Big Idea(s):

Regrouping fractional parts into wholes

Expectations:

B1. Number Sense: demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life

• Fractions: B1.6 use drawings to represent, solve, and compare the results of fair‐share problems that involve sharing up to 10 items among 2, 3, 4, and 6 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts

teacher background

Students may benefit from prior experience with:

• sharing items fairly

• partitioning shapes into equal parts

• using ordinal number names to tenth

• comparing and ordering quantities

Key concepts

• Fair-sharing or equal-sharing means that quantities are shared equally. For a whole to be shared equally, it must be partitioned so that each sharer receives the same amount.

Note

• Words can have multiple meanings. It is important to be aware that in many situations, fair does not mean equal, and equal is not equitable. Educators should clarify how they are using the term “fair share” and ensure that students understand that in the math context fair means equal and the intent behind such math problems is to find equal amounts.

• Fair-share or equal-share problems provide a natural context for students to encounter fractions and division. Present these problems in the way that students will best connect to.

• Whole numbers and fractions are used to describe fair-share or equal-share amounts. For example, 4 pieces of ribbon shared between 3 people means that each person receives 1 whole ribbon and 1 one third of another ribbon.

• When assigning these types of problems, start with scenarios where there is a remainder of 1. As students become adept at solving these problems, introduce scenarios where there is a remainder of 2 that needs to be shared equally.

• Fractions have specific names. In Grade 2, students should be using the terminology of “halves”, “fourths”, and “thirds”.

Show a red Pattern Block. Place 3 green blocks on top. Ask: “What does each green block show? (one third) How many does it take to make the whole? (3)”

Show 8 green blocks (eight thirds). Ask: “How many wholes can we make with eight thirds? Will there be any green blocks left over?”

Help students see that eight thirds make two wholes, with two thirds left over.

Use other materials to build flexible thinking around parts and wholes. Have students cut or fold hexagons (Master 55) into 2, 3, and 6 equal parts.

Give each pair Pattern Blocks and a recording sheet (Line Master 56).

• Take a yellow block. How many red blocks does it take to cover the yellow block? What part is each red block?

• Take a handful of red blocks. Count the blocks. How many wholes can you make? Are there any parts left over? Record your work with pictures, words, or numbers.

• Repeat the activity with other Pattern Blocks. How many wholes can you make with eleven sixths? with ten thirds? How do you know?

LOOK-FORS:

• Are students able to cover the yellow block (the whole) with equal parts?

• Are students able to label each part with a fractional name?

• Are students able to regroup fractional parts to make wholes?

• How are students describing the leftover parts (e.g., two, two blue blocks, or two thirds)?

How to Differentiate:

Accommodations: Focus on halves using the yellow and red blocks.

Extension: Have students make up their own “How many wholes can you make …” questions and trade questions with a partner.

Combined Grades Extension: Use fraction circles to explore different fractional parts (e.g., sixths, eighths, tenths).

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SEL Self-Assessments (English) and Teacher Rubric

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