Show How To Make A Ten To Solve 13-7 Answer

Making a ten

Alignments to Content Standards: iii.OA.D.9

Task

Below is a table showing all the means to add together the numbers from 1 to nine.

1. Each sum which is larger than 10 can exist found past first making a x. For case, to detect 8 + 5, nosotros can write

   \begin{marshal} viii+5 &= viii + (2+iii) \\ &= (8+2) + 3 \\ &= x + 3 \\ &= xiii. \end{marshal}

   Explain why this reasoning works and utilise this method to find 7 + 8. How can you visualize these equations using the table?
2. Adding 9 to some other unmarried digit number can likewise be done by first making a ten. For example

   \begin{align} three+9 &= 3 + (ten-1) \\ &= (3+10) - 1 \\ &= thirteen - ane \\ &= 12. \finish{align}

   Explicate why this reasoning works and apply this method to find 7+nine. How can y'all visualize these equations using the table?

IM Commentary

Students are expected to exist fluent with improver and subtraction within 20 in 2d course (see ii.OA.2). This task builds on that knowledge past asking them to study more carefully the make-a-ten strategy that they should already know and use intuitively. In this strategy, noesis of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than x. The 10's in the tabular array are shaded because they are essential to the technique. The second office of the task focuses on adding nine's which can also be achieved by calculation a ten and and then subtracting i. The teacher may wish to indicated to students for part (b) that showing how to add 9 by showtime making a x with the add-on tabular array requires an actress column on the table. Alternatively, students can just add together one box, with the number 17, to prove the sum 7+x. This task is intended for educational activity purposes as it takes time to identify the patterns involved and understand the steps in the procedures.

The Standards for Mathematical Practice focus on the nature of the learning experiences by attention to the thinking processes and habits of heed that students need to develop in lodge to attain a deep and flexible agreement of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While information technology is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. Possible secondary exercise connections may be discussed but not in the same caste of detail.Â

This chore helps illustrate Mathematical Practice 7, Await for and make use of construction. During this activity, third graders are actively connecting the strategy of make-a-ten along with properties of improver and subtraction to solve sums greater than 10.  During this process they are looking at the construction of the base of operations 10 system, and composing and decomposing numbers based on this structure.  Students volition have the opportunity to call up virtually the meaning and usefulness of composing tens without struggling with the computations which for a third grader will not be challenging.  They are asked to visualize this make-a-x strategy using the addition table and explain why this reasoning works (MP.3). Through this in-depth exploration of the make-a-ten strategy, students are immersed in pattern-recognition and design-generalizing which not only develops a better understanding of our base of operations 10 structure but allows them to apply this understanding to solve other issues.

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Solution

1. The offset equation comes from writing 5 as 2+iii. The reason for this is that in the next stride we volition group the two together with the 8 to make a ten. This second pace uses the associative belongings of add-on. In the third pace, nosotros add 10 + three to observe the respond of 13.

   In terms of the addition table, we can visualize calculation 5 to viii past starting at the 8 in the column of addends and moving over v spaces to the correct. Observe that after two steps, we achieve x. And so three more steps puts the states at xiii. This is shown in the moving picture below:

   

   Applying this method to summate 7+8 we find

   \begin{align} 7+eight &= 7 + (3+five) \\ &= (7+3) + 5 \\ &= 10 + 5 \\ &= xv. \cease{align}

2. This method is similar to the making a ten method in function (b). In this case, however, a ten is made by rewriting 9 every bit ten - one. So the three and 10 are grouped together beginning before performing the subtraction in the last step. This is shown in the picture beneath:

   

   Applying this method to find 7+9 gives

   \begin{align} 7+9 &= seven + (x-i) \\ &= (7+ten) - 1 \\ &= 17 - 1 \\ &= 16. \stop{align}

Making a ten

Beneath is a table showing all the ways to add the numbers from ane to 9.

1. Each sum which is larger than 10 tin be establish past outset making a 10. For case, to find eight + v, we tin can write

   \begin{align} eight+5 &= viii + (ii+3) \\ &= (viii+two) + iii \\ &= 10 + 3 \\ &= 13. \terminate{marshal}

   Explain why this reasoning works and apply this method to observe 7 + eight. How can yous visualize these equations using the table?
2. Adding 9 to another single digit number can also be washed by kickoff making a 10. For example

   \brainstorm{marshal} 3+9 &= 3 + (10-ane) \\ &= (3+ten) - 1 \\ &= thirteen - 1 \\ &= 12. \cease{align}

   Explain why this reasoning works and apply this method to find 7+nine. How tin you visualize these equations using the table?

Source: https://tasks.illustrativemathematics.org/content-standards/tasks/955

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