In Topic A, students use their understanding of fractions to explore tenths. In Lesson 1, students use metric measurement and see tenths in relation to one whole in the context of 1 kilogram, 1 meter, and 1 centimeter.

Students will:

use metric measurement to model the decomposition of one whole into tenths.

use metric measurement and area models to represent tenths as fractions greater than 1 and decimal numbers.

represent mixed numbers with units of tens, ones, and tenths with number disks, on the number line, and in expanded form.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 4

17. Express, model, and explain the equivalence between fractions with denominators of 10 and 100.

a. Use fraction equivalency to add two fractions with denominators of 10 and 100.

Unpacked Content

Evidence Of Student Attainment:

Students:

Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this technique to
find the sum of two fractions with respective denominators 10 and 100.

Teacher Vocabulary:

Equivalence

Denominator

Fraction model

Tenths

Hundredths

Sum

Knowledge:

Students know:

Strategies for generating equivalent fractions.

Strategies for adding fractions with like denominators.

Skills:

Students are able to:

Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.

Use models to illustrate equivalency between fractions with denominators of 10 and 100.

Explain equivalency between fractions with denominators of 10 and 100.

Use equivalency to add two fractions with denominators of 10 and 100.

Understanding:

Students understand that:

equivalent fractions are fractions that represent equal value.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.17.1: Recognize equivalent forms of fractions and decimals.
M.4.17.2: Demonstrate equivalent fractions using concrete objects or pictorial representation.
M.4.17.3: Recognize pictorial representations of equivalent fractions and decimals in tenths and hundredths.
M.4.17.4: Define equivalency.
M.4.17.5: Identify place value of decimals to the tenths and hundredths.
M.4.17.6: Use place value understanding to round whole numbers to the nearest 10 or 100.

Prior Knowledge Skills:

Define equivalent.

Recognize pictorial representations of equivalent fractions.

Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.

Recognize that equal shares of identical wholes need not have the same shape.

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Label a fraction with multiple representations.

Partition circles and rectangles into two and four equal shares; and describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.

Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.

Label a pictorial representation.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.17 Model equivalence between fractions of a whole, halves and fourths using visual models.

Mathematics MA2019 (2019) Grade: 4

18. Use models and decimal notation to represent fractions with denominators of 10 and 100.

Unpacked Content

Evidence Of Student Attainment:

Students:

Use models to represent decimal fractions with denominators of 10 and 100.

Use decimal notation to represent fractions with a denominator of 10 and an equivalent fraction with a denominator of 100.

Teacher Vocabulary:

Decimal notation

Decimal point

Place value

Tenths

Hundredths

Fraction

Equivalence

Visual model

Knowledge:

Students know:

strategies for finding equivalent fractions.

Skills:

Students are able to:

Represent fractions with denominators of 10 and 100 using a visual model and decimal notation.

Understanding:

Students understand that:

Fraction equivalence applies to decimal fractions with denominators of 10 and 100.

Decimals can be decomposed and described using place value understanding.
Example: 0.13 as one-tenth and three-hundredths, or thirteen hundredths.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.18.1: Compare two fractions with the same numerator or the same denominator by reasoning about their size.
M.4.18.2: Recognize that comparisons are valid only when the two fractions refer to the same whole.
M.4.18.3: Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
M.4.18.4: Convert fractions to decimals.
M.4.18.5: Compare two decimals to tenths.
M.4.18.6: Compare whole numbers.
M.4.18.7: Identify comparison symbols. Examples: >, <, and =.

Prior Knowledge Skills:

Define equivalent.

Recognize pictorial representations of equivalent fractions.

Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.

Recognize that equal shares of identical wholes need not have the same shape.

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Label a fraction with multiple representations. Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).

Partition circles and rectangles into two and four equal shares; and describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.

Recognize different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler.

Label a pictorial representation.

Recognize that a fraction is a part of a whole.

Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.

Define numerator and denominator.

Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths.

Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).

Identify parts of a whole.

Represent a fraction with a pictorial model.

Identify <, >, and = signs.

Recognize that equal shares of identical wholes need not have the same shape.

Recognize that a whole can be partitioned into equal parts (halves, fourths, eighths, etc.).

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Define greater than, less than and equal to.

Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Arrange two-digit numbers in order from greatest to least or least to greatest.

Identify zero as a place holder in two-digit and three-digit numbers.

Model using >, =, and < symbols to record the results of comparisons of two two-digit numbers.

Select numbers on a number line that are more than, less than or equal to a specified number.

Match the words greater than, equal to and less than to the symbols >, =, and <.

Determine the value of the digits in the ones and tens place.

Identify sets with more, less or equal objects.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.17 Model equivalence between fractions of a whole, halves and fourths using visual models.