Student Probe
Skip Counting to One Hundred
Sarah had 10 pages of stickers. There are 10 stickers on each page. How many stickers does Sarah have in all?
Lesson Description
This lesson helps students develop an understanding of counting objects in equal groups to 100. They will read and write numerals and represent a number of objects with a written numeral. Initially, students are asked to count linking cubes by tens, referencing a hundreds chart. The lesson may be repeated by changing the size of the groups so that students count by twos and fives.
Rationale
At a Glance What: Counting equal groups in sets by twos, fives, and tens. Common Core Standard: CC.2.OA.3 Work with equal groups of objects to gain foundations for multiplication. Mathematical Practices: Make sense of problems and persevere in solving them. Model with mathematics Who: Students who do not understand skip counting sets of equal groups. Grade Level: 2 Prerequisite Vocabulary: groups of Prerequisite Skills: students can count by ones to form equal groups connected to problems. Delivery Format: Individual or small group Lesson Length: 20 to 30 min. Materials, Resources, Technology: Linking cubes, hundred number charts Student Worksheets: None
Equal groups (repeated addition) and multiplication are very prevalent in elementary classrooms. Counting by groups of tens reinforces students’ understanding of place value while counting equal groups by the number of objects in each group provides a conceptual framework for multiplication. Research states that students should be exposed to these types of experiences in their first years of school. Preparation Hundred number charts and linking cubes should be available for students.
Lesson
The teacher says or does… 1. Sarah had 10 pages of stickers. There are ten stickers on each page. How many stickers does Sarah have in all?
Expect students to say or do… If students do not, then the teacher says or does… 10, 20, 30, 40, 50, 60, 70, 80, Represent each part of the 90, 100 problem.
The teacher says or does…
Expect students to say or do… If students do not, then the teacher says or does… 2. How many pages of stickers 10 Use linking cubes to represent does Sarah have? the ten pages of stickers. 3. Next, the problem states 10 You have one linking cube to there are ten stickers on represent one page. How each page. How many many more should you put linking cubes should you with it to make that page have connect to show that each ten in all? page has ten stickers? 9 more Yes, 9 joined with 1 makes 10. Each page has ten stickers. If you connect 9 linking cubes to the one you already have, then you will have ten on that page. 4. The problem told you that Students form 10 groups of You have one linking cube to there are ten stickers on ten using linking cubes. represent one page. How each page. Now, continue many more should you put to make each page have ten with it to make that page have stickers by joining your ten in all? linking cubes together. 9 more Yes, 9 joined with 1 makes 10. Each page has ten stickers. If you connect 9 Linking cubes to the one you already have, then you will have ten on that page. (Repeat until student has formed 10 ten groups of ten linking cubes.) 5. Finally, the story problem 10, 20, 30, 40, 50, 60, 70, 80, Let’s compare your sets of ten asks how many stickers 90, 100 linking cubes to the hundreds Sarah has in all. What will it number chart. If there are 10 sound like if you count the linking cubes (ones) on this groups of ten linking cubes tower of ten cubes, then it is you formed? the same as the first row on the hundreds number chart. Ten on the first row. 6. How many linking cubes 10 Count the blocks (spaces) on (ones) are on your second your tower. There are ten ones tower of cubes? on the tower of ten linking cubes.
The teacher says or does…
Expect students to say or do… If students do not, then the teacher says or does… 7. How many numbers/spaces 10 Count the numbers/spaces on are on the second line of the second row of the the hundreds number hundreds number chart. chart? There are ten numbers on the second row. 8. How much is two rows of 20 Look at the hundreds number ten numbers? chart. Ten is at the end of the first row and twenty is at the end of the second row. Therefore, two rows of ten is twenty. 9. Can you count these rows 10,20 You will only need to count the by tens? numbers at the end of each row in order to count by tens because there are ten numbers in each row. 10. Can you count by tens to 10, 20, 30, 40, 50, 60, 70, 80, There are ten numbers/spaces one hundred? 90, 100 in each row on the hundreds number chart. Just like ten is at the end of the first row and twenty is at the end of the second row, then 30 is at the end of the third row, forty is at the end of the forth row, etc… 11. Are your towers of ten yes Because you told me that there Linking cubes the same as are ten ones on each tower of the rows on the hundred Linking cubes and ten numbers number chart? on each line of the hundreds number chart, then the towers of ten are the same as the rows on the hundred number chart. 12. Count the towers of ten you 10, 20, 30, 40, 50, 60, 70, 80, Use the hundreds number are using to show Sarah’s 90, 100 chart to count by tens to stickers. represent how many stickers Sarah had. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
The teacher says or does…
Expect students to say or do… If students do not, then the teacher says or does… Now that you have each part of When you used towers of ten the problem represented, let’s Linking cubes to represent reread the problem. Sarah’s ten pages of ten Sarah had 10 pages of stickers. stickers, you said 10, 20, 30, 40, There are ten stickers on each 50, 60, 70, 80, 90, 100 page. How many stickers does When you count towers of ten Sarah have in all? 100 Linking cubes you should count How were you counting? By tens by tens. Remember, each tower of ten linking cubes is like each line on the hundreds number chart.
Teacher Notes: It is important for the student to conceptualize each group as a single unit.
Variations Michael has six boxes. There are two toy cars in each box. How many toy cars does Michael have in all? (Expect students to use linking cubes to help them organize six groups with two in each group by making six towers of two cubes. Then they should count by twos to find the total.) Maria had 3 fishbowls. There are five goldfish in each fishbowl. How many goldfish does Maria have in all? (Expect students to use linking cubes to help them organize three groups with five in each group by making three towers of five Linking cubes. Then they should count by fives to find the total.) Formative Assessment Students will direct model the language of the problem using manipulatives to help them form equal groups and count by twos, fives, or tens to solve word problems. The number of in each box may changed. Carla’s mother bought 7 boxes of cupcakes. There were 10 cupcakes in each box. How many cupcakes did Carla’s mother buy?
References Thomas P. Carpenter, Elizabeth Fennema, Megan Loef Franke, Linda Levi, Susan B. Empson (1999). Children’s Mathematics Cognitively Guided Instruction, Heinemann: Portsmouth, NH Mathematics Preparation for Algebra. (n.d.). Retrieved May 12, 2011, from Doing What Works: http://dww.ed.gov/practice/?T_ID=20&P_ID=48
