Students reason with shapes and their attributes, and partition shapes into equal shares, building a foundation for fractions. They relate halves, fourths, and skip-counting by 5 to tell time, and they solve story problems involving the values of coins and dollars.
Unit Narrative
In this unit, students transition from place value and numbers to geometry, time, and money.
In grade 1, students distinguished between defining and nondefining attributes of shapes, including triangles, rectangles, trapezoids, and circles. Here, they continue to look at attributes of a variety of shapes and see that shapes can be identified by the numbers of sides and vertices (corners). Students then study three-dimensional (solid) shapes, and identify the two-dimensional (flat) shapes that make up the faces of these solid shapes.
Next, students look at ways to partition shapes and create equal shares. They extend their knowledge of halves and fourths (or quarters) from grade 1 to now include thirds.
Students compose larger shapes from smaller equal-size shapes and partition shapes into two, three, and four equal pieces.
As they develop the language of fractions, students also recognize that a whole can be described as two halves, three thirds, or four fourths, and that equal-size pieces of the same whole need not have the same shape.
Which circles are not examples of circles partitioned into halves, thirds, or fourths?
Later, students use their understanding of halves and fourths (or quarters) to tell time. In grade 1, they learned to tell time to the half hour. Here, they relate a quarter of a circle to the features of an analog clock. They use “quarter past” and “quarter till” to describe time, and skip-count to tell time in 5-minute intervals. They also learn to associate the notations “a.m.” and “p.m.” with their daily activities.
To continue to build fluency with addition and subtraction within 100, students conclude the unit with a money context. They skip-count, count on from the greatest value, and group like coins, and then add or subtract to find the value of a set of coins. Students also solve one- and two-step story problems involving sets of dollars and different coins, and use the symbols $ and ¢.
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Recognize and draw shapes having specific attributes, such as a given number of angles or a given number of equal faces.
Section Narrative
In this section, students identify and draw triangles, quadrilaterals, pentagons, and hexagons. Students are likely familiar with triangles and hexagons given their previous work with pattern blocks. Here, they see that hexagons include any shape with 6 sides and 6 corners, and may look different from the pattern block they worked with in the past. For example, each of these shapes is a hexagon:
Students learn to name a shape by counting the sides and corners and come to see that, in any shape, the number of corners is the same as the number of sides. (The term “corners” is used in lieu of “vertices” because the latter requires an understanding of angles, which is developed in grade 4.)
Students come to recognize that some shapes such as rectangles and squares have “square corners,” the informal language for 90-degree angles. As they identify and draw shapes with given attributes, they measure length in centimeters and inches, revisiting previously learned skills.
At the end of the section, students relate two-dimensional (flat) shapes to three-dimensional (solid) shapes. They see that flat shapes make up the faces of solid shapes and identify solid shapes based on the flat shapes that constitute them.
Partition rectangles and circles into halves, thirds, and fourths and name the pieces.
Recognize two halves, three thirds, and four fourths as one whole.
Understand that equal pieces do not need to be the same shape.
Section Narrative
In this section, students learn that shapes can be partitioned into two, three, or four equal pieces called “halves,” “thirds,” and “fourths” or “quarters,” respectively.
Students begin by composing shapes, using pattern blocks in any combination. Later, they use a single type of pattern block, which allows them to see the composed shape partitioned into equal pieces.
In grade 1, students partitioned shapes into two and four equal pieces, and described each piece as a “half” or a “fourth” or “quarter.” (To prepare students to tell time to the quarter hour in the next section, be sure that they hear and use the terms “fourths” and “quarters” interchangeably.) Here, they add the term “thirds” to their vocabulary and partition rectangles into halves, thirds, and fourths.
Students then identify equal-size pieces in shapes, which are partitioned in different ways to build an understanding that equal-size pieces of the same whole do not need to be the same shape.
They come to understand that if the whole is partitioned into the same number of equal pieces, the names of the pieces are the same. Students also learn that two halves, three thirds, and four fourths each make up one whole.
Although students are expected to use the language of fractions (halves, thirds, and fourths), they are not expected to use the word “fraction” or see fractions in numerical form until grade 3.
Specific Side Lengths
Let’s find and draw shapes with specific side lengths.
Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
Section Narrative
In this section, students use their understanding of fourths and quarters to tell time.
In grade 1, students learned to tell time to the hour and half hour. Here, they make a connection between the analog clock and circles partitioned into halves or fourths.
Students use the phrases “half past,” “quarter past,” and “quarter till” to tell time. They skip-count by 5 to tell time in 5-minute intervals.
Students recognize that the hour hand on an analog clock moves toward the next hour as time passes. They represent time on analog clocks by drawing the hour and minute hands and writing the time with digits.
Students recognize that, as time passes, the hour hand on an analog clock moves toward the next hour. They learn that each hour comes around twice a day on a 12-hour clock, and is labeled with “a.m.” and “ p.m.” to distinguish between the times of day. Toward the end of this section, students relate a.m. and p.m. times to their daily activities.
Use addition and subtraction within 100 to solve one- and two-step word problems.
Section Narrative
In this section, students learn about money concepts while continuing to develop fluency with addition and subtraction within 100. They identify coins, such as quarters, dimes, nickels, and pennies, and find the total value of different coin combinations.
Students learn that 1 dollar has the same value as 100 cents, and then solve problems involving dollars and cents. Although students will not need to use decimal notation to represent money, they are expected to appropriately use the symbols $ and ¢.
Mai has some money. Elena has $48. They combine their money and now they have $85. How much money did Mai have?
Students are likely to have some previous experience with dollars and cents. Encourage them to share their experiences throughout the section. Consider creating an anchor chart of pictures of each coin and their values so that all students can access the content. As much as possible, give students access to real or plastic coins to support their reasoning. A blackline master with images of the coins is provided as an alternative, if needed.