1st Grade Institute 2012Mathematics

Dr. Amy SpearsCurriculum Coordinator of Mathematics Education

Agenda

• Common Core 1st grade Standards• Standards for Mathematical Practice• Examples of NUMBER – in the classroom• Updated Scope and Sequence• Subitizing• Math Journals• SHAKE THOSE BEANS• FAST FIVE• I WISH I HAD

Common Core• Match up with your number (UNO card or colored index card

given at the start of the session) – should be 5 in each group (UNO stays with UNO, index stays with index)

• Everyone read pg 9 and 10• Red – Read Operations and Algebraic Thinking• Green – Read Number and Operations in Base Ten• Blue – Read Measurement and Data• Yellow – Read Geometry• Use handout to work through the standards• Share any AHA moments about the standards with the group

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them2. Reason abstractly3. Construct viable arguments and critique the reasoning

of others4. Model with Mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

Standards for Mathematical Practice Activity

• Match up with your number (UNO card given at the start of the session) – should be 5 in each group

• Red – Read 1 and 2• Green – Read 3 and 4• Blue – Read 5 and 6• Yellow – Read 7 and 8• Using the chart given, come up with ideas of how

these can apply in 1st grade

4 Critical Areas

1. Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20

2. Developing understanding of whole number relationships and place value, including grouping in tens and ones

3. Developing understanding of linear measurements and measuring lengths as iterating length units

4. Reasoning about attributes of, and composing and decomposing geometric shapes

Examples of NUMBER

• What’s as Big as me? – Take the height of each child using string. – Cut the string and have the students use it to

discover what else is as big as them in the classroom.

– Have students categorize things that are smaller, the same, and larger than themselves.

Examples of NUMBER

• Oh, That’ll Take about a Minute– Start a stop watch and ask students to clap when

they think a minute is up– Talk about how close they are– Now do jumping jacks and ask students to stop

when they think a minute is up– Continue with different ways to help students

make sense of a minute

Examples of NUMBER

Oh, That’ll Take about an Hour– Have students talk with family members to figure

out activities that take about an hour to do– They should draw illustrations of two examples and

bring them to class to share– Have groups talk about their findings and then

identify different times during the day that an hour has passed

– Discuss all the things that happened during that hour

NUMBER Examples

• Numbers, Numbers, Where are they– Challenge students to look for numbers at home– Which room had the most numbers?– Why?– Draw a picture that includes some of the items

that had numbers

NUMBER Examples

• Number Surgery– To introduce the concept of addition, challenge

students to take apart numbers in as many ways as they can discover

– Begin with manipulatives and an easy number (ex. 10)

– Lead students from the concrete (objects) to the representational (drawing) to the abstract (numbers and operation symbols)

NUMBER Examples

• Discover Volume Sense- Bring in Various containers for students to

experiment with (gallon container, margarine tub, mustard jar, etc).

- Make water available at a station and allow students to use the container to pour water back and forth

- Have students draw which container holds the most and the least and which ones might hold the same amount

NUMBER Examples• Estimate with Little Ones

– How many scoops of beans will fill a coffeepot?– How many beads will fill a pill container?– Take predictions, then fill the container halfway and see if anyone wants

to change his or her estimate– Discuss the reasoning behind decisions– After discovering how many scoops it takes to fill the coffeepot, challenge

students to find the total number of beans it takes to fill the container– Have groups come up with an estimate and a plan to solve the problem– Students do the experiment and reflect on the reasonableness of their

estimate and plan– To encourage monitoring their understanding, students can change their

estimates along the way and share what they did

NUMBER Examples

• Handfuls #1– How many beans can you pick up in a handful?– Predict, experiment, and reflect on the

reasonableness of the predictions– Now try popcorn kernels, counters, cubes

NUMBER Examples

• Handfuls #2– Have students take another handful of objects– Challenge them to split the objects in half, thirds,

and so on and make discoveries– Lead students from the concrete to the

representational to the abstract

NUMBER Examples• Penguins and Polar Bears

– Share the following (geographically improbable) story problem:An explorer was traveling to the Artic. He was hiking one day in a terrible blizzard when, way ahead on the top of an iceberg, he spotted 5 penguins and 3 polar bears. He was curious how many feet and noses there were altogether.

• Have the students share shoulder to shoulder what the problem is• Have manipulatives available to scaffold the thinking• Have them draw the problem on paper along with the answer• Continue with similar problems (bicycles and tricycles, how many wheels

altogether)• Have students create like problems

Updated Scope and Sequence

• TBD – Resources – This is due to them not being in the current resources we

have, we will be adding them to our OCG• Time• Addition and Subtraction in base ten• Fractions

• CFL Unit – Collecting and Organizing– Kindergarten will be starting this unit this year

• Scales/Balances– Kindergarten will need to borrow yours this coming year to

expose their students to weight measurement

Dreambox

• Make sure students are using it for the right reasons

• Some students should not be using it• Not a weekly time requirement

Common Core Progressions• Get in color groups from UNO cards (Index cars) given at beginning• Reading Protocol - ? (Any questions you have), ! (Information that stood out to you or AHA)

• Red – Geometric Measurement• Blue – Geometry• Yellow – Counting and Cardinality/Operations and Algebraic Thinking• Green – Number and Operations in Base Ten and Categorical Data/Measurement Data

• Everyone read 1st grade for your topic• 1 – Overview• 2 – Overview• 3 – Overview• 4 – Kindergarten• 5 – Kindergarten• 6 – Kindergarten• 7 – 2nd grade• 8 – 2nd grade

Subitizing• (SOO-bi-tyz) • MEANING:

– verb tr., intr.: To perceive, without counting, the number of objects in a small group.

• When you throw a die, you don't count the number of pips to determine the value of the throw. You subitize. Now here's a word you want to use when you take part in one of those "How many marbles are in the jar?" contests, though subitizing works only for a small group of items. Estimates of the upper limit of humans' subitizing capability range from four to seven. Subitizing also depends on the arrangement of the objects.

• http://news.bbc.co.uk/2/hi/uk_news/6577241.stm

Subitize – Article review• Get in color groups from UNO cards given at beginning• Reading Protocol - ? (Any questions you have), ! (Information that stood out

to you or AHA)• 1 – Read pg 1 Subitizing a long History• 2 – Read pg 2 Perpetual Subitizing• 3 – Read pg 2 Conceptual Subitizing• 4 – Read pg 3 Subitizing and Counting• 5 – Read pg 3 What factors make Conceptual Subitizing easy or hard?• 6 – Read pg 4 Implications for Teaching and Conceptual Subitizing and

Number• 7 – Read pg 5 Conceptual Subitizing and Number• 8 – Read pg 6-7 Conceptual Subitizing and Arithmatic • Share with group

Math Journals

• Kindergarten students should be working in a math journal 2 to 3 times a week

• 1st grade students should be working in a math journal daily if possible

• Need to communicate more in math• Journaling includes every student• Journals can be made in a variety of ways (spirals

cut in half, or composition books cut in half)

FAST FIVE• Start with Manipulatives before marking• Can be used with 5 Frames or 10 Frames• Provide the students with a short flash on the screen, or

poster, and then students repeat what they see on their paper

• The flash helps develop number and subitizing• The flash helps students to not focus on counting• Follow up with students having to identify the # of circles

and write on a dry erase boards (higher level)• For today, use your bag of beans for manipulatives

FAST FIVE

FAST FIVE

FAST FIVE

FAST FIVE

FAST FIVE

FAST FIVE

FAST FIVE

SHAKE THOSE BEANS• 2 color counters or painted lima beans• Recording sheet• Count Purple first, then White

0 + 5 1 + 4 2 + 3 3 + 2 4 + 1 5 + 0

I WISH I HAD…

• Materials: Linking cubes, dot cards, playing cards, Journals

• I have 4, I wish I had 5. How many more do I need?

Questions????

• Please feel free to email me or call me with questions you have