enVision Mathematics Topics 1-4
Kindergarten; August – October (9 weeks); 1st Trimester
Embedded Files
Topic Title(s):
Numbers 0 to 5 (Topic 1)
Compare Numbers 0 to 5 (Topic 2)
Numbers 6 to 10 (Topic 3)
Compare Numbers 0 to 10 (Topic 4)
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP6. Attend to precision.
MP7. Look for and make use of structure.
Standard(s):
1. Number and Quantity
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
K.CC.B. Counting & Cardinality: Count to determine the number of objects.
Apply the relationship between numbers and quantities and connect counting to cardinality. (CCSS: K.CC.B.4)
When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (CCSS: K.CC.B.4.a)
Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. (CCSS: K.CC.B.4.b)
Understand that each successive number name refers to a quantity that is one larger. (CCSS: K.CC.B.4.c)
K.CC.C. Counting & Cardinality: Compare numbers.
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to 10 objects.) (CCSS: K.CC.C.6)
Compare two numbers between 1 and 10 presented as written numerals. (CCSS: K.CC.C.7)
Progress from thinking about numbers as the result of the process of counting to abstractly thinking about numbers as mental objects of their own—especially the quantity 10. (MP2)
Explain how the number reached when counting on is a relationship between the quantity started from and the quantity added. (MP3)
Make counting efficient by following rows, columns, or other patterns in a group of arranged objects. (MP7)
Make reasoned arguments about the relative sizes of groups, such as by matching objects of two groups and seeing which has extra objects, or by counting the objects in each group and seeing which has the number further in the counting sequence. (MP3)
Use precise language to describe why one quantity is less than, greater than, or equal to another, and avoid mixing and misusing different ways of quantifying such as dimension, weight, or magnitude. (MP6)
Inquiry Questions
How is counting to five different from the number five?
What number is one larger than four? What number is one larger than seven?
Other than counting, how might you decide whether one set has more objects than another?
Which is more, 3 small cookies or 2 big cookies? What makes this difficult to answer?
Coherence Connections
This expectation represents major work of the grade.
In preschool, students build conceptions of what whole numbers mean, of subitizing, of one-to-one correspondence between verbal counting and objects, and of cardinality.
In preschool, students build an understanding of same versus different numbers of items, numbers of objects versus their size, and ordering from first to fifth.
In kindergarten, this expectation is key to several progressions of learning: (a) from saying the counting words to counting out objects, (b) from counting to counting on, and (c) from spoken number words to written base-ten numerals to base-ten understanding.
In kindergarten, this expectation is key to several progressions of learning: (a) from counting to counting on and (b) from comparison by matching to comparison by numbers to comparison involving adding and subtracting.
In Grade 1, students use their understanding of counting and cardinality to add and subtract within 20.
In Grade 1, students build an understanding of ten and place value with two-digit numbers. Students also organize data into categories and compare how many more or less are in one category than in another.
Academic Vocabulary & Language Expectations:
Count, one, two, three, number, four, five, none, zero, order, compare, equal, group, same number as, greater than, less than, model, six, seven, eight, nine, ten
Assessments:
Topic 1 Assessment (PDF), Topic 2 Assessment (PDF), Topic 3 Assessment (PDF), Topic 4 Assessment (PDF)
Instructional Resources & Notes:
enVision Mathematics Topics 1-4
Additional enVision Mathematics Resources
Let's Investigate! Guinea Pig Playground (TE) (supports Lessons 1-4, 1-5)
Let's Investigate! Hiding Kittens (TE) (supports Lessons 2-1, 2-2, 2-3)
Let's Investigate! Jump to 7 (TE) (supports Lessons 3-3, 3-4)
Let's Investigate! Make It Fair (TE) (supports Lessons 4-1, 4-2, 4-3)
3-Act Math Recording Sheets (Topic 1, Topic 3)
Supplemental Lesson Resources: Topic 1, Topic 2, Topic 3, Topic 4
Additional Math Games: Numbers 1-10 (additional materials and preparation may be required)
Topic 1 Readiness Resources:
Prior to Topic 1, spend up to one week giving students the opportunity to explore math manipulatives using the "Explore Our Math Tools" lessons from Open Up Resources (create a free account to access the lessons). This allows teachers to establish expectations and norms around using manipulatives and gives students a chance to use manipulatives in an engaging way. This also provides teachers with an opportunity to pre-assess students’ math knowledge and collect evidence for DRDP-K. (If Geoblocks are not available, then skip Lesson 4).
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention Topic 1: Count Out Up to 3 Objects, Count Up to 3, Count Up to 5 Objects, Identify Numerals to 5
Tier 1 Intervention Topic 2: Compare Within 5
Tier 1 Intervention Topic 3: Identify Numerals to 10, Rote Count to 10, Making a Set Up to 10 Objects
Tier 1 Intervention Topic 4: Compare Within 10, One More, One Less
Coherence Map/Concept Progressions: K.CC.B.4.a, K.CC.C.6, K.CC.C.7
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