Authentic Problems: Grandma's Soup

ACMNA012; ACMNA013; ACMNA014

This unit for Year 1 is one of a set of ten units in the special topic “Mathematical Inquiry into Authentic Problems”. Each of these units is designed around the 4D Guided Inquiry Model, and highlights the importance of students providing mathematical evidence. The lessons adopt a carefully designed pedagogy to help students master content knowledge whilst learning about the process of inquiry. 

The inquiry is stimulated by a question: How can we grab 100 pieces of macaroni?  The unit provides an authentic context for counting large collections (around 100). Students consider ways to grab a handful of 100 pieces of macaroni and the best way to count their handfuls. They see a need for skip counting and partitioning using place value when counting large amounts. During the unit, students find better ways to grab 100 pieces of macaroni and more efficient ways to count the pieces. They use evidence to convince others their grab is close to 100 and has been efficiently counted.

Read the Teachers' Guide (also included in the download) before using this resource.

 

Lesson 1: Discover

Students hear the story of Grandma’s Soup and discover that the problem with the recipe is the ambiguity of the term ‘handful’ as a unit of measurement. They investigate the numbers of pieces of macaroni in their own handfuls by grabbing a handful and counting the pieces. They each write the total on a cut-out tracing of their own hand and order them from smallest to largest.

Lesson 2: Devise

Students are informed that Grandma’s handful was 100 pieces of macaroni. A cut-out of Grandma’s hand is added to the display of hands from the Discover phase. Using a number line is suggested, and students write their totals on a class number line, and compare it to the hands display. Next, students make several attempts to grab 100 pieces of macaroni. They record each attempt on a number line, and use its relative location to guide their next attempt. Students use different counting strategies and attempt to find the most efficient way to count.

Lesson 3: Develop

Students use the evidence they have gathered to have a last ‘grab’ of macaroni. From all the grabs in their group, they select the one closest to 100. They recount this selected grab using a variety of strategies and collectively decide on their most efficient strategy for counting numbers around 100. They gather pictorial evidence of both the count and the counting strategy to use as evidence in the Defend stage.

Lesson 4: Defend

Groups present their best handful and the counting methods to the class with prompting questions from the teacher where required. They demonstrate counting a collection using skip counting and justify