Exploring the world for number lines and integers.

Introduction

Goal

The goal for this web quest is to explore everyday situation in the world where and how integers are used and its properties:

  • Number zero 
  • Negative and positive numbers
  • Number line

 

Achieve 

Each task set will help you explore the concept and properties of integers. Follow each step and complete activity. Take your time with each task, repeat if necessary until you have a grasp on the concept, activity of each task. Once you feel that you are confident with topic take the final quiz. The quiz is aimed to show your maths thinking and proficiencies with the learning outcome of:

  1.  Have an understanding and can describe what an integers are 
  2.  Can accurately use number line to identify, show, position and order integers 
  3.  Able to problem solve using the number line
  4.  Can provide mental strategy used to solve problem

 

What is integers?

Integer is what we call set of numbers that include positive whole numbers, zero and negative whole numbers. Whole numbers are the counting numbers plus zero. Check out the you tube below and or the audio file.

 

Task

Complete the following tasks in this web quest, each task will help you grasp a concept on the properties of integers, an idea how they are used and an opportunity to practice utilising them.

Task 1 to 3 have activities that have interactive media to help give you an idea on the concept, a weblink to practice, an example of a everyday problem along the way that you can engage. While task 4 allows you the opportunity to use your mathematical thinking to help solve some everyday problems that use integers. 

Task 1. Exploring number 0

Task 2. Negative numbers

Task 3. Number line

Task 4. Compare & order

Task 5. Create a mini movie 

Process

Before commencing

  • Set up your Penzu journal. 
  • See my example. Email address: dormanluisa@gmail.com and Password: Icandoit2019
  • Make sure your name is clearly written on top. Write down the task number and date. This is where you will; be recording your rresaultds, brainstorming and thinking.

 

Task 1. Exploring the number zero

 

  • What do we know about the number zero. Record your initial brainstorm on your journali. Watch a few videos and revisit and add anymore notes on your brainstorm.

 

  • Create a graphic image, using "worldle" app, of all the words that represent what the number zero means to you. Once complete copy and save to your journal. See example below AND/ OR
  • Create an illustration using sketchpad, copy and paste final illustration onto your journal.

 

Task 2. Negative numbers

  • Explore numbers that are less than zero.

 

 

  • Checkout this song below.

https://www.youtube.com/watch?v=TPJjGMROQoc

 

  • Read this article "Negative Numbers" by Jill Howard. As a class discuss which cultures utilised negative numbers and why did it take the other cultures longer to use negative numbers?  Record notes in your journal of your understanding.

 

Task 3. Number line

  • Can you guess the number on this number line. Record your time and answer in your journal.
  • What about this numbers on a number line. Again record your results in your journal.

 

 

  • Use a number line to help you answer Problem 1 & 2. What strategy did you use to figure answer from a number line? Record in your journal. 

Problem 1: Charlotte lived in Antartica, it was 3 degrees in temperature in the morning and she checked the weather and it said it was going to  be 15 degrees during the day, how much is the temperature going to change by? 

Problem 2: During the day when it had reached 15 degrees, Charlotte checked the weather again and it said it was going to be -27 degrees at night, how much is the temperature going to change by? 

 

Task 4. Compare & order

 

  • See bellow information collected by Geoscience Australia on the heights of some towns and places in Australia. The height is compared against the sea level. 
Elevations (Geoscience Australia)
Town/ Place State Height (m)
Perisher Valley NSW 1740m
Areyonga  NT 700m
Hotham Height TAS 1700m
Lake Eyre SA 15m below sea level
Amata SA 700m
Ravenshoe QLD 930m
Mt Kosciuszko NSW 2228m
Canberra ACT 660m
Tom Price WA 750m

Problem 3: List the towns and places in order from least to greatest according to their height.

Problem 4: How would the data in the above be best represented on a number line? Order the data on a number line and ensure they are appropriately labelled.

 

 

  • See below information entered in a Money Smart budget planner of the weekly spending in a household. Where the money earned by working is seen as a positive number and the money that needs to pay bills and expenses is the negative numbers.
Weekly Money Earned (+0) and Owed (-)
Budget Planner $
Income $2000
Home & utilities -$768
Insurance -$427
Groceries -$280
Personal & medical -$129
Entertainment & eat out -$53
Transport & auto -$81
Summary 263

Problem 5: Work out what is the total of expenses are, how would you calculate this? Record your thinking in your journal.

Problem 6: Illustrate and represent the above information on a number line. 

 

 

  •  See picture below, it shows Charlotte walking west from school and Oliver walking east.  

Problem 7: It takes Charlotte and Oliver both 200m to walk home, who walked the furthest? Use a number line and record your working out and answer on your journal.

Problem 8: On Friday Charlotte stops by the shops which is 150m on the way home and Oliver walks to a friend's house which is another 130m further than his home. Who walks further on Friday? Show your working out on a number line and record finding in your journal.

 

Task 5. Create mini movie

  • In partners, create your own movie to describe to the class:
    • what integers are
    • where are they used in the world
    • how to use them to solve problem
  • Movie can contain props, white board, effects to help convey your message.
  • Some movie makers you could use
    • Filmora 9
    • Windows Movie Maker
    • iMovie
  • Show class once your film is complete
Evaluation

 

Rubric
# Poor Satisfactory Very Good Excellent Score

Knowledge and understanding of integers, role of zero, negatives and positive numbers

Demonstrates little or no knowledge or understanding of integers, role of zero, negatives and positive numbers

 Demonstrates partial level of knowledge or understanding of integers, role of zero, negatives and positive numbers
 		 Demonstrates knowledge and understanding of integers, role of zero, negatives and positive numbers

Demonstrate thorough and deeper thinking knowledge and understanding of integers, role of zero, negatives and positive numbers

 15%
Content of journal The requirement of recording in journal are minimally or not met The requirement of recording in journal are partially met The requirement of recording in journal are met The requirement for recording journal exceed minimum 35%
Participation in web quest and shares in discussion with class or partner in mini movie. Negative attitude, emotion, or effort displayed during web quest task. Participates in web quest most of the time and shares ideas most some of the time. Participates in web quest with positive effort and shares ideas with others. Motivated, enthusiastic participation in web quest and shares extensively with others ideas. 15%

Represents problems on a number line, whole numbers, positive and negative, correct sequence and labelled appropriately

 Poor representation of problem on number line. Incorrect sequence, gaps in understanding of concept. Satisfactory representation of problems on number line overall. Some sequence correct, positive and negative sides demonstrated. Number line not labelled appropriately. Very good representation overall of problem on number line. Good use of sequence number, positive and negative side demonstrated, number line labelled appropriately. Excellent representation of problems on number line. Great use of sequence number, positive and negative side demonstrated, number line labelled appropriately, even correct measurement units used ($, m, etc) 35%
        Total score 100%

 

Conclusion

 

Yay, excellent, fantastic, bravo, awesome, way to go, you rock and congrats in completing the web quest!

You have explored different ways number line and integers are used everyday and used mathematical thinking, skills and knowledge to represent integers and number lines that were related to real life situations.

Keep an eye out to see where else negative numbers are used around you and whether they use a physical number line or a mental number line!

Credits

 

The following materials utilised throughout web quest:

 

ABC Education, sourced from http://education.abc.net.au/home #!/home

ASIC Money Smart budget planner, sourced from https://www.moneysmart.gov.au/

Geoscience Australia, Elevation, sourced from https://www.ga.gov.au/scientific-topics/national-location-information/landforms/elevations

IXL Learning, sourced from https://au.ixl.com/math/

Mathsisfun, sourced from https://www.mathsisfun.com/

Mathsframe, sourced from https://mathsframe.co.uk/

NRICH, February 2011, Negative numbers, sourced from https://nrich.maths.org/5747

Origo Handbook of Mathematics, 2008, Origo Education.

Penzu Journal, sourced from https://penzu.com/

Sea Level, sourced from https://www.sealevels.org/

Siemon, D., et al., 2016, Teaching Mathematics foundation to middle years second edition, Oxford Press, Melbourne.

Sketchpad, sourced from https://sketch.io/sketchpad/

Wordle, sourced from http://www.wordle.net/

YouTube, sourced from https://www.youtube.com/

Teacher Page

Teaching/ Learning Intentions

The outcome of this web quest is to engage students in a learning trajectory that achieves mathematically thinking of integers. At the same time achieving year 6 level standard "They describe the use of integers in everyday contexts".

The content that needs to be covered is ACMNA124: Investigate everyday situations that use integers. Locate and represent these numbers on a number line. 

This will be covered using the proficiencies strands:

  • understanding what integers are, able to get a relational understanding integer numbers and their properties they have (infinity number line, zero, negative and positive). Explore where integers are used in everyday context (temperature, sea level, finance and distances).
  • fluency they become accurate and can use number line to represent and identify integers, position and order integers. 
  • problem-solving can solve everyday problems that involve the addition operation on the number line. 
  • reasoning includes explaining mental strategies for performing calculations.

 

Students Prior Knowledge

Assumption as a teacher is that students are at a year 4 (8-9 year old) Mathematics as per Australian Curriculum. According to Siemon, D. et al. (2016) at this age they should have a mathematic foundation:

  • A good sense of number (trusting the count above and below 10, mental strategies, relationship between additive/ subtractive operations) in everyday context
  • Place value (parts/ whole knowledge where whole number can be grouped, partitioned and rearranged, comparing 10 of these is 1 of those/ 1000 of these is 1 of those, ordering/ sequencing, counting forward/ backwards in place value parts)
  • Generalise patterns (observe, create and describe) in everyday world context.

The learning trajectory goal is to faciliate students learning to grow a mathematical thinking towards a year 5-6 level (9-10 year old) (Siemon, D., et al., 2016):

  • Place value is important and allows us to easily represent small and large numbers in every day context
  • Number line can be made of different types of number - counting number, whole number and integers
  • "Any real number can be placed on number line"
  • "Development of a single mental number line encompassing all types of numbers"