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CHALLENGE ZONE 4th Grade Math Problems
Welcome to our 4th Grade Math Problems. Here you will find our range of challenging math problem worksheets which are designed to give children the opportunity to apply their skills and knowledge to solve a range of longer problems.
These problems are also a great way of developing perseverance and getting children to try different approaches in their math.
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4th Grade Math Problems
Here you will find a range of problem solving worksheets.
The 4th grade math problems on the sheets are longer math problems designed to encourage children to use a range of math skills to solve them.
The skills the problems will help to develop include:
- systematic working
- logical thinking
- number fact knowledge
- fraction problems
- trial and improvement strategies
- working systematically
- searching for all possible answers.
At fourth grade, the problems are starting to become more advanced with children needing to become more systematic in their approach and experimenting using trial and improvement strategies.
Many of the problems have addition 'What if ...' questions with them to extend learning and get children looking for alternative solutions.
- 4th Grade Math Word Problems
Captain Salamander's Puzzling Problems
Captain Salamander's Puzzling Problems involves using thinking and reasoning skills to work out two math challenges. The challenges also involve an element of trial and improvement. This sheet is available in standard and metric units.
- Captain Salamander's Puzzling Problems - metric
- PDF version
- Captain Salamander's Puzzling Problems - standard
- Broken Calculator Problem 3
The Broken Calculator problem is a number problem involving using an imaginary broken calculator with only the 4, 7, +, - and = buttons working to make different totals.
There are 2 versions of the problem sheet, one with a pre-prepared template for filling in, and a second blank version for children to show their own recording system.
- Blank version
Quadra's Magic Bag Challenges
Quadra's Magic Bag Challenges involves using thinking and reasoning skills to work out two math challenges. The challenges also involve an element of trial and improvement, and also some addition.
- Quadra's Magic Bag Challenge
- Tyger's Fishy Problems
Tyger's Fishy Problems is a 4th grade math problem which involves using thinking and reasoning skills to solve two money challenges. This sheet is available in both dollars ( $ ) and pounds ( £ ).
- Tyger's Fishy Problems UK Version
- Bruno's Bones
Bruno's Bones is an activity to encourage children to work systematically to find the number of bones that a dog called Bruno has buried in his garden. This is a good problem for using lists/tables to solve and also counting in single digit steps.
- Don't Be Alarmed
Don't Be Alarmed is a sequencing problem where a burglar alarm is switching different lights on and off at different times. It is good for developing mathematical modeling and using lists/tables to help solve problems.
- Four Dogs Problem
Four Dogs Problem is a logic problem which involves using the clues to work out the owners for each of the four dogs.
Fox vs Rabbit
Fox vs Rabbit is an another mathematical modeling activity which involves looking at the routes of a fox and a rabbit and working out at if/when the rabbit is likely to get caught.
- Fox vs Rabbit #1 Standard Units
- Fox vs Rabbit #1 Metric Units
Frazer's Wall
Frazer's Wall is a trial and improvement activity which involves trying to work out the number of bricks that were laid in each day to make a set total of bricks. This problem can also be solved or modelled using algebra.
- Frazer's Wall #1
- Make Me 100
Make Me 100 is one of our 4th grade math problems designed to test children to find ways of making the numbers from 1 to 10 make 100 using different operators. It is good for developing perseverance and also for reinforcing the use of brackets of PEMDAS.
Sally's Fruit Punch
Sally's Fruit Punch is a money and scaling activity. The aim is to use the information to work out how much ingredients are needed. The ingredients then need to be priced to work out a total cost.
- Sally's Fruit Punch #2
- Sally's Fruit Punch #2 UK Version
- Share the Treasure #4
Share the Treasure is a fraction sharing activity where the aim is to work backwards to find out how many bars of treasure the pirates had before they shared them all out. It is a good activity for developing fraction problem solving and working backwards.
Something Fishy
Something Fishy is a money problem which involves working out exactly how many of each fish were bought in order to have spent $150 on the fish. It is a good activity for using lists and tables to find all possibilities.
- Something Fishy #1
- Something Fishy #1 UK Version
The Rock Race #2
The Rock Race is a 4th grade math problem which needs some perseverance to complete. The aim of the activity is to try different routes around the 6 rocks to determine which route is the shortest.
- The Rock Race #2 Metric version
- The Rock Race #2 Standard version
- Who Caught the Biggest Fish?
Who Caught the Biggest Fish is a logical number problem where you need to use trial and improvement strategies to work out the order of size of the fish from the clues given about their weights.
Looking for some easier math problems?
We have a range of easier word problems on our 3rd grade math problems page.
The problems on this page are at a simpler level than those here.
Many of the problems, e.g. Place It Right, Pick the Cards and Share the Treasure have easier versions on this page.
- 3rd grade Math Problems
Looking for some harder word problems
We have a range of more challenging word problems on our 5th grade problem solving page.
The problems on this page are at a trickier level than those here.
Some of the problems, e.g. The Rock Race and Sally's Fruit Punch and Frazer's Wall have harder versions on this page.
- 5th Grade Math Problems
Looking for some more fourth grade math word problems?
Here is our set of 4th grade math word problems to help your child with their problem solving skills.
Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.
Using these sheets will help your child to:
- 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.
- Multiplication Word Problems 4th Grade
- 4th Grade Math Puzzles
Here you will find a range of printable 4th grade math puzzles for your child to enjoy.
The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.
Using these puzzles will help your child to:
- learn and practice their addition facts;
- practice adding both positive and negative numbers;
- practice their subtraction facts;
- practice multiplication and division facts;
- develop problem solving skills and reasoning.
All the puzzles support elementary math benchmarks for 4th grade.
- Math Games 4th Grade
Using games is a great way to learn Math facts and develop mental calculation skills in a fun and easy way.
The following games involve different 4th Grade Math activities which your child will enjoy playing.
Games include using negative numbers, decimal addition and subtraction, rounding, multiplying by 10s.
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TRIGONOMETRY WORD PROBLEMS WITH SOLUTIONS
Problem 1 :
The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60 °. Find the height of the building.
Draw a sketch.
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/pracprob1.png)
Here, AB represents height of the building, BC represents distance of the building from the point of observation.
In the right triangle ABC, the side which is opposite to the angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).
Now we need to find the length of the side AB.
tanθ = Opposite side/Adjacent side
tan60° = AB/BC
√3 x 50 = AB
Approximate value of √3 is 1.732
AB = 50 (1.732)
AB = 86.6 m
So, the height of the building is 86.6 m.
Problem 2 :
A ladder placed against a wall such that it reaches the top of the wall of height 6 m and the ladder is inclined at an angle of 60 ° . Find how far the ladder is from the foot of the wall.
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/practprob2.png)
Here AB represents height of the wall, BC represents the distance between the wall and the foot of the ladder and AC represents the length of the ladder.
In the right triangle ABC, the side which is opposite to angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).
Now, we need to find the distance between foot of the ladder and the wall. That is, we have to find the length of BC.
tanθ = opposite side/adjacent side
BC = (6/√3) x (√3/√3)
BC = (6√3)/3
Approximate value of √3 is 1.732.
BC = 2 (1.732)
BC = 3.464 m
So, the distance between foot of the ladder and the wall is 3.464 m.
Problem 3 :
A string of a kite is 100 meters long and t he inclination of the string with the ground is 60°. Find the height of the kite, assuming that there is no slack in the string.
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/pracprob12.png)
Here AB represents height of kite from the ground, BC represents the distance of kite from the point of observation.
In the right triangle ABC the side which is opposite to angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).
Now we need to find the height of the side AB.
sinθ = opposite side/hypotenuse side
sinθ = AB/AC
sin60° = AB/100
√3/2 = AB/100
(√3/2) x 100 = AB
AB = 50√3 m
So, the height of kite from the ground 50√3 m.
Problem 4 :
From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring 30 ° . Find the distance between the tree and the tower.
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/pracprob3.png)
Here AB represents height of the tower, BC represents the distance between foot of the tower and the foot of the tree.
Now we need to find the distance between foot of the tower and the foot of the tree (BC).
tan30° = AB/BC
1/√3 = 30/BC
BC = 30(1.732)
BC = 51.96 m
So, the distance between the tree and the tower is 51.96 m.
Problem 5 :
A man wants to determine the height of a light house. He measured the angle at A and found that tan A = 3/4. What is the height of the light house if A is 40m from the base?
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/pracprob4.png)
Here BC represents height of the light house, AB represents the distance between the light house from the point of observation.
In the right triangle ABC the side which is opposite to the angle A is known as opposite side (BC), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (AB).
Now we need to find the height of the light house (BC).
tanA = opposite side/adjacent side
tanA = BC/AB
Given : tanA = 3/4.
3/4 = BC/40
Multiply each side by 40.
So, the height of the light house is 30 m.
Problem 6 :
A ladder is leaning against a vertical wall makes an angle of 20° with the ground. The foot of the ladder is 3 m from the wall. Find the length of ladder.
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/practprob14.png)
Here AB represents height of the wall, BC represents the distance of the wall from the foot of the ladder.
In the right triangle ABC, the side which is opposite to the angle 20° is known as opposite side (AB),the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).
Now we need to find the length of the ladder (AC).
cosθ = adjacent side/hypotenuse side
Cosθ = BC/AC
Cos 20° = 3/AC
0.9397 = 3/AC
AC = 3/0.9396
So, the length of the ladder is about 3.193 m.
Problem 7 :
A kite is flying at a height of 65 m attached to a string. If the inclination of the string with the ground is 31°, find the length of string.
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/practprob15.png)
Here AB represents height of the kite. In the right triangle ABC the side which is opposite to angle 31° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).
Now we need to find the length of the string AC.
sin31° = AB/AC
0.5150 = 65/AC
AC = 65/0.5150
AC = 126.2 m
Hence, the length of the string is 126.2 m.
Problem 8 :
The length of a string between a kite and a point on the ground is 90 m. If the string makes an angle θ with the ground level such that tan θ = 15/8, how high will the kite be ?
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/practprob16.png)
Here AB represents height of the balloon from the ground. In the right triangle ABC the side which is opposite to angle θ is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).
tanθ = 15/8 ----> cotθ = 8/15
cscθ = √(1+ cot 2 θ)
cscθ = √(1 + 64/225)
cscθ = √(225 + 64)/225
cscθ = √289/225
cscθ = 17/15 ----> sinθ = 15/17
But, sinθ = opposite side/hypotenuse side = AB/AC.
AB/AC = 15/17
AB/90 = 15/17
So, the height of the tower is 79.41 m.
Problem 9 :
An airplane is observed to be approaching a point that is at a distance of 12 km from the point of observation and makes an angle of elevation of 50°. Find the height of the airplane above the ground.
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/practprob17.png)
Here AB represents height of the airplane from the ground. In the right triangle ABC the side which is opposite to angle 50° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and remaining side is called adjacent side (BC).
From the figure given above, AB stands for the height of the airplane above the ground.
sin50° = AB/AC
0.7660 = h/12
0.7660 x 12 = h
So, the height of the airplane above the ground is 9.192 km.
Problem 10 :
A balloon is connected to a meteorological station by a cable of length 200 m inclined at 60 ° angle with the ground. Find the height of the balloon from the ground. (Imagine that there is no slack in the cable)
![problem solving wall 200 answers problem solving wall 200 answers](https://www.onlinemath4all.com/images/practprob18.png)
Here AB represents height of the balloon from the ground. In the right triangle ABC the side which is opposite to angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse (AC) and the remaining side is called as adjacent side (BC).
From the figure given above, AB stands for the height of the balloon above the ground.
sin60° = AB/200
√3/2 = AB/200
AB = (√3/2) x 200
AB = 100(1.732)
AB = 173.2 m
So, the height of the balloon from the ground is 173.2 m.
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We always appreciate your feedback.
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Maths Problem Solving Wall: Standard Form & Astronomy
Subject: Mathematics
Age range: 14-16
Resource type: Visual aid/Display
![problem solving wall 200 answers Maths Resources](https://d2w4qhtqw2dbsq.cloudfront.net/profile_live/1645778/small.jpg?_=1719147983280)
Last updated
11 April 2018
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An original collection of 22 graded mathematical problems suitable for improving the problem solving skills of your secondary school maths students. (no answers included - yet…) With this resource your students will • improve their mathematical problem solving skills • apply their knowledge of standard form to solve problems • deepen their interest in mathematics and its applications • see links between mathematics, the sciences, engineering and technology • develop their appreciation of the rich history and diverse internationalism of mathematics The tasks in this resource can be used to enrich your teaching in many ways; as a problem wall display, as a classroom activity, as extension work, as supplementary homework, as cover work or as the base of an extended research project.
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Fantastic, some really interesting problems for my class to get stuck into!
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Physics Problems with Solutions
Projectile problems with solutions and explanations, problems with detailed solutions.
An object is launched at a velocity of 20 m/s in a direction making an angle of 25° upward with the horizontal. a) What is the maximum height reached by the object? b) What is the total flight time (between launch and touching the ground) of the object? c) What is the horizontal range (maximum x above ground) of the object? d) What is the magnitude of the velocity of the object just before it hits the ground? Solution to Problem 1
A ball kicked from ground level at an initial velocity of 60 m/s and an angle θ with ground reaches a horizontal distance of 200 meters. a) What is the size of angle θ? b) What is time of flight of the ball? Solution to Problem 5
A ball of 600 grams is kicked at an angle of 35° with the ground with an initial velocity V 0 . a) What is the initial velocity V 0 of the ball if its kinetic energy is 22 Joules when its height is maximum? b) What is the maximum height reached by the ball Solution to Problem 6
A projectile starting from ground hits a target on the ground located at a distance of 1000 meters after 40 seconds. a) What is the size of the angle θ? b) At what initial velocity was the projectile launched? Solution to Problem 7
The trajectory of a projectile launched from ground is given by the equation y = -0.025 x 2 + 0.5 x, where x and y are the coordinate of the projectile on a rectangular system of axes. a) Find the initial velocity and the angle at which the projectile is launched. Solution to Problem 8
Two balls A and B of masses 100 grams and 300 grams respectively are pushed horizontally from a table of height 3 meters. Ball has is pushed so that its initial velocity is 10 m/s and ball B is pushed so that its initial velocity is 15 m/s. a) Find the time it takes each ball to hit the ground. b) What is the difference in the distance between the points of impact of the two balls on the ground? Solution to Problem 9
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pdf, 1.58 MB. A collection of 200 graded mathematical problems suitable for improving the problem solving skills of your secondary school maths students. (Note: no solutions included - by design!) With this resource your students will. • improve their mathematical problem solving skills. • deepen their interest in mathematics and its ...
Free math problem solver answers your algebra homework questions with step-by-step explanations. Mathway. Visit Mathway on the web. Start 7-day free trial on the app. Start 7-day free trial on the app. Download free on Amazon. Download free in Windows Store. Take a photo of your math problem on the app. get Go. Algebra. Basic Math.
The 4th grade math problems on the sheets are longer math problems designed to encourage children to use a range of math skills to solve them. The skills the problems will help to develop include: systematic working. logical thinking. number fact knowledge. fraction problems. trial and improvement strategies.
Problem Solving Wall - simon wise
Problem 1 : The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60 °. Find the height of the building. Solution : Draw a sketch. Here, AB represents height of the building, BC represents distance of the building from the point of observation.
Activity 2.3b - Engineering Problem Solving Answer Key. A force of 200 lbs pushes against a rectangular plate that is 1 ft. by 2 ft. Determine the. pressure in lb and lb that the plate exerts on the ground due to this force. ft. in. 2. SOLUTION. Press = P/A Area = A = 2' x 1' = 2 ft2 convert to in2. = 2 ft. 2 x 12 in x.
Maths Problem Solving Wall: 200 Classic Problems in Mathematics. FREE (28) A collection of 200 graded mathematical problems suitable for improving the problem solving skills of your secondary school maths students. (Note: no solutions included - by design!) With this resource your students will • improve their mathematical problem solving ...
Khan Academy's 100,000+ free practice questions give instant feedback, don't need to be graded, and don't require a printer. Math Worksheets. Khan Academy. Math worksheets take forever to hunt down across the internet. Khan Academy is your one-stop-shop for practice from arithmetic to calculus. Math worksheets can vary in quality from ...
Add your answer: Earn +20 pts. Q: A 2.0 kg wood box slides down a vertical wood wall while you push on it at a 45 angle. What is the force applied to slide the box down at a constant speed?
Step 1. art A The 2.0 kg wood box in the figure (Figure 1) slides down a vertical wood wall while you push on it at a 45 angle. The coefficient of kinetic friction of wood on wood is μk = 0.200. What magnitude of force should you apply to cause the box to slide down at a constant speed?
Maths Problem Solving Wall: Standard Form & Astronomy. An original collection of 22 graded mathematical problems suitable for improving the problem solving skills of your secondary school maths students. (no answers included - yet…) The tasks in this resource can be used to enrich your teaching in many ways; as a problem wall display, as a ...
Problem 2. A projectile is launched from point O at an angle of 22° with an initial velocity of 15 m/s up an incline plane that makes an angle of 10° with the horizontal. The projectile hits the incline plane at point M. a) Find the time it takes for the projectile to hit the incline plane. b)Find the distance OM. Solution to Problem 2.
Before we begin the problems, it helps to list your known's and unknowns/what we are solving for. This helps with organization by identifying the what the problem is asking for. Also, red represents the solution. Section 9.2: Solving Impulse and Momentum Problems 12) A 250 g ball collides with a wall. The figure below shows the ball's ...
Practice the questions given in the worksheet on word problem on measuring length (i.e. addition and subtraction). Addition and subtraction in meters and centimetres is done in the similar way as in the case of ordinary numbers. 1. Shelly purchased 40 m 200 cm long rope and Jenny purchased 16 m 370 cm long rope.
Solving Density Problems. 13m. Dimensional Analysis. 10m. Counting Significant Figures. 5m. Operations with Significant Figures. 11m. 2. 1D Motion / Kinematics 3h 56m. Worksheet. ... The 2.0 kg wood box in FIGURE P6.58 slides down a vertical wood wall while you push on it at a 45° angle. What magnitude of force should you apply to cause the ...
To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.
The 2.0 kg wood box in (Figure 1) slides down a vertical wood wall while you push on it at a 4 5 ∘ anglew The coefficient of kinetic friction of wood on wood is μ k = .200.For help with math skills, you may want to review: Vector Components For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Ready for takeoff.
Now is the time to solve some examples to understand Archimedes' principle. Example: a block of wood floats in freshwater with two-fifth of its volume V submerged and in oil with 0.75V submerged. Find the density of (a) the wood (b) the oil. Solution: Since wood floats in water so its weight must be balanced with the buoyancy force.
The 2.0 kg wood box in (Figure 1) slides down a vertical wood wall while you push on it at a 4 5 ∘ angle. The coefficient of kinetic friction of wood on wood is μ k = 0.200. What magnitude of force should you apply to cause the box to slide down at a constant speed? For help with math skills, you may want to review: Vector Components For general problem-solving tips and strategies for this ...
Science. Physics. The 2.0 kg wood box in the figure (Figure 1) slides down a vertical wood wall while you push on it at a 45 ∘ angle. The coefficient of kinetic friction of wood on wood is μk = 0.200. What magnitude of force should you apply to cause the box to slide down at a constant speed.
Problem (11): A $0.06-\rm kg$ golf ball strikes a wall at an angle of $37^\circ$ with a speed of $28\,\rm m/s$ and rebounds at the same angle and speed. ... You can also check this out for solving simple problems on Momentum. Author: Dr. Ali Nemati Published: ...
A wall clock has a second hand 20.0 cm long. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Fast car, flat curve. Part A What is the radial acceleration of the tip of this hand? Express your answer in centimeters per second squared.
Physics. Physics questions and answers. Review Constants n The 2.0 kg wood box in the figure (Figure 1) slides down a vertical wood wall while you push on it at a 45" angle. The coefficient of kinetic friction of wood on wood is le = 0.200. Part A You may want to review (Page 131) What magnitude of force should you apply to cause the box to ...