GRADE 2 Daily Routines for Building Number Sense Description and Examples Choral Counting Implementation Strategies for Getting Started In this routine, the class counts aloud a number sequence all together. Ideas for choral counting include counting by ones, tens, fives, twos starting at zero and then starting at other numbers, counting by tens starting from 53 or 320, counting backwards by ones or tens. Counting Around a Circle (Table Group) Students are in a circle. One student starts counting from the number that is written on the card. Go around the circle by having each student say the next number. Count from any starting number and you can change counting pattern so you don’t always count by 1s. Need to count by 10s Counting on Number Lines Use an open number line to write numbers on the number line in the counting sequence. In this case, you will begin drawing the open number line as students are counting. Starting and Stopping Counting The class counts a number sequence all together, with a starting number and a stopping number. For example, have the class count by tens, starting with 26 and Counting Type of Routine Standards/Concepts Variations and Questions to Pose 2.NBT.2 Count Record the numbers as students are counting to within 1000, skip help students see and use the patterns. Prior to count by 2s, 5s, 10s, doing the activity, think about how many numbers and 100s. you want to record in a row to help facilitate 2.NBT.8 Mentally students noticing particular patterns. What do you +10/+100 to a notice? number; -10/-100 Use a number grid or number lines as students are from a number. counting to help students see and use the patterns. 2.NBT.2 Count Variations on this routine include the following: within 1000, skip Count by ones or tens, count by 2s, 5s, 10s, Count by ones or tens starting at various numbers. and 100s. 2.NBT.8 Mentally To facilitate understanding of the patterns, write +10/+100 to a the numbers on the board as students say them. number; -10/-100 from a number. Ask a variety of questions to differentiate the level of difficulty, such as: How did you know what comes next? Ask students to predict what another student will count after giving them the counting pattern. 2.NBT.2 Count within 1000, skip count by 2s, 5s, 10s, and 100s. 2.NBT.8 Mentally +10/+100 to a number; -10/-100 from a number. 2.NBT.2 Count Ask questions to facilitate discussion about within 1000, skip patterns, such as odd/even patterns: count by 2s, 5s, 10s, If we start with twenty-five and count by fives, and 100s. what numbers could we stop at? References Include: Parrish, S. (2010). Number talks helping children build mental math and compuation strateiges. Sausalito, CA: Math Solutions. Shumway, J. F. (2011). Number sense routines: building numerical literacy every day in grades K-3. Maine, Maine: Stenhouse Publishers. McCoy, A.C. (2013). High yield routines. Reston, VA: National Council of Teachers of Mathematics, Inc. Page 1 GRADE 2 Daily Routines for Building Number Sense Quick Images and Visuals Visual Dot Cards, Pictures, and Images Ten Frames stopping at 176. In addition to whole class, this routine works particularly well with small groups and individual students. You place dots on cards arranged in various groups. You can make your dot cards based on twos, fives, tens, doubles, or the visual arrangement of dice or dominoes. You flash the amount quickly, giving students 3-5 seconds to visualize what they say. You want students to move from counting ones to thinking of the dots in groups. Quantities can be displayed using the same coloring or in different colors. Arrangements determine the difficulty for students with dots grouped in rows and columns as the easiest, linear is next and scattered or circular arrangements as the hardest. Ten frames are like Visual Dot Cards. The difference is that you are using the ten frame and are highlighting the configuration of the frame. Ten frames can highlight part to whole relationships, number decomposition as well as teen numbers. You can also emphasize properties such as the commutative property. 2.NBT.3 Read and write to 1000, number names, expanded notation 2.OA.2 Fluently +/within 20 2.G.1 Recognize and draw shapes with special attributes 2.OA.2 Fluently +/within 20 If we count by twos and start with 1,222, what numbers could we stop at? Why would the number need to be even? Thinking: How many dots did you see? How did you figure it out? How did you know so quickly? What did you see? Perceptual Subitizing: Did you count each dot or did you see the amount? How many dots? How did you know? Visual images should build from number combinations into groups of equal numbers (arrays of dots). Visual images can also include geometric shapes for students to recreate or describe. Having students write about what they see in a special figure informs you about they think about geometric figures. Numbers Less Than 10: How did you figure out how many are there? How many dots are in the top row? How many are in the bottom row? How many more are needed to make ten? Numbers Greater Than 10: How many extra dots are there? How many dots are in the first ten frame? How many dots are in the second ten frame? References Include: Parrish, S. (2010). Number talks helping children build mental math and compuation strateiges. Sausalito, CA: Math Solutions. Shumway, J. F. (2011). Number sense routines: building numerical literacy every day in grades K-3. Maine, Maine: Stenhouse Publishers. McCoy, A.C. (2013). High yield routines. Reston, VA: National Council of Teachers of Mathematics, Inc. Page 2 Making Numbers GRADE 2 Daily Routines for Building Number Sense Today’s Number (variations include :+/1, +10/-10, +100/-100, next even, double it, Today’s number provides students with the opportunity to think about the relationship of a number to different situations and scenarios. Students might use a template to think about Today’s Number so that they can also think about relationships such as one more or one less than Today’s Number. Be sure Today’s Number is connected to real world uses. . Open Number Sentences Students are presented with an equation. They have the opportunity to think about the equation, to determine whether it is a true equation or a false equation. When this routine is introduced, consider using a number balance as a visual tool for representing addition equations. Number Sentences can and should be devised to highlight and emphasize particular mathematical ideas. For instances, if your class is working on developing fluency with ten facts, equations can be presented such as: 10 = 7 +2; 6 + 4 = 10; and 9 + 1 = 5 + 5. 2.NBT.2 Count within 1000, skip count by 2s, 5s, 10s, and 100s. 2.NBT.3 Read and write to 1000, number names, expanded notation 2.NBT.5 Fluently +/within 100 2.NBT.7 +/- within 1000 2.NBT.8 Mentally +10/+100 to a number; -10/-100 from a number. 2.NBT.2 Count within 1000, skip count by 2s, 5s, 10s, and 100s. 2.NBT.5 Fluently +/within 100 2.NBT.7 +/- within 1000 2.NBT.8 Mentally +10/+100 to a number; -10/-100 from a number. How did you see the number? What did you notice about this number? In order to help students understand numbers in various contexts, ask questions like these: When is this number considered a large number? When is this number not very much? What other ways do you think about ___? Today’s Number is how close to 10? It is important to use statements that include both true and false statements (some are false below). Group 1: Group 2: 6+0=0+6 156 = 100 + 50 + 6 12 – 9 = 3 7 + 80 = 87 5+3=6+3 93 = 9 + 90 Open Number Sentences can also look like this where students are figuring out the missing part of the number sentence. 6 + 3 = ___ + 6 6 + 3 = __ + 4 12 = 9 + ___ 56 = 50 + ___ ___ = 7 + 80 References Include: Parrish, S. (2010). Number talks helping children build mental math and compuation strateiges. Sausalito, CA: Math Solutions. Shumway, J. F. (2011). Number sense routines: building numerical literacy every day in grades K-3. Maine, Maine: Stenhouse Publishers. McCoy, A.C. (2013). High yield routines. Reston, VA: National Council of Teachers of Mathematics, Inc. Page 3 GRADE 2 Daily Routines for Building Number Sense Number Lines Ways to Make a Number This is a routine where students are provided with open number lines. You provide students with some values on the number line and they have to estimate the placement of other values. For example, you show students an open number line that includes 10 and 70. You have them place 20, 60 and 80 on the number line. Another example might be a number line that shows 3 and 10 where students have to place 7 and 0. After the teacher announces “the target number”, the students record as many different representations of the number on one side of their small paper. Then, after a few minutes of think and record time, students are asked to pick their “favorite way” and put that one on the back of the same paper (using a large font). The teacher then collects the ideas (the papers) on chart paper/board to show all the different “ways” that were discovered. Students write as many ways as they can think of to “make” a selected number. They might use visuals of the quantity, equations, models, and so on. 2.NBT.2 Count within 1000, skip count by 2s, 5s, 10s, and 100s. 2.NBT.5 Fluently +/within 100 2.NBT.7 +/- within 1000 2.NBT.8 Mentally +10/+100 to a number; -10/-100 from a number. 2.NBT.3 Read and write to 1000, number names, expanded notation 2.NBT.5 Fluently +/within 100 2.NBT.6 Add up to 4 two-digit numbers 2.NBT.7 +/- within 1000 2.NBT.8 Mentally +10/+100 to a number; -10/-100 from a number. 2.MD.8 Working with money combinations This routine is open ended and you need to support students in building open number lines. One way to do this is by using a base ten rod along the number line to count by tens. You can also begin with three ones to students can build a number line by counting by 10s beginning at 3. Use a rope and clothes pins to pin a number on a number line. Build from empty number lines to use mental math skills. Begin by asking about values close to halfway marks to make this assessable for students. Questions to ask would be: How did you decide where to place the numbers? What helped you make your decision? This routine can be open-ended (just give students the number and no guidelines) or it can have constraints (such as, Think of ways to make this number with three addends). You can vary the ways you ask students to show the ways to make the number using the following: - Place value representation - Expanded notation - Number Bonds (Number Mountains) - Up to 4 Addends - Commutative Property References Include: Parrish, S. (2010). Number talks helping children build mental math and compuation strateiges. Sausalito, CA: Math Solutions. Shumway, J. F. (2011). Number sense routines: building numerical literacy every day in grades K-3. Maine, Maine: Stenhouse Publishers. McCoy, A.C. (2013). High yield routines. Reston, VA: National Council of Teachers of Mathematics, Inc. Page 4 GRADE 2 Daily Routines for Building Number Sense Data and Calendars Calendar Data Use a real calendar as well as premade calendars. Integrate in special days and count days. Notice the days before and the days after today. Make connections to the days of the week. Notice the time each day it is when we do specific events. Collect data on temperatures, weather, sunrise time, number of students in class, sack lunch vs. school lunch, etc. Use the data to build problems and make graphs. 2.MD.7 Time and relationships of time. 2.MD.10 Picture and bar graphs, draw and/or interpret Patterns: What do you notice about the data? What does it tell us? What do you think the graph will look like next month? Descriptive Questions: What is the most common temperature this month? How many students will most likely be here at school tomorrow? How many students do we think will have school lunch next week? References Include: Parrish, S. (2010). Number talks helping children build mental math and compuation strateiges. Sausalito, CA: Math Solutions. Shumway, J. F. (2011). Number sense routines: building numerical literacy every day in grades K-3. Maine, Maine: Stenhouse Publishers. McCoy, A.C. (2013). High yield routines. Reston, VA: National Council of Teachers of Mathematics, Inc. Page 5