Presentation on theme: "Goals for today Share “what works” with each other"— Presentation transcript:
1Goals for today Share “what works” with each other Possibly learn some new things about K and 1st grade mathGet new resources and do some planningGo inside other’s classroomsThink about how to provide support as needed (“Daily 5”)
33 sessions Early number concepts (today) Adding and subtracting to solve problems (Mar. 13)Describing shapes, measuring length, telling time (Apr. 21)
4Big Ideas about K-1 MathWhat children learn in K and 1st grade is a foundation for all other mathematics.Early number concepts lead to addition and subtraction fluency.Common Core is a clear outline of learning expectations.Great resources are available for early numeracy activities.Diagnostic assessments can help students who are behind their classmates.
5Framework Resources Counting – More/Less – Number Relationships Add/Subtract Situations – Strategies – FluencyTens and Ones – Place Value – Multi-digit OperationsVan de Walle and LovinKathy RichardsonGrayson WheatleyElementary Math Resources wikiGeorgia and New York lesson plansResources
6Classroom Visits Sharing and Planning Teaching Channel Number Talks Eventually your own classrooms??Always shareKeep track of “What I Want to Try”Make and take – Daily 5 – Math Work StationsSharing and Planning
7In a first grade class…Three children successfully solved addition and subtraction tasks for two digit numbers.Fourteen of the twenty-one children used their fingers to count all or count on as they solved such problems as = ___ and = ___.Three of the children needed cubes to solve such problems and counted all the cubes.One child had difficulty counting more than seven cubes accurately.
8Your kindergarten class? Say the number sequence to 20? higher?Tell which group of objects has more? which has less? or whether they are equal?Count a group of objects up to 10? to 20?Show a set of counters to represent a number?Recognize dot card groupings and say the number represented, without counting.Responsive teaching: learn to recognize where students are now in order to help move them forward.Look at the math on the diagnostic assessment – what percent have accomplished each task?
9Your 1st grade classStart counting at a number other than 1 and continue the sequence?Count objects up to 20 in a group and write the numeral?Answer "How many more are needed to make 5 (or 10)?" perhaps using 5- or 10-frame cards.Answer simple adding or subtracting problems like "Corey has 4 markers. Her sister gives her 3 more markers. Now how many markers does Corey have?" What strategies do they use?
10Common Core StandardsTake a few minutes to look over the CCSS for K and 1.Put a check next to those standards that your students learn well.Put a 0 next to those standards that are introduced but not always learned to mastery.Put an X next to those standards that you currently don’t address in a meaningful way.It’s important to know the standards inside-out because they guide your planning and teaching.
11K-1 Number Concepts More, less, equal Counting objects, “counting on” Number relationshipsAddition and subtraction problems using strategies based on number relationshipsPlace value (two digits)Use CCSS critical areas
12Counting & number relationships Fluency with whole numbers are the basis forProblem solvingwhich leads toFluency with whole numbers
14More, less, and sameEntering kindergarten children can most always pick the set that is more.Although the concept of less is logically equivalent to more, the word “less” is often more difficult for children than “more.”Whenever you ask “Which is more,” also ask “Which is less.”Elementary Math ResourcesActivities 1 & 2
15CountingCounting tells how many things are in a set. When counting a set of objects, the last word in the counting sequence names the quantity for that set.Children will learn how to count before they understand that the last count word indicates the amount of the set. (the cardinality principle)Resources: Let’s Count: Learning Numbers in Meaningful Ways (T.C.) Illuminations Let’s Count to 10Activities 3 & 4
16Counting on and backFrequent short practice drills are recommended for children who have difficulty with this.Number Talks Kindergarten video: Counting BookActivities 5, 6 & 7
17Counting on and backFrequent short practice drills are recommended for children who have difficulty with this.Number Talks Kindergarten video: Counting BookActivities 5, 6 & 7
18Developing Number Concepts: Kathy Richardson (golden) Read the section on counting, pp. 2-11What difficulties have you found? What works for you? What new activities might you try?Partner pair/choose one/table talk
19Number relationshipsNumbers are related to each other through a variety of number relationships. The number 7, for example, ismore than 4, less than 9,composed of 3 and 4 as well as 2 and 5,is three away from 10,and can be quickly recognized in several patterned arrangements of dots.Number relationships for 7 further extend to an understanding of 17, 57 and 370. Starting at 17, how many more are needed to make 20?
20Simon Says Simon says, Show six fingers. Janice, tell us about the way you showed six fingers.Peter, yours is different. Tell us about yours.Does anyone have a different way to show six fingers?Simon says, Show nine fingers.
21Number relationships 1-10 BTW, on the diagnostic assessment,See the diagnostic assessment for a few dot patternsActivities 8, 9 & 10
22SubitizingSee the Dot-card packetQuick ImagesNumber Talks
23Number relationships 1-10 Activities 11, 12 & 13Frogs on a Log
25Five and ten frame cards The frame for seven provides a visual model of seven as two more than five and three less than ten.Working with this model supports the eventual connection to = 7 and 10 – 3 = 7.VideoHow to Teach a Child Math – Part 1How to Teach a Child Math - Part 2PacketWatch the videos at this point and explore the packets. Choose 3 target students, one advanced, one on grade level, one who is struggling, and find an activity for each of them.
26Number relationships 1-10 Focus on a single number throughout the session (e.g. different combination to 7). Also do “missing part” activities.Graphics are from Van de Walle & Lovin, Teaching Student-Centered Mathematics: Grades K-3Activities 17 – 22
27Be Patient!The principal tool that children will use as they construct these relationships is the one number tool they possess: counting.Initially, then, you will notice a lot of counting, and you may wonder if you are making progress.Have patience! Counting will become less and less necessary as children construct these new relationships and begin to use the more powerful ideas.Activities 23 – 26
28Good basis for assessing Careful observation during number relationship station activities will tell you a lot about where your children are with number concepts. Usually classroom work is sufficient for moving most students along the learning progressions. But when informal observation leads you to believe that a child needs additional support, direct assessment is crucial.Benjamin’s videoKathy Richardson Assessing Math Concepts
29Assessing Math Concepts Kathy Richardson’s Assessment Series Concept 1: Counting Objects Concept 2: Beginning Number Relationships Concept 3: Comparing Numbers Concept 4: Identifying and Combining Parts Concept 5: Number Combinations Concept 6: Decomposing Numbers to Ten Concept 7: One Ten and Some More
30Changing Numbers Assessment Kathy Richardson Show the numeral 6. What is this numeral? Can you make a pile of 6?Show the numeral What is this numeral? Can you change this pile (of 6) so there are 10?Show the numeral 7. What is this numeral? If you change this pile (of 10) so there are 7, do you think you need to get some more or take some away?Do you know how many you need to add/take away? Go ahead and change the pile to 7.
31Show the numeral 9. What is this numeral Show the numeral 9. What is this numeral? If you change this pile (of 7) so there are 9, do you think you need to get some more or take some away?Do you know how many you need to add/take away? Go ahead and change the pile to 9.Going Back – to 5: If the child tried to change one number to another but had difficulty, continue with the following numbers: Show me 2. Change 2 to 5. Change 5 to 4.Going On – to 15: If the child was able to change the numbers with ease, continue with the following: Change 9 to 13. Change 13 to 11. Change 11 to 15.Count off 1 to 6. Rearrange tables by those numbers. Group by pairs, one the teacher, one the student.Popsicle Stick Math: Making 10How could you use this in your class?
32Developing Number Concepts: Kathy Richardson (golden) Read the section on more and less, ppDig deeply into More/Less ActivitiesRead the More/Less Trains assessment (purple p. 3)
34Number Relationships 10-20 Very important for basic addition fact families.Kindergarten and early first grade children should be able to see a set of six with a set of 10 and know that the total is 16 – but they should not be asked to state that the 1 in 16 represents “one ten” or that the 6 represents “six ones.” (what’s a one?)Beyond Fingers: Place Value & the Numbers 11-19Activities 27, 28 & 29
35Double and near-doubles Double 3 is the bug doubleDouble 4 is the spider doubleDouble 5 is the hand doubleDouble 6 is the egg carton doubleDouble 7 is the two-week doubleDouble 8 is the crayon doubleDouble 9 is the 18-wheeler doubleAll about the games we play…
36Numbers to 100: IntroThe hundreds chart is an essential tool for every K-3 classroom!Counting Collections to 100Skip Counting with Counting CollectionsNotice the “Questions to Consider”
38Real world number sense Estimation and measurement:Will it be more or less than 10 footprints long? Will the apple weigh more or less than 20 wooden blocks? Are there more or less than 15 unifix cubes in this long bar?Closer to ______ or to _______? 5 or 20 footprints, 10 or 30 blocks, 10 or 50 cubes?About _______? … how many footprints? how many blocks? how many unifix cubes?Activities 30 & 31
40Is it reasonable? Could the teacher be 15 feet tall? Could your living room be 15 feet wide?Can a person jump 15 feet high?Could three children stretch their arms 15 feet?Number sense is the bridge to mathematical proficiency at all levels.
41Counting & number relationships Fluency with whole numbers are the basis forProblem solvingwhich leads toFluency with whole numbersTo recap
42Math Talks…to develop basic number concepts After the video, go around your table one at a time and describe one thing you liked or noticed in the teaching episode. Then open up the discussion to responses and further discussion.
43Benefits Students have the opportunity to: Clarify their own thinking. Consider and test other strategies to see if they are mathematically logical.Investigate and apply mathematical relationships.Build a repertoire of efficient strategies.Make decisions about choosing efficient strategies for specific problems.
44The teacher’s roleSince the heart of number talks is classroom conversations, it is appropriate for the teacher to move into the role of facilitator.“By changing my question from ‘What answer did you get?’ to ‘How did you solve this problem?’ I was able to understand how they were making sense of mathematics.”
45Procedures and expectations Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions.Provide appropriate wait time for the majority of the students to access the problem.Accept, respect, and consider all answers.Encourage student communication throughout the number talk.
46Five small stepsStart with smaller problems to elicit thinking from multiple perspectivesBe prepared to offer a strategy from a previous student.It is all right to put a student’s strategy on the back burnerif you’re not following their thinking or can’t think of a good question to help them untangle their reasoning.As a rule, limit your number talks to 5 to 15 minutes.Be patient with yourself and your students as you incorporate number talks into your regular math time.
47Instructional Resources Our own wiki for sharing teaching ideas, resources, web links
48Choose something from today’s session (or a couple things) to try before the next session. Come back with examples of students’ work from what you tried.Next session March 6, here.Focus on addition and subtraction.Something to try…