About this Unit
The final second grade computation unit completes the standards for strategies, properties, and relationships in second grade addition and subtraction skills. It then introduces multiplication through reviewing odd and even numbers, reviewing repeated addition, introducing skip counting, and demonstrating the association between addition and multiplication. Activities include an emphasis on concrete and pictorial problems, and TouchMath techniques with visual cues that ensure proficiency.
Module 1: Multiples of 10 and 100
The activities in this module are scaffolded from adding and subtracting multiples of 10 to/from 100 and then to/from each multiple of 100 in sequence. Skills are extended to adding and subtracting multiples of 10 within a three-digit number that is also a multiple of 10 (e.g., 540 + 40 and 580 – 40). The instruction then progresses to adding multiples of 10 to all three-digit numbers without regrouping (e.g., 649 + 30 and 679 – 30). The same process is used for adding and subtracting multiples of 100. Computation strategies (including doubles and number families) are reinforced, in/out tables provide practice in a variety of formats, and visual cues and word problems assist students throughout the activities.
Module 2: Addition Within 1,000
This module extends addition with regrouping to sums within 1,000. It reviews and extends the concept of regrouping presented in Unit 2. The instruction is again scaffolded from the kinesthetic, to the kinesthetic/pictorial and to the pictorial level to ensure students work through the process in a meaningful way. The cluster uses base ten blocks, place value mats, and ten frames to ensure development of the concept. Place value charts relate to the models. The representational level is scaffolded from the models to visual cues as reminders of the steps in the process. Comparisons and word problems increase the value of the skill to the learners. It provides practice applying the skill with three-digit numbers. All visual cues have been eliminated now. The focus is on developing proficiency with the algorithm. The mixed practice includes three-digit addends with one-digit, two-digit, and three-digit addends. Unknowns and multiple addends continue throughout the practice. The cluster reinforces ordering numbers and relating locations on number lines.
Module 3: Subtraction Within 1,000
This module extends subtraction with regrouping within 1,000. The presentation mirrors the previous module, Addition within 1,000. Cluster 1 reviews and extends the concept of regrouping that was presented in Unit 2. The instruction is again scaffolded from the kinesthetic, to the k kinesthetic/representational, and then to the representational level to ensure students work through the process in a meaningful way. The cluster uses base ten blocks and place value mats to ensure development of the concept. Place value charts help students relate to the models. The representational level is scaffolded from the models to visual cues as reminders of the steps in the process. Word problems using previously learned strategies increase the value of the skill to the learners. Cluster 2 provides practice applying the skill with three-digit numbers. All visual cues are eliminated. The mixed practice includes expressions without and with regrouping. The complexity of the expressions is scaffolded from subtracting a one-digit number, then a two-digit number, then a three-digit number, and lastly mixed subtrahends. The cluster includes unknowns, word problems, ordering numbers, and comparisons throughout. Students apply previously learned skills (e.g., subtracting multiples of 10 and 100).
Module 4: Mixed Operations
This module provides mixed practice with addition and subtraction without and with regrouping. It reviews and extends computation and problem solving strategies. Cluster 1 provides practice to develop fluency and proficiency with computation with no visual cues. The activities are scaffolded to increase in the number of digits and the complexity of the problems. Word problems foster previously presented problem solving strategies. The cluster emphasizes place value, properties, and the relationship of addition and subtraction throughout. Cluster 2 introduces two new problem-solving strategies: work backward and choose an operation. Mixed practice concludes the cluster.
Module 5: Multiplication 1
This module introduces multiplication with odd and even numbers, pairs, and equal addends. Cluster 1 reviews even numbers as pairs using pictures of familiar objects. The numbers are presented in sequence, with the basic concept of pairs as partners. The activities move to odd numbers as pairs plus one. Students practice matching and seeing odd and even as numbers in counting order. The idea of even numbers within 15 is extended to include pairs of equal addends. Cluster 2 continues the practice with a focus on equal addends, doubles as a strategy for addition, generalizations about even numbers, and scaffolded application with numbers to 100. Pictures, charts, tables, and sequences of numbers reinforce the skill.
Module 6: Multiplication 2
This module uses pictures, Pictorial TouchPoints, regular TouchPoints, numerals, and arrays to extend the introduction of multiplication through 5 x 5. Cluster 1 (activity sheets 126–137) introduces the concept through structured activities for multiplication by 2, 3, 4, and 5 in order. Each factor is first represented with pictures of objects, then Pictorial TouchPoints using those objects, and then regular TouchPoints. Groups of objects, dots in arrays, and TouchPoints are used first for repeated addition and then for multiplication. The traditional TouchMath approach is reinforced throughout the instruction and guided practice. Cluster 2 (activity sheets 138–150) applies the concept in word problems. Students draw pictures to represent the problems and create repeated addition as well as multiplication number sentences that relate to the pictures. TouchPoints help students skip count to find the product. Recognizing and naming multiples are the final steps in building the foundation for multiplication. Cluster 3 (activity sheets 151–159) relates all the strategies from the module. Students’ understanding is reinforced through the commutative property, a generalization about multiplication, inclusion of the factor 1, and dots in arrays. Addition and multiplication equations relate to arrays, and word problems with arrays tie together the various presentations. Pairs with an extra is a reminder of odd numbers.
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