In this unit, students will use their familiarity with money to make connections and understand decimals. Students will show decimals in different contexts, expressing them in tenths and hundredths. Using models to represent fractions, students will generate equivalent fractions and use decimal notation to express them. Since students can write decimal fractions as either a decimal or a fraction, we are still able to compare them. Students may struggle with understanding the size of numbers is not based on the number of digits, and understanding that as we increase the number of decimal places to the right of the decimal, the value of the digits in those places is getting smaller.
Key Concepts:
 Decimal notation is based on denominators that are powers of 10.
 Because we can write fractions with a denominator of 10 as an equivalent fraction with a denominator of 100, we can also write these numbers in decimal notation.
 Because decimal fractions can be written in either fraction or decimal form, the place value system holds when comparing decimals.
Prior Knowledge Needed:
 Understand two fractions as equivalent if they are the same size or on the same point of the number line (Grade 3, Unit 10, 3.NF.A.3.A)
 Recognize and generate equivalent fractions (Grade 3, Unit 10, 3.NF.A.3.B)
 Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record comparisons with the symbols <, =, > and justify the conclusions. (Grade 3, Unit 11, 3.NF.A.3.D)
 Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4, Unit 4, 4.NBT.A.2)
 Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. (Grade 4, Unit 4, 4.NBT.A.1)
Units on the Horizon:
 Using equivalency to add and subtract fractions with unlike denominators (Grade 5, Unit 3)
 Expanding understanding of place value to decimals (Grade 5, Unit 4)
Lessons

Lesson objective: Model and represent fractions as decimals through money. Students bring prior knowledge of fractions from 3.NF.A.1, 3.NF.A.2, and 3.NF.A.3. This prior knowledge is extended to decimals as students model money in different scenarios usi...

Lesson objective: Writing decimal, fraction and word form with models. This lesson helps to build procedural skill with writing decimals, fractions, and the word form associated with them. Models such as base ten flats and number lines are used here bec...

Lesson objective: Connect student conceptual understanding of decimals and fractions with equivalence in word problems. This lesson provides an opportunity for students to apply their knowledge and understanding of decimal and fraction equivelancy to a ...

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...

Lesson objective: Add fractions of unlike denominators using base ten models (flats). This lesson helps to build procedural skill with adding fractions with denominators or 10 or 100. Base ten flats are used here because it supports the conceptual under...

Lesson objective: Solve more difficult problems related to combining fractions using models. This lesson provides an opportunity for students to apply their knowledge and understanding of fractions to a reallife situation. Students are asked to find th...

Lesson objective: Understand that we can compare tenths and hundredths written as fractions or decimals. Students bring prior knowledge of comparing fractions from 3.NF.A.3. This prior knowledge is extended to comparing fractions and decimals as student...

Lesson objective: Compare fractions and decimals on a number line. This lesson helps to build procedural skill with comparing both fractions and decimals. Number lines are used here because they provide a mental and visual strategy to show less than, gr...

Lesson objective: Solve word problems that compare fractions and decimals. This lesson provides an opportunity for students to apply their knowledge and understanding of comparing decimals and fractions to a realworld situation. Students are asked to c...

Lesson objective: Solve more complex word problems that compare decimals and fractions. This lesson provides an opportunity for students to apply their knowledge and understanding of comparing decimals and fractions to a real situation. Students are ask...