Mathematical Word Problems

In maths, we have been developing our skills to solve mathematical word problems.

We have been following a five step process to solve word problems:

Some word problems require one calculation, while others are multi-step problems. When calculating their answers, students are required to:

  • record all of their working out
  • justify their calculations to ensure their final answer is a reasonable solution to the problem.

The word problems we have been solving involve all four processes:

  • addition
  • subtraction
  • multiplication
  • division

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In your comment, please type a mathematical word problem for someone to solve!

Money, Money, Money!

This week, we have been learning all about money in our maths lessons!

Enthusiasm and engagement have been high in our classroom as the 3/4C students participated in a range of fun warm up games and real-life maths tasks related to money.

Our learning has focussed on:

  • Adding totals of money using mental strategies
  • Adding totals of money using calculators
  • Calculating change
  • Rounding prices to the nearest 5 cents.
  • Estimating the prices of grocery items
  • Creating a daily menu within a budget using online catalogues.

We have had lots of class discussions about money this week. One interesting fact is that Australia used to have 1 cent and 2 cent coins but they were eliminated from our currency system in 1992. The video below investigates whether the Australian 5 cent coin will eventually be phased out too.

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How has your money knowledge improved this week?

When do you use money in real life?

Were you surprised by the prices of any particular grocery items during your class tasks this week?

Have you ever saved up your money to purchase something special?

Amazing Addition!

Last week we focussed on addition strategies in our maths lessons.

We use addition in every day life all the time, so it is important to improve our skills in this area of maths. Here are some effective addition strategies that we used in class:

  • The addition tens and twenties facts
  • Doubles and near doubles addition facts
  • Double doubles (for example, 8+8=16 and 16+16=32)
  • The Jump Strategy to add hundreds, then tens, then ones by jumping on a number line
  • The Split Strategy to split the hundreds, tens and ones and add them separately
  • The Compensation Strategy when a number we are adding is close to a “round” number we can add or take to the nearest 10
  • 100 facts (addition equations that equal 100)
  • Bridging to the nearest 10 as these numbers are easy to add to.

Students enjoyed practising a variety of these addition strategies during our learning tasks and it was fantastic to hear their mathematical discussions and explanations.

Everyone was so focussed and keen to develop their addition skills!

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What addition strategies do you enjoy using?

When do you use addition in everyday life?

 

Fun with Perimeter!

We are currently learning about measurement in our maths lessons.

Today, we focussed on perimeter.

We set up ‘perimeter stations’ around the classroom. Some of the shapes were regular shapes and some were irregular shapes.

Students worked in pairs to complete the ‘perimeter stations’ challenge. They recorded their work on their iPads in Google Sheets. To complete the task, students had to…

  • Make educated estimates of each shape.
  • Carefully measure the actual perimeter of each shape using centimetres.
  • Calculate the difference between their estimation and the actual perimeter.

Some of the regular shapes were quite easy and students estimated correctly, and some of the irregular shapes were quite challenging!

It was fantastic to listen to the mathematical language and conversations the students had as they estimated and calculated the perimeter of the different shapes.

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How has your measurement knowledge improved during this unit of work?

Calculate the perimeter of something and tell us the answer in your comment!

Learning About Place Value

We are currently studying place value in maths.

Place value is defined as the value of a digit based on its position in a number.

For example: in the number 946 the 4 is in the “tens” position so it shows a value of 40. The 9 is in the “hundreds” position so it shows a value of 900.

Students have been developing their place value skills using four, five, six and seven digit numbers.

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Numbers can be represented in different ways. Consider the five digit number in the place value chart below.

Five digit number

Standard form: 28,362

Word form: Twenty eight thousand, three hundred and sixty two

Expanded form: 20,000 + 8,000 + 300 + 60 + 2

We can also rename numbers in different ways. The number above can be renamed in a variety of ways including:

28 thousands, 36 tens and 2 ones

283 hundreds and 62 ones

2836 tens and 2 ones

28 thousands and 362 ones

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Base 10 materials (sometimes referred to as MAB) are a very useful resource to model numbers.

Students have been building their knowledge by participating in a range of individual, partner, small group and whole class tasks. One highlight has been the Base 10 Race!

To play this game, students worked in collaborative groups outside. Each team rolled dice repeatedly and had to collect the required amount of Base 10 materials after each roll. They had to “trade” the materials when necessary. For example, when they had 10 ones, they exchanged for 1 ten. Or when they had 10 tens, they exchanged for 100. Teams kept a record of their number as the game progressed. It was a fun way to develop place value knowledge!

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How has your place value knowledge improved?

What place value activity have you enjoyed?

If you were designing a place value game, what would it be?

What is your favourite maths topic?

All About Mass!

Yesterday we started a measurement unit in maths.

Our first lesson focused on mass. Mass is defined as the quantity of matter in an object. Mass is measured in grams and kilograms.

Our learning focus was:

  • I am learning how to estimate and record using grams and kilograms.

Our success criteria was:

  • I can make estimates about the mass of an object using grams and kilograms.
  • I can make conversions between grams and kilograms.

Students were presented with a variety of supermarket items. They had to estimate the mass of each item and record their estimations. We also had lots of weights in the classroom so students could make informed estimations.

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Today, we discovered the actual mass of each supermarket item. We compared our estimations and reflected on how close or distant our estimations were.

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How did you go with this estimating task?

What was challenging about this task?

How can you practise your estimating skills?

When do we estimate in real life?

More Fun With Problem Solving!

Today in maths, 3/4C enjoyed another problem solving session.

Our school numeracy coach, Mrs Hillbrick, joined in the fun and participated with the 3/4C mathematicians.

Today’s lesson was called “Plants” and was adapted from the NRICH site.

Watch the presentation below to see how the problem unfolds.

The students did a fabulous job of using problem solving strategies. The main strategy the students adopted was “guess, check and improve” and some students moved on to “working systematically“.

Here are the 3/4C mathematicians using counters and Venn diagrams to solve the problem.

All students experienced success by finding multiple solutions. The highest amount of solutions found was 16!

How many solutions to the plants problem can you find?

Did you achieve the success criteria for this lesson?

What strategies did you use to solve the problem?

What are the benefits of problem solving activities?

 

Mathematical Problem Solving

Today, our numeracy coach Mrs Hillbrick visited our classroom for some mathematical fun.

We started our maths lesson with one of our favourite warm up games – Hit the Target.

We then worked on a problem solving task with Mrs Hillbrick.

Our learning focus for the lesson:

We are learning to find multiple solutions to a problem.

Our success criteria for the lesson:

We can:

  • Read the problem in our head
  • Share our understanding
  • Use guess, check and improve
  • Check for accuracy
  • Reflect as mathematicians

Mrs Hillbrick posed the following question…

My telephone number has 8 digits. When I add up each of the 8 digits, I get a 2 digit number. When I add those 2 digits together, I get a number less than 4. What could my telephone number be?

To break down the problem, we had to:

  • Circle the numbers
  • Put a box around the key words
  • Underline the key question

Students then had a go at finding solutions to this problem.

At the conclusion of the lesson, we reflected on the success criteria to determine how we went with this task.

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Did you achieve the success criteria?

What skills did you need to use to complete this problem solving task?

In your comment, have a go at coming up with a solution to the problem!

Fantastic Fractions!

We have been learning about fractions in maths.

We know that a fraction is an equal part of a whole.

Our learning this week has focussed on:

  • Understanding numerators and denominators
  • Identifying and naming a variety of fractions
  • Using and understanding a fraction wall
  • Recognising equivalent fractions
  • Using fractions in problem solving.

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To introduce our fractions unit, students used play dough to make and label a variety of fractions.

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Today, students enjoyed making paper “fraction pizzas” to demonstrate their learning. Students could choose to make a pizza in quarters, eighths or sixteenths. They then added a variety of toppings and labelled the fraction of each ingredient on the pizza.

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We are looking forward to continuing our fractions knowledge next week. We will be focussing on:

  • Putting fractions on a number line
  • Comparing fractions and identifying fractions that are greater than/less than other fractions
  • Identifying fractions in a collection of objects
  • Understanding mixed fractions and improper fractions.

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What have you learnt about fractions during our maths lessons this week?

How has your fractions knowledge improved?

Do you have a fractions tip for other students?

 

Delightful Division!

This week we have been improving our division skills.

Specifically, our learning focus has been: To apply appropriate strategies to solve division equations mentally.

In order to improve our mental division strategies, we completed a variety of lessons practising several helpful strategies.

Some of these strategies are:

  • Skip counting
  • Counting on from a known fact
  • Using inverse operations (this is the relationship between multiplication and division).

We discussed that all division problems can be solved using your knowledge of multiplication. This is a very helpful method to solve division problems!

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Of course, sometimes the number you start with (the dividend) isn’t evenly divisible by the number of groups (divisor). In this case, you have remainders. During the week, students used their times tables and skip counting skills to solve a variety of remainder problems.

During the week, students could challenge themselves by using larger dividends and divisors to extend their knowledge.

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The slideshow below has images of dominoes. Try to say or write the multiplication and division fact family using the number of dots on each domino to create inverse operations.

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Division can be a tricky process but it has been excellent to see the 3/4C students show a lot of persistence and determination to succeed with this mathematical concept.

It is important to keep practising multiplication and division facts as we use them regularly in everyday life!

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What have you learnt about division this week?

How have your mental strategies improved?

Do you have any division tips?

When do you use division in real life?