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Understanding Numbers to 1,000

Understanding Numbers to 1,000. Unit of Study 2: Place Value Concepts to 1,000 Global Concept Guide: 1 of 4. Content Development.

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Understanding Numbers to 1,000

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  1. Understanding Numbers to 1,000 Unit of Study 2: Place Value Concepts to 1,000 Global Concept Guide: 1 of 4

  2. Content Development • Often times it is assumed that students do not need base-ten blocks when learning place value with three digit numbers. This is a misunderstanding. Because students have no experience with hundreds and thousands. they need multiple opportunities to explore and build these numbers. • Teacher and student should refer to base-ten manipulatives as (unit, rod /long, flat) In 2nd grade the value of each manipulative is a one, ten, hundred. Since in future learning the value of each manipulative will change, we need to refer to the name of the manipulative not the value. For example get out 7 rods, what is the value of 7 rods? Each rod is worth 10 and 7 tens has a value of 70. (SMP 6) • Use the place value mats provided for students to build their numbers throughout this GCG. • A huge portion of the lessons in the GO Math! resource focus on the pictorial representations of base-ten blocks. Jumping too soon to this step will create wide gaps in place value understanding. • Learnzillion • Quick Code 3435 • Quick Code 3478 • Quick Code 3384 • As always, the following steps are VITAL in creating sound understanding of new mathematical content: Concrete Pictorial Abstract

  3. Day 1 • Essential Question: How do you use groups of tens to make hundreds? • Lessons 2.1 and 2.2 would be best combined for this dayto build an understanding that our place value system is built on groups of 10. • Have manipulatives (e.g. links, unit cubes, snap cups, two color counters , stackable counters) available for students. Engage: Cora dropped 100 M&Ms. As she picks them up she puts them in groups of 10. How many groups of 10 can Cora make? • When monitoring problem solving, notice which students count out 100 and then put in groups of 10, and which students count out groups of 10 and then count by 10s to 100. When selecting students to share, make sure to compare the efficiency of these two strategies. • Highlight students that used a manipulative that concretely models groups of 10 (links, stackable counters, snap cubes) to launch a discussion connecting regrouping and place value. (We expand on the concept that 10 ones make a ten and now 10 tens make a hundred). • For students that solve quickly challenge them with HOT questions like, “What if there were 200 M&Ms, how would your answer change? • Base-ten blocks are just one way to show groups of tens. Help students make connections between the different manipulatives they used and the base-ten manipulatives.

  4. Day 1 continued • Essential Question: How do you use groups of tens to make hundreds? • Continue using manipulatives to solve additional word problems, such as, Mrs. Kingsbury has 12 packages of pencils. There are 10 pencils in each package. How many pencils does Mrs. Kingsbury have? Select and sequence students for sharing. Ask students questions like, “How did you use groups of ten to make 100?” • GO Math p. 60 and 64 provide further opportunity for problem solving with groups of ten. • A common error is that students think regrouping changes the value. Show 12 rods along with 1 flat and 2 rods. Ask students which is greater. Have students stack the rods on top of the flat to show 10 rods is equal to 1 hundred. • By the end of Day 1 students should be able to count out 10 groups of 10 and explain how it is the same as 100.

  5. Day 2 • EQ: How do you model a 3-digit number with base-ten blocks? • Engage: Tyler has 34 tens and 8 ones. Tyler said he has 3 hundreds. Do you agree or disagree with Tyler? Make a model and explain your thinking. • Continue to develop understanding with questions like Math Talk on p. 65 and p. 68 #11. Encourage students to justify their thinking with base-ten models. • It is important to create some examples where given a picture of base-ten blocks, students write the number. base-ten blocks should be shown out of order to help develop student understanding of the place value system. This can be done with base-ten blocks under the Elmo or through iTools . (See picture on next slide) • For further investigation use p. 93 and 94 from the Voyages Anchors. Encourage continued use of concrete models. • By the end of Day 2 students should be able to build three digit numbers using base-ten blocks.

  6. Day 3 • EQ: How do you use base-ten blocks to find the value of a digit? • Mrs. Clark asked the students to represent the 4 in the number 439. Which model is correct? (Teachers will have four models built in the four corners of the room.) • Model 1 – 4 unit cubes • Model 2 – 4 rods • Model 3 - 40 rods • Model 4 - 4 flats Have students move to the corner that has the correct model. Have students discuss why they chose their model. Facilitate a discussion that 40 rods and 4 flats both represent the value of the 4 in 439 because they both show a value of 400. • One way to introduce 1,000. Put a thousands cube at each group of students. Ask students to predict the value of the cube. Have students use what they know about other base-ten blocks to build a model equivalent to the cube. Facilitate discussion that 10 hundreds can be regrouped as 1,000. • For further exploration and practice use GO Math Lesson 2.5 essentials. • If students struggle with understanding the question, “What is the value of the number 5?”, you can rephrase it by saying, “How much is the digit five worth in this number?” • By the end of Day 3 students should be able to find the value of a digit within a number using base-ten blocks.

  7. Day 4 – Enrich/Reteach/Intervention Reteach • If you find some students struggling, it would be appropriate for them to still use the tools. In this case, the teacher should be encouraging students to move to the pictorial representations and onto the standard form of the number. • Students who need more time developing an understanding of grouping tens and hundreds, could use the Reteach lesson idea from TE p. 57B. • Go to Learn Zillion and enter Quick Code LZ3294 for video on understanding the value of a number. • Animated Math: Hundreds, Tens, and Ones Core • Another lesson idea for this day would be to use riddles or clues like the ones listed from Lesson 2.5 Enrich p. E 14 Enrich • The Enrich idea from lesson 2.5, TE 73B • By the end of Day 4 students should be able to find the value of a digit in a 3-digit number without base-ten blocks.

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