Lesson objective: Understand how we can use models to make comparisons between decimals and fractions.

Students bring prior knowledge of fractions and decimals from 3.NF.A.1, 3.NF.A.2, and 3.NF.A.3. This prior knowledge is extended to making comparisons as students combine playing cards with different fractional values to equal one whole. A conceptual challenge students may encounter is adding tenths and hundredths together by using equivalent fractions (ex: 9/10+3/100= 90/100+3/100)

The concept is developed through work with base ten flat, which allows students to see the model of decimals and fractions with the denominator of 10 or 100 when added together.

This work helps students deepen their understanding of equivalence because it supports their exploration and use of equivalence.

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they are asked to choose their own entry point into the problem and explain their reasoning to others. The prior knowledge connection asks students to critique the reasoning of two characters and defend their own arguments.

**Key vocabulary:**

- decimal
- denominator
- flat
- model
- numerator
- representation
- rod
- unit
- tenth
- hundredth
- whole

**Special materials needed:**

- base 10 manipulatives
- paper copies of flats
- paper copies of rods
- tiles