Transitioning to the Common Core State Standards – Mathematics 4 th Grade Session 3 Pam Hutchison

AGENDA Multi-Step and Other Word Problems Review Math Practice Standards Fractions and Decimals Lines, Line Segments, Angles and Rays  What’s an Angle  Classifying Angles  Measuring Angles Data and Line Plots

Multi-Step Word Problems A pair of hippos weighed 5,201 kg together. The female weighed 2,038 kg. How much more did the male weigh than the female?

Multi-Step Word Problems A copper wire was 240 m long. After 60 m was cut off, it was double the length of a steel wire. How much longer was the copper wire than the steel wire at first?

Multi-Step Word Problems Jennifer has 256 pink beads. Stella has 3 times as many beads as Jennifer. Tiah has 104 more beads than Stella. How many beads does Tiah have?

Multi-Step Word Problems Sandy’s garden has 42 plants in each row. She has 2 rows of yellow corn and 20 rows of white corn. How many plants does she have?

CCSS Mathematical Practices REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically OVERARCHING HABITS OF MIND 1. Make sense of problems and perseveres in solving them 6. Attend to precision SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Math Practice Standards Using the MP descriptions from the 4 th Grade Flipbook, describe how you are developing each of these practices in your students. Be ready to share an example for each of the 8 Math Practices Standards. Which standard is the hardest to implement?

4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.)

4.NF.5 Focus on working with grids, number lines and other models (not algorithms) Base ten blocks and other place value models can be used to explore the relationship between fractions with denominators of 10 and denominators of 100 This work lays the foundation for decimal operations in fifth grade.

3 tenths = 30 hundredths 0.3 = 0.30 =

5 tenths + 7 hundredths =57 hundredths

4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.6 Focus on connections between fractions with denominators of 10 and 100 and the place value chart. Connect tenths and hundredths to place value chart Connect to 0.32 to

4.NF.6 Students connect with 0.32 and represent it on a place value model.

4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Planning a Lesson Connecting fractions, decimals, and place value. Review  Name the fractions  Tenths grid  Hundredths grid  Number line – tenths and hundredths  Write in expanded form

Planning a Lesson Word Problem: In the school chorus, of the students are girls. If there are 10 boys in the chorus, how many girls are there?

Place Value Hundreds Tens Ones

Place Value Hundreds Tens Ones

Place Value Hundreds Tens Ones

Place Value Hundreds Tens Ones

Place Value OnesTenths

Decimal Place Value OnesTenths

Decimal Place Value OnesTenthsHundredths

Fractions and Decimals So we can name some fractions as decimals How do we know which fractions we can also name as decimals?

Fractions and Decimals How do we know which fractions we can also name as decimals? When the denominator is a place value number (also called a power of 10)

Fractions and Decimals For example: can also be written as 0.3 can also be written as 0.72 What about ?

Classwork See Fractions and Decimals worksheet

Engage NY Fluency Practice  Designed to promote automaticity of key concepts  Daily Math is another form of fluency practice Application Problem  Designed to help students understand how to choose and apply the correct mathematics concept to solve real world problems  Read-Draw-Write (RDW): Read the problem, draw and label, write a number sentence, and write a word sentence

Engage NY Concept Development  Major portion of instruction  Deliberate progression of material, from concrete to pictorial to abstract Student Debrief  Students analyze the learning that occurred  Help them make connections between parts of the lesson, concepts, strategies, and tools on their own

Engage NY Module 5 Lesson 28 MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Engage NY Module 4: Angle Measures and Plane Figures Topic A: Lines and Angles Topic B: Angle Measurement Topic C: Problem Solving with Angle Measurement Topic D: Two-Dimensional Figures and Symmetry

Topic A – p A.2

4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Lesson 1 Identify and draw points, lines, line segments, rays, and angles and recognize them in various contexts and familiar figures. Concept Development p A.4 (bottom)  Problem 1: Draw, identify, and label points, a line segment, and a line.  Problem 2: Draw, identify, and label rays and angles.  Problem 3: Draw, identify, and label points, line segments, and angles in a familiar figure.  Problem 4: Analyze of a familiar figure.

Lesson 1 Problem Set A  Student Debrief Questions A.9-10  Exit Ticket A.13 Homework A.14-15

Lesson 2 Use right angles to determine whether angles are equal to, greater than, or less than right angles. Draw right, obtuse, and acute angles. Fluency Practice p A.17  Identify Two-Dimensional Figures  Physiometry Application Problem – Line Segments

Lesson 2 Conceptual Development p A. 18 Problem 1: Creating right angles through paper folding activity. Problem 2: Determine whether angles are equal to, greater than, or less than a right angle.  Practice Sheet p A.24 Problem 3: Draw right, acute, and obtuse angles.

Lesson 2 Problem Set A  Student Debrief Questions A  Exit Ticket A.28 Homework A.29-31

Lesson 3 Identify, define, and draw perpendicular lines. Fluency Practice p A.32  Identify Two-Dimensional Figures  Physiometry Application Problem – Line Segments (A.34)

Lesson 3 Conceptual Development p A.35 Problem 1: Define perpendicular lines. Problem 2: Identify perpendicular lines by measuring right angles with a right angle template. Problem 3: Recognize and write symbols for perpendicular segments. Problem 4: Draw perpendicular line segments.

Lesson 3 Problem Set A  Student Debrief Questions A  Exit Ticket A.42 Homework A.43-35

Lesson 4 Identify, define, and draw parallel lines. Fluency Practice p A.46  Identify Two-Dimensional Figures  Physiometry Application Problem - reviews perpendicular and intersecting lines (A.48)

Lesson 4 Conceptual Development p A.49 Problem 1: Define and identify parallel lines. Problem 2: Identify parallel lines using a right angle template.

Lesson 4 Conceptual Development Problem 3: Represent parallel lines with symbols. Problem 4: Draw parallel lines.

Lesson 4 Problem Set A  Student Debrief Questions A  Exit Ticket A.57 Homework A.58-60

Topic B – p B.2

4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a) An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b) An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.6

Lesson 5 Use a circular protractor to understand a 1-degree angle as 1/360 of a turn. Explore benchmark angles using the protractor. Fluency Practice p B.2  Identify Two-Dimensional Figures  Physiometry Application Problem – right angles (B.5)

Lesson 5 Conceptual Development p B.5 Directions for Constructing a Paper Protractor:

Lesson 5 Conceptual Development p B.5 Problem 1: Reason about the number of turns necessary to make a full turn with different fractions of a full turn.

Lesson 5 Problem 2: Use a circular protractor to determine that a quarter-turn or a right angle measures 90 degrees, a half turn measures 180 degrees, a three quarter-turn measures 270 degrees, and a full rotation measures 360 degrees.

Lesson 5 Problem 3: Measure and draw benchmark angles with the protractor.

Lesson 5 Problem 3: Measure and draw benchmark angles with the protractor.

Lesson 6 Use varied protractors to distinguish angle measure from length measurement. Fluency Practice p B. Application Problem – (B.) Conceptual Development p B.

Lesson 7 Measure and draw angles. Sketch given angle measures and verify with a protractor. Fluency Practice p B. Application Problem – (B.) Conceptual Development p B.

Lesson 8 Identify and measure angles as turns and recognize them in various contexts. Fluency Practice p B. Application Problem – (B.) Conceptual Development p B.