaningful and frequent homework

When it comes to homework, it pays to think outside of textbooks and worksheets. Repetition is important, but how can you keep it fun?

Create more meaningful homework by including games in your curriculum plans. Encourage board game play or encourage families to play quiz-style games at home to improve critical thinking, problem solving and basic math skills.

Sometimes you need homework that doesn’t put extra work onto the parents. The end of the day is already full for many families. To encourage practice and give parents a break, assign game-based options like Prodigy Math Game for homework.

With Prodigy, students can enjoy a fun, video game experience that helps them stay excited and motivated to keep learning. They’ll practice math skills, while their parents have time to fix dinner. Plus, you’ll get progress reports that can help you plan future instruction . Win-win-win!

Set an Assessment through your Prodigy teacher account today to reinforce what you’re teaching in class and differentiate for student needs.

$The Assessment creation screen in a Prodigy teacher account.$

Ready to make homework fun?

6. Puzzle pieces math instruction

Some kids excel at math. But others pull back and may rarely participate. That lack of confidence is hard to break through. How can you get your reluctant students to join in?

Try giving each student a piece of the puzzle. When you’re presenting your class with a problem, this creates necessary collaboration to get to the solution.

Each student is given a piece of information needed to solve the problem. A number, a unit of measurement, or direction — break your problem into as many pieces as possible.

If you have a large class, break down three or more problems at a time. The first task: find the other students who are working on your problem (try color-coding or using symbols to distinguish each problem’s parts). Then watch the learning happen as everyone plays their own important role.

7. Verbalize math problems

There’s little time to slow down in the classroom. Instruction has to move fast to keep up with the expected standards. And students feel that, too.

When possible, try to set aside some time to ask about your students’ math struggles. Make sure they know that they can come to you when they get stuck. Keep the conversation open to their questions as much as possible.

One great way to encourage questions is to address common troubles students have encountered in the past. Where have your past classes struggled? Point these out during your explicit instruction, and let your students know this is a tricky area.

It’s always encouraging to know you’re not alone in finding something difficult. This also leaves the door open for questions, leading to more discovery and greater understanding.

8. Reflection time

Providing time to reflect gives the brain a chance to process the work completed. This can be done after both group and individual activities.

Group Reflection

After a collaborative activity, save some time for the group to discuss the project . Encourage them to ask:

What worked?
What didn’t work?
Did I learn a new approach?
What could we have done differently?
Did someone share something I had never thought of before?

These questions encourage critical thinking. They also show the value of working together with others to solve a problem. Everyone has different ways of approaching a problem, and they’re all valuable.

Individual Reflection

One way to make math more approachable is to show how often math is used. Journaling math encounters can be a great way for students to see that math is all around.

Ask them to add a little bit to their journal every day, even just a line or two. Where did they encounter math outside of class? Or what have they learned in class that has helped them at home?

$Zoomed in image of a student's hand writing in a journal$

Math skills easily transfer outside of the classroom. Help them see how much they have grown, both in terms of academics and social emotional learning .

9. Making Math facts fun

As a teacher, you know math is anything but boring. But transferring that passion to your students is a tricky task. So how can you make learning math facts fun?

Play games! Math games are great classroom activities. Here are a few examples:

Design and play a board game.
Build structures and judge durability.
Divide into groups for a quiz or game show.
Get kids moving and measure speed or distance jumped.

Even repetitive tasks can be fun with the right tools. That’s why engaging games are a great way to help students build essential math skills. When students play Prodigy Math Game , for example, they learn curriculum-aligned math facts without things like worksheets or flashcards. This can help them become excited to play and learn!

How teachers can refine Math strategies

Sometimes trying something new can make a huge difference for your students. But don’t stress and try to change too much at once.

You know your classroom and students best. Pick a couple of your favorite strategies above and try them out.

If you're looking to freshen up your math instruction, sign up for a free Prodigy teacher account. Your students can jump right into the magic of the Prodigy Math Game, and you’ll start seeing data on their progress right away!

Math Problem Solving Strategies

In these lessons, we will learn some math problem solving strategies for example, Verbal Model (or Logical Reasoning), Algebraic Model, Block Model (or Singapore Math), Guess & Check Model and Find a Pattern Model.

Related Pages Solving Word Problems Using Block Models Heuristic Approach to Problem-Solving Algebra Lessons

Problem Solving Strategies

The strategies used in solving word problems:

What do you know?
What do you need to know?
Draw a diagram/picture

Solution Strategies Label Variables Verbal Model or Logical Reasoning Algebraic Model - Translate Verbal Model to Algebraic Model Solve and Check.

Solving Word Problems

Step 1: Identify (What is being asked?) Step 2: Strategize Step 3: Write the equation(s) Step 4: Answer the question Step 5: Check

Problem Solving Strategy: Guess And Check

Using the guess and check problem solving strategy to help solve math word problems.

Example: Jamie spent $40 for an outfit. She paid for the items using $10, $5 and $1 bills. If she gave the clerk 10 bills in all, how many of each bill did she use?

Problem Solving : Make A Table And Look For A Pattern

Identify - What is the question?
Plan - What strategy will I use to solve the problem?
Solve - Carry out your plan.
Verify - Does my answer make sense?

Example: Marcus ran a lemonade stand for 5 days. On the first day, he made $5. Every day after that he made $2 more than the previous day. How much money did Marcus made in all after 5 days?

Find A Pattern Model (Intermediate)

In this lesson, we will look at some intermediate examples of Find a Pattern method of problem-solving strategy.

Example: The figure shows a series of rectangles where each rectangle is bounded by 10 dots. a) How many dots are required for 7 rectangles? b) If the figure has 73 dots, how many rectangles would there be?

a) The number of dots required for 7 rectangles is 52.

b) If the figure has 73 dots, there would be 10 rectangles.

Example: Each triangle in the figure below has 3 dots. Study the pattern and find the number of dots for 7 layers of triangles.

The number of dots for 7 layers of triangles is 36.

Example: The table below shows numbers placed into groups I, II, III, IV, V and VI. In which groups would the following numbers belong? a) 25 b) 46 c) 269

Solution: The pattern is: The remainder when the number is divided by 6 determines the group. a) 25 ÷ 6 = 4 remainder 1 (Group I) b) 46 ÷ 6 = 7 remainder 4 (Group IV) c) 269 ÷ 6 = 44 remainder 5 (Group V)

Example: The following figures were formed using matchsticks.

a) Based on the above series of figures, complete the table below.

b) How many triangles are there if the figure in the series has 9 squares?

c) How many matchsticks would be used in the figure in the series with 11 squares?

b) The pattern is +2 for each additional square. 18 + 2 = 20 If the figure in the series has 9 squares, there would be 20 triangles.

c) The pattern is + 7 for each additional square 61 + (3 x 7) = 82 If the figure in the series has 11 squares, there would be 82 matchsticks.

Example: Seven ex-schoolmates had a gathering. Each one of them shook hands with all others once. How many handshakes were there?

Total = 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes.

The following video shows more examples of using problem solving strategies and models. Question 1: Approximate your average speed given some information Question 2: The table shows the number of seats in each of the first four rows in an auditorium. The remaining ten rows follow the same pattern. Find the number of seats in the last row. Question 3: You are hanging three pictures in the wall of your home that is 16 feet wide. The width of your pictures are 2, 3 and 4 feet. You want space between your pictures to be the same and the space to the left and right to be 6 inches more than between the pictures. How would you place the pictures?

The following are some other examples of problem solving strategies.

Explore it/Act it/Try it (EAT) Method (Basic) Explore it/Act it/Try it (EAT) Method (Intermediate) Explore it/Act it/Try it (EAT) Method (Advanced)

Finding A Pattern (Basic) Finding A Pattern (Intermediate) Finding A Pattern (Advanced)

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4th Grade Math IEP Goal Bank Based On The Common Core Standards

Math goals are often tricky to line up with the Common Core Standards (which aren’t endorsed by the department of Ed anymore but are still used by almost every curriculum). Meeting a low skill level to an upper grade level can take a lot of thought. Hopefully these examples can give you some new ideas, get you thinking about new ways to track, and if they are written well, they should lead you to progress monitoring.

A question I hear a lot is: How can I use standards that are often too advanced for grade level students, to guide my students who are below grade level? My first thought is to take only the meat of the standards. Many textbooks create math problems that are “interpretations” of the standards. However, when you get to the meat of the standard, there is one or two key skills that students can learn. It’s okay if students can’t do every aspect of the standard. If they can access the basic skill, or one aspect of the content, that is still grade level content AND is differentiating.

There’s a common misconception that if a student receives a goal on grade level, that they no longer need services. This is not true if the IEP goals are creating a way to access grade level standards through differentiating and narrowing down content. I am always a proponent of getting students in special education as much grade level content as possible. So to wrap this up, look for narrowing down the standards to a specific skill that can be taught. Talk with general education teachers to help guide you to which skills are most important. And of course, look at their testing to see which skill areas they are deficient in. Sometimes I write a goal that is skill specific and then another that is grade specific (but still under their area of weakness). Other times, I write them together.

Operations And Algebraic Thinking

Use the four operations with whole numbers to solve problems.

These standards and example goals, would all be working on skills around actual computation. So if a student is struggling in computations, I would try to tie into one grade level of these standards.

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. CCSS.MATH.CONTENT.4.OA.A.1

Complex Example: Student will be able to take a product in a single digit multiplication problem, and then use the multiplier and multiplicand to make statements about the product being so many times larger. Student will master this goal when they can verbally say the product is ___ times larger across 5 equations, with an average accuracy rate of 70%, across 10 trials.

Complex Example : Using a check list with steps to remember, Student will be able to interpret a single digit multiplication statement that a product is a specific times as many as the multiplier. Student will show mastery when they solve this across 3 statements, with an average accuracy rate of 80% across 10 trials.

Simple Example: Using a visual representation of a single digit multiplication equation, Student will be able to say the product is ___ times larger than ____, across 3 equations, with an average accuracy rate of 75% across 4 consecutive trials.

Simple Example: Student will be able to solve a multiplication problem with digits 1-5 and then say the multiplication sentence using correct vocabulary with on 3 multiplication problems, with 80% accuracy across 10 trials.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. CCSS.MATH.CONTENT.4.OA.A.2

Note: see definition of multiplicative comparison here .

Complex Example: Using a calculator, Student will be able to write a multiplication equation from a single digit multiplicative comparison, on 2 equations, with an average accuracy rate of 70% across 10 trials.

Simple Example: Given a multiplication chart, Student will be able to write a multiplication equation from single digit sentence using “twice as many” across 2 equations, and 10 total trials, with at least 80% accuracy. (consider doing a few other goals on three times, four times, etc.)

Simple Example: Given a multiplication problem from 1-10, Student will be able to draw a picture of two times as many, on 2 equations per trial, across 10 total trials with an average accuracy rate of 80%.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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. CCSS.MATH.CONTENT.4.OA.A.3

Note: This would be a great standard to create a goal and then benchmarks that include writing an equation with a missing quantity, check their work, or use estimation strategies.

Complex Example: Using a graphic organizer, Student will be able to write an equation with a missing variable from a 4th grade level division or multiplication problem, with an average accuracy rate of 90% across 10 trials.

Complex Example: Student will be able to use estimation strategies to check their answer on two digit multiplication and division problems.

Simple Example: Using a graphic organizer, student will be able to solve 3 double digit multiplication word problems, with an average accuracy rate of 75% across 10 trials.

Gain familiarity with factors and multiples

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. CCSS.MATH.CONTENT.4.OA.B.4

Complex Example: Student will be able to use multiple addition or subtraction to find the factors of numbers 1-100, on 3 numbers at a time, across 10 trials with an average accuracy rate of 80%.

Simple Example: Given 5 numbers that are a multiple and factors, Student will be able to identify which number is a multiple and which numbers are factors. Student will master this goal when they can identify 3 sets of multiples, with 90% accuracy across 10 trials.

Generate and analyze patterns

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way . CCSS.MATH.CONTENT.4.OA.C.5

Complex Example: Student will be able skip count by 5, 6, and 7’s with an average accuracy rate of 70% across 10 trials.

Simple Example: Student will be able to use a number line to count by 2’s across 10 trials with a 90% accuracy rate.

Number & Operations in Base Ten

Generalize place value understanding for multi-digit whole numbers.

These standards and example goals are all related to understanding numbers and counting. If a student is showing a weak understanding with “mathematical thinking” or “processes” these goals would be under those umbrella terms. (Also, when determining goals, you only need data to show that a student needs a goal. If you give them a test that shows these specific skills are a weakness, that is good enough.)

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division . CCSS.MATH.CONTENT.4.NBT.A.1

Complex Example: Student will be able to divide by multiples of 10 up to 1,000 on 5 sample problems per trial, across 10 trials, with an average accuracy rate of 70%.

Complex Example: Student will be able to multiply by multiples of 10 up to 1,000 on 3 sample problems per trials, across 10 trials, with an average accuracy rate of 90%.

Simple(er) Example: Student will be able to able to write the place value of 4 sample numbers (that could be between 1-1,000) in base ten numerals (450 is 400 + 50) across 10 trials with an average accuracy rate of 90%.

Simple Example: Student will be able to identify the place value of 5 numbers (from 1-100,000) with an average accuracy rate of 70% across 10 trials.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. CCSS.MATH.CONTENT.4.NBT.A.2

Note: For this standard, and with most students, I would break it up into a few different goals. You could just benchmarks if you wanted to. You could put these examples together or use all of them.

Complex Example: Student will be able to write the place value of 2 sample numbers (between 1-1,000,000) in base ten numerals and then determine which is larger or equal to each other across 20 trials with an average accuracy rate 90%.

Simple Example: Student will be able to look at two numbers written as a base ten numeral (1-1,000), and determine if the number is greater, less, or equal, across 20 trials with an average accuracy rate of 90%.

Simple Example: Student will be able to compare two numbers (1-1,000) and determine if they are greater, less, or equal across 20 trials with an average accuracy rate of 80%.

Use place value understanding to round multi-digit whole numbers to any place. CCSS.MATH.CONTENT.4.NBT.A.3

Complex Example: Student will be able to round 5, 4-digit numbers to the nearest thousand or hundred, across 10 trials with an average accuracy rate of 80%.

Simple Example: Student will be able to determine if 3, two digit numbers are closer to lower or upper multiple of ten (26 is closer to 30), across 20 trials with an average accuracy rate of 70%.

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

These standards go back to computing goals, but could also be used under mathematical concepts.

Fluently add and subtract multi-digit whole numbers using the standard algorithm. CCSS.MATH.CONTENT.4.NBT.B.4

Example: Student will be able to add 3, 4 digit numbers (or less) with an average accuracy rate of 80% across 10 trials.

Example: Using graph paper to help organize numbers, Student will be able to add 2, 2 digit by 2 digit numbers with an average accuracy rate of 70% across 15 trials.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CCSS.MATH.CONTENT.4.NBT.B.5

Example: Using a multiplication chart, Student will be able to multiply 2, four digit by one digit, with an average accuracy rate of 80% across 10 trials.

Example: Student will be able to draw a picture to show 10, two digit multiplication problems, with 80% accuracy across 3 consecutive trials.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CCSS.MATH.CONTENT.4.NBT.B.6

Example: Student will be able to use a multiplication chart to help them divide four-digit dividends and one-digit divisors across 10 trials with an average accuracy rate of 90%.

Example: Student will be able to use a calculator to find the correct answer to a multi-digit division problem, with 100% across 3 consecutive trials.

Numbers and Operations – Fractions

Extend understanding of fraction equivalence and ordering.

Explain why a fraction a / b is equivalent to a fraction ( n × a )/( n × b ) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. CCSS.MATH.CONTENT.4.NF.A.1

Complex Example: Student will be able to draw 3 picture of two equivalent fractions pairs, with an average accuracy rate of 80% across 10 trials.

Complex Example: Student will be able to use multiplication to find an equivalent fraction with 90% accuracy across 5 consecutive trials.

Simple Example: Student will be able to use a manipulative to show two equivalent fractions with 90% accuracy across 3 consecutive trials.

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. CCSS.MATH.CONTENT.4.NF.A.2

Complex Example: Using a calculator, Student will be able to find a common denominator between two fractions, across 10 trials, with 5 fractions per trial, with an average accuracy rate of 90%.

Complex Example: Using a calculator, Student will be able to find a common denominator, then determine which fraction is greater or lesser, across 5 trials, with 2 fractions per trial, having an average accuracy rate of 70%.

Simple Example: Student will be able to compare two fractions with the same denominator across 5 trials with an average accuracy rate of 90%.

Build fractions from unit fractions

Understand a fraction a / b with a > 1 as a sum of fractions 1/ b . CCSS.MATH.CONTENT.4.NF.B.3.A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. CCSS.MATH.CONTENT.4.NF.B.3.B Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8 . CCSS.MATH.CONTENT.4.NF.B.3.C Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. CCSS.MATH.CONTENT.4.NF.B.3.D Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. CCSS.MATH.CONTENT.4.NF.B.3

Complex Example: Student will be able to solve a fraction addition or subtraction word problem (with the same denominator), and create a picture of the two fractions, with 80% accuracy across 10 trials.

Simple Example: Student will be able to use fraction manipulatives to show how many equal pieces are in a fraction, with 100% accuracy across 3 consecutive trials.

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. CCSS.MATH.CONTENT.4.NF.B.4

Complex Example: Student will be able to determine the operation being used in a word problem, and then multiply a fraction by a whole number, with 80% accuracy across 10 trials.

Simple Example: Student will be able to use manipulative to solve a multiplication problem of a fraction and whole number, with 70% accuracy across 15 trials.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. 2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100 . CCSS.MATH.CONTENT.4.NF.C.5

Example: Student will be able to change a fraction with a denominator 10, to an equivalent fraction with denominator 100, across 10 trials with an average accuracy rate of 75%.

Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram . CCSS.MATH.CONTENT.4.NF.C.6

Example: Student will be able to change a fraction with denominator 100 into a decimal with 80% across 20 trials.

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. CCSS.MATH.CONTENT.4.NF.C.7

Example: Student will be able to compare two, two-digit decimals, across 5 questions, with 80% accuracy across 10 trials.

Measurement and Data

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), … CCSS.MATH.CONTENT.4.MD.A.1

Example: Student will be able to multiply to find out the equivalent units in km, m, and cm. Student will mastery this when they can do this 5 times, across 5 trials, with 70% accuracy.

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. CCSS.MATH.CONTENT.4.MD.A.2

Complex Example: Student will set up a fraction multiplication problem using distances across 10 trials with 70% accuracy.

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor . CCSS.MATH.CONTENT.4.MD.A.3

Complex Example: Student will be able to use fraction multiplication rules to solve a missing unit problem with 90% accuracy across 10 trials.

Complex Example: Student will be able to use a set up a fraction problem with a missing unit with 70% accuracy across 10 trials.

Represent and interpret data

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection . CCSS.MATH.CONTENT.4.MD.B.4

Example: Student will be able to read a line plot and answer 3 literal questions about the data with 100% accuracy across 3 consecutive trials.

Geometric measurement: understand concepts of angle and measure angles AND Geometry

For these goals, I would only use them as needed. If a student is all caught up in other areas, it may be time to consider if they need a math goal. However, there is always an outlier case. Or if a student is in a classroom where they are never in the general education classroom, they may have a goal for this.

math problem solving strategies 4th grade examples

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