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  Joining and Separating Equal Groups
  
  # Joining and Separating Equal Groups
  
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  Comprehensive Teacher's Guide Grades 1-2 Lesson 4-1
  Comprehensive Teacher's Guide Grades 1-2 Lesson 4-1
  
  Categories:Types, School Work
  
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  07/09/2013
  
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  J
  ust like addition and subtraction,multiplication and division are a way of thinking about joining and separating groups.This initial exploration withsingle blocks exposes children to these two actions and the relationshipbetween them.
  ®
  
  Joining Equal Groups of Blocks
  For the process of joining equal groups of blocks, children know both thenumber of groups and the number in each group. They model the groups with the blocks and then find the number in all.Have children work in pairs with single blocks and empty holders. Ask thechildren to make 3 groups of 5 blocks. When the children have arrangedthese groups, ask,
  How many blocks are there altogether?
  Many children will count the single blocks or pack them and count. Somechildren might skip count by fives to 15. Have them demonstrate their techniques to one another.Repeat with additional examples, changing the number of groups and thenumber in each group. For the last example, have the children record their  work on paper using drawings, the Digi-Block stamps, or words. Providetime for children to share their recordings.
  ®
  
  Separating Equal Groups of Blocks
  For the process of separating blocks, children know the total number of blocks. If they also know the number of groups, then they find the number ineach group. If they know the number in each group, they find the number of groups. These are two different ways to model division.Have children work in pairs with single blocks. Ask them to take 12 blocks,then make groups of 3 with those 12 blocks. When they have arranged theblocks, ask,
  What did you do with the blocks? How many groups are there?
  4-1
  Joining and Separating Equal Groups
  4-1
  Focus
  Joining and separating equal groups of blocksand making connections between these actions
  
  93
  4-14-1
  After the children have described the process (starting with 12 blocks andseparating groups of 3), ask,
  If we put these blocks together again, how many will there be?
  Do not be surprised if the children don’t immediately recognize the answer of 12. They need many opportunities to join and separate equal groups tounderstand this inverse relationship.Finally, have the children model a situation in which they know the total andthe number of groups, but not how many in each group. For example, havethem take 10 blocks and put them in 5 equal groups. When they havearranged the blocks, ask,
  What did you do with the blocks? How many blocks are there in each group?
  After the children have described the process and their thinking, ask,
  If you put the blocks back together, how many will there be?
  Repeat with additional examples, always asking how many there would be if the blocks were combined again.
  Practicing Key Ideas
  Making Equal Groups
  Children work in pairs.They roll a die to determine the number of groups.Then theyfind the total when they place first 1 block in each group,then 2 blocks,3 blocks,andfinally 4 blocks.They can record their work in a table.
  Separating 12
  Children count out 12 blocks and explore how the blocks can be separated intoequal groups.Children should record each way they find using pictures,stamps,or words.
  Assessing Learning
  1. Ask the child to make 4 groups of 2 blocks and find the total number of blocks. Does the childmake the groups correctly?find the correct total?
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