Grade 1 Unit 4: Place Value, Comparison, Addition and Subtraction of Numbers to 40

(7 Weeks) Stage 1 – Desired Results

Established Goals Unit Description Students will learn that the focus of adding and subtracting within 40 is on establishing “1 ten” as a new unit. Before students loosely grouped 10 objects to make 10. Now they transition to thinking of that 10 as a single unit (using 10 linker cubes stuck together, for example). Students will begin to see problems like 23+6 that they can mentally push the “2 tens” in 23 over to the side and concentrate on the familiar addition problem 3+6. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices. Common Core Learning Standards

The standards listed below are not intentionally sequenced and should not simply be taught consecutively. Strong units weave these standards together in a thoughtful and coherent way. Schools and teacher teams can use this document to compare their current curriculum to and choose high leverage moments to enhance instruction. Extend the counting sequence. 1.NBT.1: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. Understand place value. 1.NBT.2: Understand that the two digits of a two-digit number represent amounts of tens & ones. Understand the following as special cases: The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight or nine tens (and 0 ones).

a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

1.NBT.3: Compare two two-digit numbers based on meanings of the tens & ones digits, recording the results of comparisons with the symbols >, =, & <. Use place value understanding and properties of operations to add and subtract. 1.NBT.4: Add within 100, including adding a two digit number and a one digit number, and adding a two-digit number and a multiple of 10, 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 & explain the reasoning used. Understand that in adding two digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

1.NBT.5: Given a two digit number, mentally find 10 more or 10 less than the number, without having to count:

explain the reasoning used. 1.NBT.6: Subtract multiples of 10 in the range 10-100 from multiples of 10 in the range 10-100 (positive or zero differences) using concrete models or drawings & strategies based on place value, properties of operations, &/or the relationship between addition & subtraction: relate the strategy to a written method & explain the reasoning used.

Common Core Standards of Mathematical Practice

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.

5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

ESL Language Standards 1.10 Demonstrate a basic understanding of facts (S,W) 3.8 Apply self-monitoring and self-correcting strategies to adjust language production to effectively express ideas and opinions. Such strategies include asking questions, starting over, rephrasing and exploring alternate ways of saying things. (L, S, R, W) 4.7 Follow oral and written directions to participate in classroom and social activities. (L, R)

Big Ideas 1. The Base Ten Numeration System: The base ten numeration system is a scheme for recording numbers using digits 0-9, groups of 10 and place value. 2.Two numbers may be compared by examining the amount of tens and ones in each number using words, models and symbols greater than (>), less than (<), and equal to (=). 3. Basic Facts and Algorithms: Basic facts and algorithms for operations with rational numbers use notions of equivalence to transform calculations into simpler ones.

Essential Questions 1. How does using 10 as a benchmark help us compose numbers? 1.How can we represent a number using tens and ones? 1. Why do we need to be able to count objects in a set? 1. How can large quantities be counted efficiently? 2. How can words and symbols be used to illustrate the comparison of numbers? 2. How can numbers be compared using greater than, less than or equal? 3. Why are powers of 10 an important benchmark in our numeration system? 3. How can numbers be broken apart and grouped in different ways to make calculations simple?

Content (Students will know….) A. Counting sequence to 120 (1.NBT.1) B. A bundle of ten ones is called a ten and can be thought

of as a unit (1.NBT.2a) C. Numbers from 11 to 19 are composed of a ten & a

number between one and nine (1.NBT.2b)

D. The numbers 10, 20, 30, 40…. refer to one, two, three, four …tens and zero ones (1.NBT.2c)

E. Two digit numbers can be compared based on place

value (1.NBT.3)

F. Strategies for Addition within 100 (1.NBT.4)

Skills (Students will be able to…) A.1. Count to 120 starting with any number less than 120 A2. Count forwards, backwards and in patterns (by 2, 5, or 10) A3. Read and write numerals in and out of sequence A4. Represent a quantity with a written numeral B1. Represent ten ones as a ten B2. Group objects in tens and realize for example that 42 cubes is the same as 4 tens and 2 leftover B3. Count by tens C1. Given a number between 11 and 20, make groups of tens and ones. C2. Count by tens and ones D1. Represent multiples of ten D2. Count by tens E1. Compare numbers based on the number of tens and ones in each respective number using <, > symbols F1. Add 2 digit and one digit numbers

G. Mental addition and subtraction of 10 (1.NBT.5) H. Subtraction of multiples of 10 (1.NBT.6)

F2. Add 2 digit number with a multiple of 10 F3. Compose tens when adding F4. Use concrete models, drawings and strategies based on place value, operations and or the relationship between addition and subtraction to add numbers F5. Explain the strategy used with a written explanation G1. Identify the tens and ones place of a given number G2. Explain why a number is ten more or less G3. Mentally add or subtract ten from a given number G4. Explain the strategy used in written form H1. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 H2. Demonstrate taking tens away from a number using manipulatives H3. Solve subtraction problems using strategies based on place value, properties of operations and or the relationship between addition and subtraction H4. Explain the strategy used in written form

Terms/ Vocabulary Addition, benchmark, chart, compare, compose, counting on, data, decompose, equal to, less than, more than, same, number line, place value-tens and ones, representation, subtraction, table, tally mark, ten frame

Stage 2 – Assessment Evidence

Initial Task: George Washington’s Cherry Orchard Final Performance Task: Winter Fun

Other Evidence Teacher observation, conferencing, teacher designed assessment pieces, student work, exit slips, journal entries

Stage 3 – Learning Plan

Everyday Mathematics/Impact Mathematics Lessons – The following lessons may support some of the CCLS & essential questions outlined in this unit map:

1.NBT.1: 1-1, 1-2, 1-4, 1-5, 1-7, 1-8, 1-9, 1-10, 1-12, 1-13, 2-1 through 2-7, 2-11, 2-13, 3-6, 4-10, 5-1, 9-1, 9-4, 10-7, Project 3, Project 5 1.NBT.2: 5-1, 5-2, 5-3, 5-5, 5-6, 5-8, 5-9, 8-2, 8-3, 8-4, 8-5, 10-4, 10-7 1.NBT.3: 1-6, 5-3, 5-6, 5-7, 8-1, 8-2, 10-3 1.NBT.4: 2-1, 2-13, 3-9, 4-2, 5-5, 5-8, 5-9, 6-4, 6-9, 8-4, 8-5, 8-6, 9-2, 9-3, 9-4, 10-3, 10-4, 10-6, Project 9 1.NBT.5: 3-9, 8-5, 8-6, 9-1, 9-3, 9-5, 10-4, 10-6, 10-7, Project 9 1.NBT.6: 8-4, 9-2, 9-3, 9-4, 10-4, 10-6 Additional Resources: k-5 Math Teaching Resources http://www.k-5mathteachingresources.com/1st-grade-number-activities.html Utah Education Network Curriculum Guides, lesson plans and activities listed by standard 1.NBT.1 -http://www.uen.org/core/displayLinks.do?courseNumber=5110&standardId=71359 1.NBT.2, 1NBT.3 -http://www.uen.org/core/displayLinks.do?courseNumber=5110&standardId=71361 1.NBT.4, 1.NBT.5, 1.NBT.6 - http://www.uen.org/core/displayLinks.do?courseNumber=5110&standardId=71367

Common Core Aligned Tasks by standard: http://insidemathematics.org/index.php/1st-grade (scroll down to 1NBT2, 1NBT3 and 1NBT4) Tennessee Teacher’s Math Toolkit Lesson Plans and activities by standard (click on left menu on the standard and examples, media, teaching strategies, lesson plans and activities are available per standard) http://www.readtennessee.org/math/teachers/k-3_common_core_math_standards/first_grade/number_operations_in_base_ten.aspx

Name: _____________________________ Date: ______________

Grade 1 Unit 4

Initial Performance Task: George Washington’s Cherry Orchard

1. There are 100 cherry trees in the orchard. The trees are arranged in rows of 10. There are ten rows as shown in the diagram below. George is picking cherries from the 38th tree. How will George get to the 95th tree? Show (by filling in the numbers) of the path George can take and explain your strategy on the lines below.

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

2. George picked 67 cherries on Monday and 92 cherries on Tuesday (1NBT2b, 1NBT3)

a) Use the least amount of base ten blocks to represent the number 67. Draw and label your thinking.

b) Use the least amount of base ten blocks to represent the number 92. Draw and label your thinking.

c) Write a number sentence comparing 67 and 92. Use one of the symbols <, > or = in your number sentence:

3. On Wednesday, George picks 52 cherries. He is hungry on his way home so he eats 30 cherries. How many cherries does George have left? Show and explain your mathematical thinking

4. George likes to put his cherries in groups of ten. Over the week, he collected 120 cherries. How

many groups of ten will George make? Represent your answer with a diagram 5. The cherry orchard has 100 cherry trees. George chops down 10 cherry trees. How many cherry trees are left in the orchard? Use the open number line to show your work

How many cherry trees are left in the orchard? _________________________________

Grade 1 Unit 4 Initial Task: George Washington’s Cherry Trees

George Washington’s Cherry Trees Scoring Guide Points Section Points

1. 1NBT1, 1NBT4, 1NBT5

Student shows a path by filling in the numbers to go from 38 to 95. For example 38 to 48 to 58 to 68 to 78 to 88 to 89 to 90 to 91 to 92 to 93 to 94 to 95.

Student explains their corresponding strategy (teacher can write for the student if necessary)

1

1

2

2. 1NBT1, 1NBT2b

Student draws and labels tens and ones using the least amount of blocks correctly – 6 tens and 7 ones

Student draws and labels tens and ones using the least amount blocks – 9 tens and 2 ones

Student writes a correct number sentence such as 92 > 67 or 67 < 92

1

1

1

3

3. 1NBT5, 1NBT6

Student correctly subtracts 30 from 52 and arrives at a correct answer of 22

Student shows a correct model, drawing or strategy

Student explains the strategy chosen in word form

1

1 1

3

4. 1NBT2a, 1NBT2c

Student correctly answers that there will be 12 groups of ten

Student represents their groups of ten with a correct diagram

1 1

2

5. 1.NBT.5, 1.NBT.6

Student uses number line to correctly show the number of cherry trees left (30) = 1pt.

Student writes correct answer on answer line = 1 pt.

1

1

2

Total Points

12 12

Novice Apprentice Practitioner

Expert

0-2 3-6 7-10

11- 12

Name: ______________________________________ Date: ______________

Grade 1 Unit 4

Final Performance Task: Winter Fun

1. Mary made 65 snowballs. Tom made 55 snowballs.

a) Use the least amount of base ten blocks to

represent the number 65. Draw and label your thinking.

b) Use the least amount of base ten blocks to

represent the number 55. Draw and label your thinking.

c) Write a number sentence comparing 65 and 55. Use one of the symbols <, > or = in your number sentence:

2. Mary made 65 snowballs. Tom made 55 snowballs. Show one way they could count them to figure

out how many they have altogether.

Show your mathematical thinking.

3. Tom has 55 snowballs. He makes 7 more.

How many groups of 10 can he make? ____________________________

Does he have any leftover? ___________________________________

How many snowballs are leftover? _________________________________

Use the ten frames to show your work.

4. David put 23 mini marshmallows in his cup of hot chocolate. David added 20 more mini

marshmallows to the cup of hot chocolate. How many mini marshmallows are in David’s cup of

hot chocolate now? Use the hundred-chart to show your thinking.

How many marshmallows does David have now?

________________________________________

5. Sam has 40 mini marshmallows. He gives 10 mini marshmallows to Rachel. How many mini

marshmallows does Sam have now?

Use the open number line to show your work.

0 10 20 30 40 50

How many marshmallows does Sam have now?

_________________________________________

Grade 1 Unit 4

Final Performance Task: Winter Fun

Winter Fun Scoring Guide Points Section

Points

1. 1NBT2, 1NBT3

Student draws and labels tens and ones using the least amount of blocks correctly – 5 tens and 5 ones

Student draws and labels tens and ones using the least amount blocks – 6 tens and 5 ones

Student writes a correct number sentence such as 65 > 55 or 55 < 65

1

1

1

3

2. 1NBT1

Student demonstrates counting strategy starting at 65 or 55 and counting on to reach 120.

1

1

3. 1NBT4

Student correctly adds 55 and 7 to get 62

Student shows six 10s frames and 2 ones filled in

Student writes 6 10s and 2 1s

1

1

1

3

4. 1NBT5

Student correctly answers 43

Student represents their mathematical thinking on the provided 100s chart

Student writes correct answer on answer line = 1 pt.

1

1

1

3

5. 1NBT6

Student uses number line to correctly show the number of marshmallows left (30).

Student writes correct answer on answer line = 1 pt.

1

1

2

Total Points 12 12

Novice Apprentice Practitioner Expert

0-2 3-6 7-10 11-12