Elementary Mathematics

1st Grade Unit 8: Twos, Fives, and Tens

BEGIN WITH THE END IN MIND! common core expectations...

Students begin practicing counting on in Investigation 1 with Ten Turns. They continue to practice this skill throughout Investigation 1 and as they solve “How many” problems in Investigation 2. Encourage students to apply this skill to solve other problems that require counting on. For example, The Pet Snake challenges students to figure out how long a snake is after it has grown. Students can work with numbers within their counting range. They can also consider what would happen if the snake continued to grow a certain amount each week.

In Investigation 3, students return to their work with 10. They find combinations of 10. Then they apply these numbers to decompose addends to make numbers easier to work with. This work requires an understanding of equivalent expressions. Students can also work with equivalent expressions in Twenty Tickets. This task challenges students to find multiple-addend combinations of 20. Help struggling students complete the activity by first spending 10 tickets. Then talk about what would happen if they doubled their number of tickets.


Unit at a Glance

SUGGESTED DATES:
MARCH 26 - MAY 5

Estimated Duration: 23 days

*Investigation 1: 4 lessons, including Session 1.3A instead of Session 1.3
*Investigation 2: 8 lessons 
*Investigation 3: 6 lessons
*Investigation 4: 5 lessons

Smart Board, Promethean, and Power Point Files: 
 

Notebook File Daily Weather

 How Many Hands Smart Board File

Unit 8 Smart Board File (with Common Core Additions)




Tools for Teachers

Additional word problems with three addends 

Ideas for warm-ups that support mental math

Ten Turns on a Number Line recording sheet

Discovery Education Videos: Math Monsters: The Making of Tens (Spanish Version); Math Monsters: Doubles and Their Neighbors (Spanish Version)

 Discovery Ed Video: Math Investigations: Part 01; Beginning Math Adventures of the Lollipop Dragon: Place Value

End of Unit Rubrics 1st Grade

Unit 8 Vocabulary

Unit 8 Assessment

1st Grade At a Glance

1st Grade Investigations Extension Projects

1st Grade Story Problem Routine

Investigations K-2 Literature List

Progression for choosing numbers for tasks




OPPORTUNITIES FOR DIFFERENTIATION...

Suggestions for students who fully understand...

Teach students to use a number line with increments of 10. For example, students can create a number line to solve: 13 + 30 = ?. They should draw 13, 23, 33, and 43. After students have mastered drawing number lines to add multiples of 10, see if students can decompose two-digit numbers into multiples of ten and some ones. Students can draw a number line to add two two-digit numbers. For example, students can solve 13 + 33 = ? by drawing 13, 23, 33, and 43 then 44, 45, and 46. Pull students into a small group and closely monitor their use of this strategy. It takes away the concrete model of place value that the majority of first grade students need.

Many students will become adept at noticing patterns on the hundreds chart and in their own work in How Many problems. Challenge these students to understand the reasoning of others in Sam’s Base Ten Blocks. Students can compare their work to their peers to see if they all came up with the same strategies and solutions.




STANDARDS FOR MATHEMATICAL PRACTICE

MP1. Make sense of problems and persevere in solving them.

In this unit, students must combine multiple addends to find a total. To do so, students must understand the meaning of multiple variables. They determine the number of hands, feet, or eyes in a group of people or animals. This requires students to recognize that different animals have different numbers of hands and feet and to understand the difference between the number of animals or people in a group and the number of hands and feet on one animal. As students are working, they need to continually ask, “Does this make sense?” Encourage students to evaluate their work as they are solving problems. Ask questions like, “If each person has 10 fingers, does it makes sense that there were be fewer than 10 fingers in a group of people?”

MP8. 8. Look for and express regularity in repeated reasoning.

In Investigation 2, students being counting multiples (for example, the number of hands, feet, and eyes in a group of people). Students should look for patterns that will help them simplify problems. Encourage students to combine numbers that will help them add and subtract more quickly. For example, when counting the number of fingers in a group, students can notice that 5 fingers on one hand and five fingers on another hand gives them ten fingers per person. Encourage students to recognize numbers that are easy to work with (such as 10) and identify ways to combine quantities so they can use “easy” numbers.

MP4.  Model with mathematics

What math strategies would help us? Can we illustrate the problem? Act it out?

MP7. Look for and make use of structure

Do you see a pattern? Describe a pattern that you see in the problem.


TEAM TIME!
DISCUSS THE FOLLOWING WITH YOUR GRADE LEVEL TEAM:

Unit 8 requires students to work with larger numbers than they have before. They do this within the context of “How Many” problems. Students can approach these problems in many ways, and you will see a wide variety of strategies as students work through them! The role of the teacher is to encourage students to evaluate their work and that of others to check and build upon the reasoning. This can be done by purposeful questioning. Read “Using Questions to Help Children Build Mathematical Power” and focus on the question prompts that encourage children to rely on themselves and connect and apply mathematics. Discuss, “What might we see the students doing as they attempt these problems? What questions should we be asking in each situation to encourage students to build mathematical power?”

In this Unit, students build algebraic thinking by counting in groups. This lays the foundation for multiplication. Read, “Counting is More than 1, 2, 3” (Unit 8, pages 131 – 132). Then consider observations of particular students. Where are these students in their counting? What experiences do they need to move to the next level? Discuss possible interventions and extensions with your teammates.

Read over page 131-132, Counting is more than 1,2,3 and Observing students as they count – this information will help you to understand exactly where your students are when it comes to counting and understanding the number sequence. Offer practice to students that are struggling and are still in the Rote Counting group. By the end of first grade most students should be able to count in groups and keep track of what they are counting. (see page 136 for more information about counting by groups) 

Don’t forget about the Student Math Handbook, this provides students a visual and allows you to show how some children learn and strategies that they may not think of independently. This also provides students with the instructions to games and vocabulary that they will need to know.


OPPORTUNITIES FOR DIFFERENTIATION...

Suggestions for students who are struggling...


Students who are struggling may need help organizing their work with How Many story problems. Give these students manipulatives that help them track their progress. For example, students can color one box on a hundreds chart for every hand on a person. Then they can change to a different color for the next person. This helps students to see the difference between the number of hands on each person and the number of people in the group.

Students may also need additional practice counting on, especially with numbers later in the counting sequence. Students can work at a Show One More station to practice this skill.

Investigation 3 requires students to apply combinations of 10 to fluently add and subtract other numbers. To do this, students must quickly know their combinations of 10. Some students may need additional practice identifying combinations of 10. Facts of Ten supports struggling students by giving them cards with tens frames that are partially full. Students can practice identifying the missing addend by counting the empty squares on the card.

The goal of Investigation 4 is for students to be able to mentally add and subtract multiples of 10. To do this, students must be able to easily count by 10s. The hundreds chart is an excellent tool to build this ability. Have students look for patterns on the hundreds chart and color code the patterns. Students can also practice sliding the What Number Is…? Box up and down the hundreds chart to find one more and one less or ten more and ten less than a number.

Math Balance Scale – use when discussing the game Ten Plus – students need a visual and the balance scale provides students a chance to work with a manipulative that provides a visual. For example, if the cards they flip over are 8 and 5, they can put a weight on 8 and 5, then one on the 10 and see what they need to add to make the scale balance.

Addition Lessons 3-7 

www.xtramath.org
 – Free to sign up, allows teacher to set up an account and monitor student progress on addition. Once mastered, students can move forward to subtraction or continue practicing addition. 

www.pearsonsuccessnet.com  - eTool Workshop:Making 10 to Add; Math Facts Practice; eTool Workshop: Numbers Made with Tens; eTool Workshop: Using Related Facts; eTool Workshop: Number-Line Estimation: Numbers to 100 




COMMON CORE STATE STANDARDS IN THIS UNIT

Click here for the NCDPI CCSS Unpacking Document

In this unit, students work on efficient strategies for counting and combining numbers. The lessons correlate to the Number Sense and Operations and Algebraic Thinking standards.  Students must think algebraically about problems (as demonstrated in the Common Core State Standards Video, 1.OA.6). They must also apply properties of place value to add and subtract larger numbers (as demonstrate in the Common Core State Standards Video, 1.NBT.4) or the link to the unpacking document

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.

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 and 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 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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.

Represent and solve problems involving addition and subtraction.

1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Understand and apply properties of operations and the relationship between addition and subtraction.

1.OA.3. Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. 

Add and subtract within 20.

1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Work with addition and subtraction equations.

1.OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _.

Words you should hear students use in Mathematical Conversations...

counting on, pattern, addition equation, combine, addition notation, addend, less than, equals, combination, the same as (teach with equals, students need to understand that equals means the same as, not "here comes the answer")

Play “One More/One Less/Ten More/Ten Less.” Write the four prompts on the board (One more, One less, Ten more, Ten less). Present students with a dot or number card and call on students to put that number into a relationship. Students can use whichever prompt makes them feel comfortable. For example, some students will be comfortable saying, “One more than 17 is 18,” whereas others will be more comfortable saying, “Ten less than 17 is 7.” This helps all students successfully participate.  For dot cards for this activity as well as an explanation of other similar warm-ups, please visit
Tens Frames and Dot Cards.

Have students create a Show Me to present their approach to a story problem. Students can read the problem, write and draw to show their solution, and record their voice as they explain how the understood and solved the problem. Students can view the Show Me of other students to evaluate their reasoning too.


*Remember to upload files to share with others, or locate files to use, on the wiki. Be sure to join discussion posts with other colleagues to ask questions, answer questions, and discuss math.

TAKE NOTE FOR EACH INVESTIGATION
INVESTIGATION 1

Concepts to highlight - Counting and keeping track of amounts up to 60; counting on from a known quantity and Identifying and using patterns in the number sequence and on the 100 chart; organizing objects to count them more efficiently.

Concepts to enhance - Identifying, reading, writing, and sequencing numbers to 100 and beyond.

INVESTIGATION 2

Concepts to highlight – Counting and combining things that come in groups of 1, 2, 4, 5, and 10; counting by 2s, 5s, and 10s; counting by numbers other than 1; recording strategies for counting and combining

Concepts to enhance – Exploring a 2:1 and 5:1 relationship; developing strategies for organizing sets of objects so that they are easy to count and combine.


INVESTIGATION 3

Concepts to highlight – Developing fluency with the 2-addend combinations of 10; solving a problem in which the total (10) and one part are known; organizing objects to count them more efficiently; counting by 10s; using addition notation to record; adding single-digit numbers.

Concepts to enhance – developing meaning for counting by groups of ten; considering notation for equivalent expressions; thinking about numbers to 20 in terms of how they relate to 10; determining equivalent expressions for a given expression; considering a 2-digit number as tens and ones.



INVESTIGATION 4

Concepts to highlight – identifying, reading, writing and sequencing numbers to 120 and beyond; counting by groups of 10s; using a number to represent a set of objects; using cubes in tens and ones to represent a two-digit number; adding a one-digit number or 10 to a two-digit number.


Concepts to enhance – comparing two two-digit numbers and using notation to record the results of the comparison; adding and subtracting 10 to/from a two-digit number; adding a multiple of 10 to a two-digit number; subtracting a multiple of 10 from a two-digit number.


CLASSROOM ROUTINES
START WITH, GET TO

1.NBT.1 – count to 120, starting at any number less than 120. Begin introducing place value, counting 
by tens using a number line or hundred chart.
TELL A STORY

1.OA.1 – Use addition and subtraction within 20 to solve word problems. Students create a story of their own – have one student share a story, another illustrate and solve and a third student explain what was done.
TIME

1.MD.3 – tell and write time in hours and half-hours using analog and digital clocks. Have students practice using clocks on SMARTboard or use clocks found within the school. Incorporate into all morning routines and throughout school-day.