Elementary Mathematics
Kindergarten Unit 4: MEASURING AND COUNTING

BEGIN WITH THE END IN MIND...Common Core Expectations...

 
Illustrative Mathematics Tasks

Dice Addition

What's Missing?

Bobbie Bear's Buttons

Christina's Candies

How Heavy

Size Shuffle

Which weighs more? Which weighs less?



UNIT AT A GLANCE

Suggested Dates:
December 12- February 7

Estimated Duration: 30 days

*Investigation 1: 8 lessons (include 1.6a, 1.6b, 1.6c)
*Investigation 2: 5 lessons 
*Investigation 3: 7 lessons
*Investigation 4: 9 lessons





TOOLS FOR TEACHERS

K-1 Investigations Online Games and Activities

Race to Trace! (11-22)

Represent Numbers in Three Ways

Handwriting Sheets 1-10

Handwriting Sheets 11-20

Ten Frame Flash

Ten Frame Numeral Match

Addition Plate

Bears in the Cave

Dot Card Addition

Addition Bag

Facts of Ten

Measurement: Long-Short

Measurement: Tall-Short

The Number Crew: The Roller Coaster: Part 1

The Number Crew: The Roller Coaster: Part 2

Math Monsters: Standard and Non-Standard Measurement

I Can Count to 100  is a great way to learn number names and practice counting. K.CC.1, K.CC.3

Kindergarten at a glance document

Ongoing Assessments Unit 4
End of Unit Assessment rubric 

Preparing a Deep Dive Unit 4 PPT

Directions for Measuring With My Feet Game, and the 
 Recording Sheet

K Math Vocabulary
Investigations Vocabulary

Kindergarten Investigations Data Sheet

K Story Problem Routine Poster

Investigations K-2 Literature List 

Progression for choosing numbers for tasks 

TECHNOLOGY CONNECTIONS: ONLINE ACTIVITIES FOR STUDENTS

The Number Track. Players complete a number track that goes to 20 by placing 5 numbers (or 10, or all of them) in the appropriate empty spaces. Students can also design their own game. K.CC.1, K.CC.3

IXL Number Lines

K.CC.1, K.CC.3

Math Monsters
 Standard and Non Standard Measurement
STANDARDS FOR MATHEMATICAL PRACTICE

K-5 Unpacking document for standards for mathematical practice 

During this unit, introduce students to MP1 and MP2.

At the end of investigation 1 bring the students together for a mathematical discussion. Ask, why do you suppose that we got different measurements for the same strip of tape? MP2

How well do students make sense of and solve problems in Investigations 3? MP1        

 

TEAM TIME!
How can you help students to verbalize algebraic thinking? Read “Algebra Connections in this Unit” (page 16) and discuss with your team. 

At what age do students develop an understanding that length is a stable, measurable dimension? Read “Learning About Length: Lining Up Units” (page 169). Then, facilitate a classroom discussion at the end of lesson 1.1 to discuss the strategies that students used to measure.

What story problem structures are appropriate for kindergarten? Read Kindergarten Addition and Subtraction Problem-types Common Core Unpacked page 20. 
Common Core Unpacked
 

Provide students with one problem for each type of situation (add to, take from, put together/ take apart) using the same numbers and the same context.  After students solve, ask, “How was solving each of these problem types different?”   Then, bring student samples to your team meeting.  Read “Story Problems in Kindergarten on page 174; discuss,  “How do the actions in each type of situation differ?”  Do you agree that a student can use the same solution strategy to solve any of these types?

Also, read the teacher notes “Creating Your Own Story Problems” (page 172).

How should I assess the students’ ability to determine what is one more or one less than a number?  Read “Assessing One More, One Fewer” (page 176), play a few rounds of the game One More, One Fewer during planning, and anticipate what the students will do.

Double Compare: Strategies for Combining and Comparing Investigations unit 4 page 178. During planning discuss which strategies you observed students using. “What can you do to encourage students to use different strategies?”

WORDS YOU SHOULD HEAR STUDENTS USE IN MATHEMATICAL CONVERSATIONS

more
less
equal
long
longer
short
shorter
heavy
sort

Ask students to discuss what is happening in addition and subtraction stories and games.  Listen for the use of the words combining and separating.

Encourage students to use words such as shorter, longer and equal to when comparing the lengths of different items.  


OPPORTUNITIES FOR DIFFERENTIATION

Suggestions for students who are struggling:

-Measuring Shoes: describe the measurement “heal to toe” or “left to right”

-Practice counting to 20 using a number line and/ or give them personal number lines

-Build It: fill in a row of five before starting another

-Grab and Count: grab, count, and record one handful at a time.

- Racing Bears: play in a small group facilitated by the teacher or adjust the rules of the game see page 93

- Six Tiles in All: play on a paper plate or colored construction paper

-Double-check total each time they create a new arrangement

-One More, One Fewer: split in 3 days (one more, one less, both)

COMMON CORE STATE STANDARDS

Link to Unpacking Document

K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.

K.CC.4a  When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.


K.CC.4b  Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.


K.CC.4c  Understand that each successive number name refers to a quantity that is one larger.

K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Check out this video:

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from K.OA.2

K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

K.MD.2  Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.






OPPORTUNITIES FOR DIFFERENTIATION

Suggestions for students who fully understand...
-Measuring Shoes: provide several adult shoes from around the school

-Measuring shoes: once students have measured a number of shoes, make a list of the shoes from shortest to longest.

-Measuring with Sticks: make lines that require a half stick (ex: line B is 2 and a half sticks long)

-Measuring: use smallest place value cubes as unit of measurement

-Build It: p. 62

-Collect 10 Together: record (might use plus sign) –use 2 color chips so they can see combinations

-Build On: use 2 colors

-Roll and Record 2: ask and answer data questions (Which has more? Less? The same?)

-Racing Bears: only use 2 columns; each student has their own column. Record their rolls to make 10

-Word Problems: work within 10 or 12, work with unknowns in different places

-Double Compare: Record work in T-chart, circle the greater (possible plus sign)

-Build It/Change It: record (possible: 3 column chart: start/end/add or remove)

-Toss the Chips: write a number sentence 

It is a great idea for teachers to make a model or representation of how the investigations games are played. This could be a picture of the game with all materials or written directions in “kid friendly” words. This will allow students or other adults to help students when they are in the math centers. 

*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 ABOUT EACH INVESTIGATION

INVESTIGATION 1

Students need to be able to describe the measurable attributes of objects. For example, “This shoe is long.” K.MD.1

Students need to compare two objects by a measurable attribute when they are placed next to each other. For example, “This block is a lot longer than this one.”  Students also need to develop conservation of length where they understand that objects should be lined up at one end to get accurate measurements. K.MD.2


INVESTIGATION 2

Focus on understanding the concept of addition and subtraction as joining and separating quantities, respectively. K.OA.1  

INVESTIGATION 3  

During closing discussions, ask students to act out and solve unknown problems presented in a story context.
  Use the story problem routine. Numbers should not exceed 10. K.OA.2


INVESTIGATION 4

Incorporate opportunities for students to sort a collection of objects by one attribute. For example, sort some buttons by color, count the amount of buttons in each color, and organize the buttons by the quantities in each group (5 blue, 4 green, 4 yellow, and 3 orange buttons). K.MD.3

Decompose numbers between 5 and 10. K.OA.3

Incorporate opportunities for students to state what number needs to be added to a given number to make a set of 10. K.OA.4

IMPORTANT! CLASSROOM ROUTINES

ATTENDANCE

Develop strategies for counting accurately and compare quantities.  Use a number line as an alternative representation while counting. K.CC.1; K.CC.4 a, b; K.CC.5; K.CC.6

CALENDAR

Use calendar for keeping track of time and develop strategies for counting accurately.  K.CC.2; K.CC.4 a, b; K.CC.5

Incorporate questions such as what number/month comes before/after certain numbers. K.CC.2

Add a word problem that students can work out in their math journals.K.OA.1

TODAY’S QUESTION

Collect, count, represent, describe, and compare data.

 K.CC.2, K.CC.4abc, 5, 6, 7

Use multiple ways to represent the data ex. names, tally marks and then count to tell “how many?” K.CC.5

Add a third column of data to compare ex. Would you rather be a monkey, elephant or tiger? K.CC.6

PATTERNS ON THE POCKET CHART

Determine what comes next in a generating pattern; describe repeating patterns.

Identify the units in the pattern.