Mathematical Inquiry into Authentic Problems

This special topic presents ten inquiry units for Years F to 6. based in authentic real world situations with an accompanying teacher’s guide. The major aim is for students to learn to use mathematics to help make sensible decisions in response to the ill-structured and open-ended questions that are  often encountered in life. 

The emphasis is on extended mathematical inquiry problems that: (1) are driven by an inquiry question; (2) contain ambiguities that require negotiation; and (3) require mathematical evidence to address the problem and justify a proposed solution.

Each unit is presented using the ‘4D Guided Inquiry model’ with four phases—Discover, Devise, Develop and Defend. Each unit aims to develop content knowledge as well as assisting students to understand the process of inquiry and the importance of providing mathematical evidence.

Resources

Authentic Problems Teachers' Guide - read this first

Authentic Problems: Tea Party

Students plan a tea party for a small group. As they prepare, they connect number names, numerals and quantities using one-to-one correspondence.

Australian curriculum number (ACMNA001; ACMNA002; ACMNA289; ACMNA003; )

  • F

Authentic Problems: Grandma's Soup

Students estimate how many macaroni in a handful by various methods of skip counting and grouping strategies to get 100 macaroni for soup.

Australian curriculum number (ACMNA012; ACMNA013; ACMNA014)

  • Y1

Authentic Problems: Target Ball

Students use progressively more sophisticated measurement strategies to find the best ball and where to place the target to play a game.

Australian curriculum number (ACMNA013; ACMNA019; ACMSP263; ACMSP262; )

  • Y1

Authentic Problems: Bunches of Balloons

Students investigate dividing a packet of balloons into equal groups to decorate a room. They count how many in each group and the left overs.

Australian curriculum number (ACMNA031; ACMNA032)

  • Y2

Authentic Problems: What's for Lunch?

Students estimate how many sandwiches they eat in a year using informal strategies, prior to learning standard multiplication algorithms.

Australian curriculum number ( ACMNA028; ACMNA030; ACMNA031; ACMSP049; ACMNA027)

  • Y2

Authentic Problems: Bottle Flipping

Children find the fraction of a bottle to fill for good bottle flipping. They provide evidence using tallies from trials of flips.

Australian curriculum number (ACMNA058; ACMMG061; ACMSP069; ACMSP068; ACMSP070)

  • Y3

Authentic Problems: 10 000 Centicubes

Students design a box to hold 10 000 centicubes by combining smaller boxes and by finding possible lengths, widths and heights.

Australian curriculum number (ACMNA073; ACMNA076; ACMMG290; ACMNA072; ACMMG084)

  • Y4

Authentic Problems: Expanded Square

Expanding a square is an art technique that flips cut-out shapes from the inside to the outside. Students design one that flips out half the area.

Australian curriculum number (ACMNA077; ACMMG087; ACMMG088; ACMMG091)

  • Y4

Authentic Problems: Reaction Time

Students work with decimals to measure, record, compare and analyse reaction times of students in their class.

Australian curriculum number (ACMNA104; ACMNA105; ACMSP119; ACMSP118; ACMSP120)

  • Y5

Authentic Problems: Pyramids in a Box

Nets and other features of 3D objects are explored to design and construct a box that can hold two pyramids.

Australian curriculum number (ACMMG140; ACMMG141)

  • Y6