A. Evaluate whether the attached "Formative Assessment: Multiplying Tenths" is an appropriate measurement instrument for the learning objectives and academic standards in the attached "Lesson Plan: Multiplying Tenths" by doing the following:

1. Analyze the alignment of the formative assessment to the lesson's learning objectives and academic standards.

2. Discuss the appropriateness of the rigor and relevance of the formative assessment.

3. Discuss how well the formative assessment measures student understanding and progress and informs future instruction.

B. Evaluate the effectiveness of the attached "Lesson Plan: Multiplying Tenths" on student outcomes, as measured by the formative assessment data in the "Formative Assessment Results" supporting document.

1. Analyze student learning for the class as a whole based on the data in the attached "Formative Assessment Results."

C. Discuss specific learning needs for each of the three students in the attached "Student Profiles."

1. Explain how the learning needs from part C may have affected the performance of each of the three students based on the information in the attached "Student Profiles" and the data in the attached "Formative Assessment Results."

D. Explain how you would address the learning needs of all students in a follow-up lesson plan the next day by doing the following:

1. Describe the instructional strategies you would use in the next day's lesson plan to address the needs of the entire class based on the results from the "Formative Assessment Results" supporting document.

2. Explain how you would differentiate instruction in the next day's lesson to meet the learning needs of each of the three students in the attached "Student Profiles."

a. Justify how the differentiation from part D2 would meet the learning needs of each student in the "Student Profiles" supporting document.

3. Describe the formative assessment you would use during the lesson described in parts D1 and D2.

a. Justify how the assessment described in part D3 would measure individual students' learning.

The Lesson Plan

Direct Instruction Lesson Plan Prerequisite Skills/Prior Knowledge: It is assumed in this lesson that students understand from fourth grade that \"half* means 0.5. Students are taught in fourth grade that the multiplication sign can represent \"groups of,\" " \"rows of,\" etc., and can be shortened to \"of " Standards and Objectives 5 tate/Mational Academic Standard(s): Standard 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. In this standard, dividing decimals is limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor. Compare the value of the quotient on the basis of the values of the dividend and divisor. P 'jumps of, Learning Objective(s): Given a problem and a 10x10 graph, the student will be able to multiply tenths by tenths using concrete and pictorial representations with 80% accuracy. EE I Hundredths grids, colored pencils, assessment Learn Zillion video: Multiply a tenth by a tenth Language Demands Specific ways that academic language (vocabulary, functions, discourse, syntax) is used by students to participate in learning tasks through reading, writing, listening, andyor speaking to demonstrate their understanding. Language Function(s): Students will create and analyze models of tenths-by-tenths multiplication. They will explain why multiplying tenths by tenths equals hundredths. Vocabulary: Tenths - each of ten equal parts into which something is divided. The place to the right of the ones place in the base-ten system. Hundredths one of 100 equal parts of a whole. The place directly to the right of the tenths place in the decimal system. Expression a math sentence with a minimum of two numbers and one math operation Discourse and/or Syntax: Students will create hundredths grids that represent tenths-times-tenths multiplication problems. Planned Language Supports: It is assumed in this lesson that students understand from fourth grade that \"half* means 0.5. Students " are taught in fourth grade that the multiplication sign can represent \"groups of\Diego's mother made four pans of brownies two is one. and sent half of them to school for Diego's . Students will say that half of one is a birthday. How many brownies did Diego take half. They notice the product gets to school? smaller. 0.5 x 0.5. Read the expression together as a class \"half of half\" or a. What equation could be written for \"five tenths of five tenths\" this situation? Since \"half\" is \"0.5" in decimal notation and \"of\" means multiply, write 0.5 x4 =2 Now change the problem so that Diego's mom made two pans of brownies. How many brownies did Diego take to school? Write 0.5x 2 = 1 on the board under the first equation. Now change the problem so that Diego's mom made one pan of brownies. How many brownies did Diego take to school? Write 0.5x 1 = 0.5 on the board under the second equation. What do students notice happens to the product as the total (whole) gets smaller? Now change the problem so that Diego's mom only made half of a pan of brownies. Ask students what expression could represent the situation and write it on the board. The first factor represents the part Diego is taking to school. The second factor represents the half of a pan of brownies that his mom made. Presentation Procedures for New Information and/or Modeling: Activity Description/Teacher Student Actions 2. Have students locate the first Write 0.5 to the left of the square. This hundredths grid on their papers and amount represents the part Diego took to explain that one square represents a school. pan of brownies. . Write 0.5 on the top of the square. This a. Write 0.5 to the left of the square. amount represents the half of a pan of This amount represents the part brownies that his mom made. Diego took to school. . With one color (red), shade five tenths b. Write 0.5 on the top of the square. columns (the amount Diego's mom This amount represents the half of a pan of brownies that his mom made. With one color (red), shade five tenths columns (the amount Diego's mom made). .5 ! ! I 1 ! T With a different color (bl.ue}, shade five I I teaths rows (the amount Diego took to school). 5 d. With a different color (blue), shade five tenths rows (the amount Diego took to school). 5 e. Where the two colors overlap (purple); 0.25, 25 hundredths, or some students may say 1/4. e. Where is the product represented? 3. Student responses may vary. 3. Write the answer 0.25 next to the expression on the board and ask students what they observe about the product when multiplying a number less than a whole by another number less than a whole. e Present the following problem. Ask 4, Write 0.2 x 0.4 or 2/10 x 4/10 students what expression best represents the situation and write it on the board. 5a. Write 0.2 to the left of the hundredths grid and 0.4 on top of the hundredths grid. b. Shade in four tenths with one color (four columns). It represents the original piece of Mrs. Miller, an interior designer, is making a throw pillow for a customer. She has a piece fabri of fabric that is 0.4 yards. She uses 0.2 of the ARIE: 0.4 yards. How much fabric (in yards) is she . Use a different color and shade the two tenths using? 5. Have students follow the same steps as in the previous example. b. What does this represent? . What does this represent? d. Where is the product represented? e. Why? Recall the way the expression was read: \"two tenths of four tenths.\" 6. Present the following problem and repeat the steps above to evaluate: Lucas and Eva are walking to school. Their school is 0.8 miles from their house. So far, they have walked half of the way (0.5) to school. How far have they walked? Ask students what expression best represents this situation and write it on the board. Write 0.5 to left of the hundredths grid and 0.8 on top of the hundredths grid. Shade in eight tenths with one color (eight columns). What does this represent? Use a different color and shade the five tenths (five rows). What does this represent? 'Where is the product represented? How else can 40 hundredths be written or read? The expression is read as \"five tenths of eight tenths\" but can also be read \"half of eight tenths.\" Therefore, it makes sense that the answer is four tenths. (two rows). It represents the piece Mrs. Miller cut off for the pillow. d. Where the two colors overlap is eight hundredths. e. Students are taught in fourth grade that the multiplication sign can represent \"groups of\Give the students the \"Multiplying Tenths\" Students will complete the \"Multiplying Tenths" worksheet. worksheet. Culminating or Closing Procedure/Activity: Show the Learn Zillion video \"Multiply a tenth by a tenth\". Differentiated Instruction Consider how to accormmodate for the needs of each type of student. Be sure that you provide content specific accormmadations that help to meet o variety of learning needs. Gifted and Talented: For students who need a challenge, have them use the commutative property and shade two bundredths grids one for each factor pair. Another suggestion is to have students explore how to represent the examples in the lesson using base-ten blocks. EL: For students who need help understanding what tenths and hundredths mean, use a dollar to represent a whole, dimes as tenths, and pennies as hundredths. Students with Other Special Needs: For students who are struggling at present with the problem 0.4 = 0.3, have students use a flat base-ten block to represent the hundredths grid. Use two index cards. Place one index card on top of the flat to show three tenths vertically (the card should cover seven tenths). Place the second card on top of the flat to show four tenths horizontally (the card should cover six tenths). The two cards together form and \"L\" shape to expose the array and product of 12 hundredths. For students who need additional instruction to understand that 0.5 is a half, write 0.5 as a fraction (5/10]). Draw a square, partition it into 10 pieces, and shade 5 of the pieces. Show how this is equivalent to 1/2. Formative Students will show that they understand multiplying tenths by tenths equals hundredths by completing a worksheet where they will use a hundredths grid to complete tenths-times-tenths problems. They will analyze a model to identify the expression represented within the model and explain why multiplying tenths by tenths equals hundredths. Summative (Quizzes, Tests, products) DGM2: Task 3 - Assessment Strategies Formative Assessment Results Assessment Topic: Multiplying Tenths Class Formative Assessment Results Student Score for Responses for Question 5 Name Questions 1-4 Dakota I. I don't know Bella Y. You count where they cross Traci C. Because 10 times 10 equals 100. Daniel B. (blank) will s. 100 Multiplying a decimal by a decimal makes a smaller number Maria E. You shade them. Landon S. Michael P. A tenth times a tenth equals a hundredth Abby M. You multiply Owen J. Line up the decimals Jake C. 100 Decimals times decimals make hundredths Leo K. They only go half as far Ben W. (blank) Lily A The amerwer is shaded. Bryce C. Where they cross over WESTERN GOVERNORS UNIVERSITY.Formative Assessment Results Jack K. 100 Tenths make tenths smaller so the answer is hundredths Tima P. 100 I count the number of squares that are shaded where the tenths cross Josie I. We use tenths to make hundredths when multiplying. Marcus L Multiplying by small numbers makes smaller numbers. Miguel N. Multiplying by decimals make bigger decimals. Katy C. The decimal number gets bigger Jon R. 100 (blank) Jeremy C. I don't know Penny B. 100 Anytime you multiply by a decimal the anewer is smaller. Hundredths are smaller than tenthe. Joe S The answer is where they cross. Jenny B. Count the number of squares that are dark4. Will and Evie are walking to school. Their school is 0.8 miles from their home. So far, they have walked halfway (0.5)- How far have they walked? S. Explain why multiplying tenths by tenths equals hundredths.Student Profiles Student: Michael Michael is a fifth-grade student and is considered gifted and talented. Observational data shows the student is sometimes unmotivated by traditional instructional strategies. Last school year the student scored \"On Track\" on the state standardized assessment. The student scored a C on the latest unit test, and the classroom teacher has attempted to contact the student's mother to schedule a conference about her concerns that the student is not working up to potential. However, the teacher cannot leave a message because the student's mother is out of cell phone minutes. The student lives in an apartment with their mom and two younger sisters. Student: Maria Maria is a fifth-grade student and an English learner (EL). Observational data show that the student is a hard worker but is sometimes confused by new vocabulary. Last year, the student scored \"Approaching\" on the state standardized assessment. On the last unit test, the student scored a D. The student's mother is concerned about their academics, but she does not speak English and does not know the best way to contact the school. The student lives in a house with their mom, dad, grandmother, older sister, and two younger brothers. Student: Daniel Daniel is a fifth-grade student and has an Individualized Education Program (IEP) for ADHD. Observational data shows that the student is significantly behind their peers academically, and struggles to focus on grade-level content. Last year the student scored \"Basic\" on the state standardized assessment. The student failed the last unit test, even with accommodations, including having the test read aloud and being given fewer answer choices. This student's parents are proactive and have contacted the classroom teacher and special education teacher to schedule a conference regarding this student's performance. This student lives with their mom, dad, and younger sister