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Times tables: multiplication and division facts - Problem-Solving Investigation - Year 4
Subject: Mathematics
Age range: 7-11
Resource type: Worksheet/Activity
Last updated
4 October 2019
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This in-depth maths investigation is an open-ended problem solving activity for Year 4 children. It can be used to support teaching towards the objectives: Times tables: multiplication and division facts.
In-depth Investigation: Table Digital Roots Children find the digital roots of multiples of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. They identify patterns and relate these to what they know of numbers.
This investigation will develop maths meta-skills, support open-ended questioning and logical reasoning, and enable children to learn to think mathematically and articulate mathematical ideas.
This problem-solving investigation is part of our [Year 4 Multiplication and Division] ( https://www.hamilton-trust.org.uk/maths/year-4-maths/multiplication-and-division-2/ ) block. Each Hamilton maths block contains a complete set of planning and resources to teach a term’s worth of objectives for one of the National Curriculum for England’s maths areas.
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Year 4 Multiplication & Division - Problem-Solving Investigations
These in-depth maths investigations are open-ended problem solving activities for Year 4 children. **In-depth Investigation: Doubling forever** Children double numbers up to 20 and look for duplicate sequences. **In-depth Investigation: Doubling forever** Children double numbers up to 20 and look for duplicate sequences. **In-depth Investigation: Magical Nines** Children look for patterns when multiplying ‘nearly numbers’ by 9 using mental multiplication strategies. **In-depth Investigation: Table Digital Roots** Children find the digital roots of multiples of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. They identify patterns and relate these to what they know of numbers. **In-depth Investigation: Rocking Remainders** Children divide 11, 22, 33… 99 by 3, 4, 5 and look for patterns in the remainders. **In-depth Investigation: Race to 200** Children apply knowledge of factors within the 2, 3, 4, 5, 9 and 10x tables. **In-depth Investigation: Set Square** Use digits 1-9 once only to complete a calculation grid with given answers for each row and column. These investigations will develop maths meta-skills, support open-ended questioning and logical reasoning, and enable children to learn to think mathematically and articulate mathematical ideas. These problem-solving investigations come from our [Year 4 Maths Blocks](https://www.hamilton-trust.org.uk/maths/year-4-maths/). Each Hamilton maths block contains a complete set of planning and resources to teach a term’s worth of objectives for one of the National Curriculum for England’s maths areas.
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Reasoning/Problem Solving Maths Worksheets for Year 4 (age 8-9)
This category is all about children choosing the most appropriate method to achieve a quick and accurate answer and to be able to explain their methods and reasoning.
Problem solving: finding the missing digits in 4-digit numbers. Tricky!
Problem solving: finding the values of missing counters. Logical thinking and careful work needed here!
Reasoning about numbers on a number line and rounding numbers.
More reasoning about number and place value.
Not only do the questions have to be answered, but explanations given. These pages really show how well children understand what they are doing.
More written explanations on which operation to use and whether the question should be done mentally or on paper.
Lots of questions, most of which can be done mentally. The important thing is to explain how they were tackled.
Decide which operation is needed (add, subtract, multiply, divide) and whether a calculator, or pencil and paper are needed, or whether it can be done, 'in your head'.
Solving problems
A selection of problem solving activities and word problems.
Here are some problems written in words. Fairly straightforward as they require just one mathematical step to work out the answer
Some word problems that need at least two steps to find the answer. This makes them much harder, so careful thinking is needed.
5 pages of word problems, all involving money. Some are suitable for calculator work as they are specially written to make the process the most important factor: it is no use having a calculator if you don't know what calculation to carry out!
A range of number and money problems, typical of those found in KS2 test papers.
More number and money problems, typical of those found in KS2 test papers.
Tricky word problems involving time and money.
More word problems; this time on measurement of length, mass and capacity. These really test children's understanding of when to use addition, subtraction, multiplication or division to solve a problem.
Time problems are especially tricky, especially when finding lengths of time that cross the hour boundary. A good knowledge of the number of days in each month is also needed.
Not many problems on a page, but there is an awful lot within each question. Each is a mini investigation, which can be explored in depth.
Number patterns, remainders, number machines and much more in this mixed selection of problems.
Working out the missing value.
More working out missing values.
Using the instructions on the packet what is the maximum number of bulbs that can be grown in the garden?
Using the instructions on the packet what is the maximum number of seeds that can be sown in the garden?
Using the instructions on the packet what is the maximum number of vegetables that can be grown in the garden?
An addition challenge suitable for year 4 on.
The fish are all called numbers. Can you work out their names by solving the clues?
Investigations
More open ended activities where children choose the approach to the task.
Making rules for sequences is an early step towards understanding algebra, and an important part of Year 5 maths. More 'How would you...?' type questions as well.
How many different three course meals can Sam choose?
Investigate patterns made by placing consecutive numbers in a number square.
A great little investigation which has plenty of extension possibilities.
Fun addition investigation using the date: 22.02.2022.
Some thoughts on how important this area of maths is.
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Resources tagged with: NC Yr 4
There are 51 NRICH Mathematical resources connected to NC Yr 4 , you may find related items under NC .
Satisfying Four Statements
Can you find any two-digit numbers that satisfy all of these statements?
Representing Numbers
Find as many different ways of representing this number of dots as you can.
Ordering Journeys
How would you put these journey lengths in order?
What Distance?
Can you use addition and subtraction to answer these questions about real-life distances?
Count Me In
How do you know whether you will reach these numbers when you count in steps of six from zero?
Dicey Operations in Line
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Seeing Squares
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Reasoned Rounding
Four strategy dice games to consolidate pupils' understanding of rounding.
Round the Dice Decimals 1
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Let Us Divide!
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
Discuss and Choose
This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.
Bryony's Triangle
Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?
Sorting Logic Blocks
This activity focuses on similarities and differences between shapes.
Light the Lights Again
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
A task which depends on members of the group noticing the needs of others and responding.
What Shape?
This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
Counters in the Middle
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Table Patterns Go Wild!
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Times Tables Shifts
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Reflector ! Rotcelfer
Can you place the blocks so that you see the reflection in the picture?
Nice or Nasty
There are nasty versions of this dice game but we'll start with the nice ones...
The Remainders Game
Play this game and see if you can figure out the computer's chosen number.
Four-digit Targets
You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Venn Diagrams
How will you complete these interactive Venn diagrams?
Eight Hidden Squares
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Shape Times Shape
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
Multiplication Square Jigsaw
Can you complete this jigsaw of the multiplication square?
Twice as Big?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Multiples Grid
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Coordinate Challenge
Use the clues about the symmetrical properties of these letters to place them on the grid.
Torn Shapes
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
Take Your Dog for a Walk
Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?
Fractional Wall
Using the picture of the fraction wall, can you find equivalent fractions?
Stringy Quads
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Nine-pin Triangles
How many different triangles can you make on a circular pegboard that has nine pegs?
Carrying Cards
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Andy's Marbles
Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.
How Big Are Classes 5, 6 and 7?
Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.
Fractional Triangles
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
The Deca Tree
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Symmetry Challenge
How many symmetric designs can you make on this grid? Can you find them all?
Let Us Reflect
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
A Cartesian Puzzle
Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
Fractions in a Box
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Shapes on the Playground
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
Zios and Zepts
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
Four Triangles Puzzle
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
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Solve Problems with Multiplication-Reasoning and Problem Solving
Solve Problems with Multiplication - Reasoning and Problem Solving
This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of Solve Problems with Multiplication.
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What's included in the pack?
Solve Problems with Multiplication reasoning and problem solving worksheet Answer sheet
National Curriculum Objectives:
(6C8) Solve problems involving addition, subtraction, multiplication and division (6C6) Perform mental calculations, including with mixed operations and large numbers
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COMMENTS
Reasoning and Problem Solving - Multiply 3 Digits by 1 Digit - Year 4 Developing 4a.Which calculation has an answer with a digit sum of 12. 4b. Which calculation has an answer with a digit sum of 15. Reasoning and Problem Solving - Multiply 3 Digits by 1 Digit - Year 4 Expected 7a.Match the numbers which have an 7b. Match the numbers which have an
Mathematics Year 4: (4C7) Multiply two-digit and three-digit numbers by a one-digit number using formal written layout Differentiation: Questions 1, 4 and 7 (Problem Solving) Developing Identify the most efficient method to solve a multiplication calculation. Supporting using informal written methods to multiply 2-digits by a 1-digit number.
1a. Various answers, for example: 43 x 100 = 4,300 with correct drawings. 2a. No, Julia is incorrect because she needs 18 boxes. 18 x 100 = 1,800 which will be enough for her company. 3a. The statement is incorrect as the wrong symbol has been used. The correct statement is: 17 x 100 < 41 x 100.
Reasoning and Problem Solving Efficient Multiplication Developing 1a. 27 x 3 = 81 2a. False because 42 x 3 = 126, not 114. 40 x 3 = 120, 2 x 3 = 6 and 120 + 6 = 126. 3a. 14 x 5 = 70. Alicia's completed method should look like this: Expected 4a. 36 x 3 = 108. Ruby's completed method should look like this: 5a. False because 49 x 7 = 343, not 300.
Reasoning and Problem Solving - Multiply by 10 - Year 4 Greater Depth Reasoning and Problem Solving Multiply by 10 Developing 1a. Marco = 30; Noah = 3; Florence = 300 2a. Yes, because 8 x 10 = 80 which is bigger than 78. 3a. Emily has the most because 10 x 5 > 10 x 4 Expected 4a. Phoebe = 21; Kayden = 230; Alex = 23; Chloe = 210 5a.
You can use these Year 4 multiplication and division reasoning cards as a brilliant way to challenge learners. The cards pose questions or problems for the children to solve using their multiplication and division knowledge. Perfect for challenging early finishers or to challenge children's understanding of multiplication and division. Show more
Mathematics Year 4: (4C6a) Recall multiplication and division facts for multiplication tables up to 12 × 12 Mathematics Year 4: (4C7) Multiply two-digit and three-digit numbers by a one-digit number using formal written layout Mathematics Year 4: (4C8) Solve problems involving multiplying and adding, including using the distributive law to multi...
1a. Hannah is incorrect because her working out should be: 50 x 4 = 200, 4 x 4 =16 and 200 + 16 = 216. 2a. Various answers, for example: 3a. Various answers, for example: (inefficient method) 10 x 4 + 10 x 4 + 10 x 4 + 10 x 4 + 10 x 4 + 10 x 4 + 10 x 4 = 280 added to 2 x 4 = 8 which equals 288 (efficient method) 70 x 4 = 280 and
1a. If 5 monsters each split into 10 monsters, how many monsters will there be? 1b. If 3 monsters each split into 10 monsters, and then all of those monsters each split into 10 monsters, how many monsters will there be? 1c. If 7 monsters each split into 100 monsters, how many monsters will there be? 1d.
Reasoning and Problem Solving - Multiply 2 Digits by 1 Digit - Year 4 Expected. 7a.Karis skied 36 miles a day for 7 days Sally skied 43 miles a day for 6 days. 7b. Tara's horse rode 27 miles a day for 6 days and Piers's horse rode 28 miles a day for 5 days. Reasoning and Problem Solving - Multiply 2 Digits by 1 Digit - Year 4 ...
Mastery - Fluency, Reasoning and Problem Solving Year 4 Multiplication and Division Teach Efficient Multiplication to Year 4 with this Resource Pack Use this Diving into Mastery resource to help teach efficient multiplication to year 4 pupils.
Year 4 Maths Worksheets for improving reasoning and problem solving skills: Rapid Reasoning. ... Download All Kinds of Word Problems: Multiplication . Year 4 Maths Worksheets for multiplication: Let's Practise Using the Bar Model. These worksheets include a range of word problems that can be solved using bar models. The questions cover times ...
Year 4 | Autumn Term Week 9 to 11 - Number: Multiplication & Division Reasoning and Problem Solving Multiply by 100 Which representation does not show multiplying by 100? Explain your answer. The part whole model does not represent multiplying by 100 because it is incorrect. It is used for addition and subtraction so there should be 100 parts ...
This in-depth maths investigation is an open-ended problem solving activity for Year 4 children. It can be used to support teaching towards the objectives: Times tables: multiplication and division facts. In-depth Investigation: Table Digital Roots Children find the digital roots of multiples of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.
Word Problems Year 4 Multiplication. Help your pupils apply their understanding of multiplication to an unfamiliar context using these worded problems. 11 questions to develop reasoning and problem solving skills. This worksheet contains 10 multiplication questions of ascending difficulty plus one challenge question.
Reasoning/Problem Solving Maths Worksheets for Year 4 (age 8-9) This category is all about children choosing the most appropriate method to achieve a quick and accurate answer and to be able to explain their methods and reasoning. Problem solving involves measures, shape, time and money.
Resources tagged with: NC Yr 4. TypesAge range. Challenge level. There are 51 NRICH Mathematical resources connected to NC Yr 4, you may find related items under NC. Broad Topics > NC > NC Yr 4. ProblemPrimary curriculumSecondary curriculum.
Maths Resources & Worksheets › Year 6 Maths Resources & Worksheets › Year 6 Autumn Maths - Four Operations › 02.1 Solve Problems with Multiplication › Solve Problems with Multiplication-Reasoning and Problem Solving
Year 4 Diving into Mastery: Step 1 Factor Pairs Teaching Pack. 4.5 (4 reviews) Year 4 Diving into Mastery: Step 15 Efficient Multiplication Teaching Pack. 4.0 (2 reviews) Year 4 Diving into Mastery: Step 6 The 3, 6, and 9 Times Tables Teaching Pack. 5.0 (1 review) Multiply 2- or 3-Digit Numbers by 10 Mastery Activity Sheets.
Reasoning and Problem Solving - Multiply by 4 - Year 3 Greater Depth Reasoning and Problem Solving Multiply by 4 Developing 1a. William has 24 pencils because 6 x 4 = 24. 2a. 4 x 2 = 8 + 0 or 4 x 3 = 8 + 4 3a.
Efficient Multiplication: Reasoning and Problem Solving, Maths, Year 4, Number, Multiplication and Division, Multiplication, Sign Up to Download
Reasoning and Problem Solving The 4 Times Table Developing 1a. Rueben is correct: 2 x 4 = 8 and 4 x 2 = 8. 2a. 4 x 9 = 36; 36 ÷ 9 = 4; 36 ÷ 4 = 9